Julie M Reimer

Rodolphe Devillers

Joachim Claudet

Benefits and gaps in area-based management tools for the ocean Sustainable Development Goal

Keywords: Sustainable Development Goal 14, marine spatial planning (MSP), marine protected areas

Sustainable Development Goal (SDG) 14 provides a vision for the world's oceans; however, management interventions needed to achieve SDG 14 remain less clear. We assessed the potential contributions of seven key area-based management tools (such as fisheries closures) to SDG 14 targets. We conducted a rapid systematic review of 177 studies and an expert opinion survey to identify evidence of the ecological, social and economic outcomes from each type of tool. We used these data to assess the level of confidence in the outcomes delivered by each tool and qualitatively scored how each tool contributes to each target. We demonstrate that a combination of tools with diverse objectives and management approaches will be necessary for achieving all SDG 14 targets. We highlight that some tools, including fully and partially protected areas and locally managed marine areas, may make stronger contributions to SDG 14 than others. We identify gaps in the suitability of these tools to some targets, particularly targets related to pollution and acidification, and identify evidence gaps for social

and economic outcomes. Our findings provide operational guidance to support progress toward SDG 14.

The United Nations Sustainable Development Goals (SDGs) provide a transformational vision of sustainable development across the environmental, social, and economic dimensions.

Sustainable Development Goal 14: Life Below Water (SDG 14) aims to "conserve and sustainably use oceans, seas, and marine resources for sustainable development" [START_REF] Nations | Transforming our world: the 2030 Agenda for Sustainable Development[END_REF] . Through its seven primary targets, SDG 14 addresses ocean challenges: reducing marine pollution (SDG 14.1), restoring marine ecosystems (SDG 14.2), reducing ocean acidification (SDG 14.3), enabling sustainable fisheries (SDG 14.4), conserving marine areas (SDG 14.5), ending harmful fishery subsidies (SDG 14.6), and increasing economic benefits to Small Island Developing States and least developed countries (SDG 14.7). Achieving SDG 14 was shown to benefit other SDGs, most notably SDG 1: No Poverty and SDG 2: Zero Hunger [START_REF] Singh | A rapid assessment of co-benefits and trade-offs among Sustainable Development Goals[END_REF][START_REF] Claudet | Perspective A Roadmap for Using the UN Decade of Ocean Science for Sustainable Development in Support of Science , Policy , and Action[END_REF] . A focus on sustaining marine ecosystem services may foster fair and equitable benefit-sharing that contributes to multiple interconnected SDGs [START_REF] Ntona | Connecting SDG 14 with the other Sustainable Development Goals through marine spatial planning[END_REF] ; however, SDG 14 was criticized for being largely aspirational rather than operational and measurable [START_REF] Cormier | SMART marine goals, targets and management -Is SDG 14 operational or aspirational, is 'Life Below Water' sinking or swimming?[END_REF] , and management-level guidance is critically needed to support progress toward SDG 14 targets [START_REF]Preliminary analysis of area-based management measures to support SDG implementation[END_REF][START_REF] Diz | Mainstreaming marine biodiversity into the SDGs: The role of other effective area-based conservation measures (SDG 14.5)[END_REF][START_REF] Haas | Big fishing: the role of the large-scale commercial fishing industry in achieving Sustainable Development Goal 14[END_REF] .

Management of human activities and natural resources often has a spatial dimension, reflecting various social, sectoral, or geopolitical boundaries. This spatial lens extends to planning and management of oceans and their natural resources [START_REF] Claudet | Spatial management of near shore coastal areas: the use of Marine Protected Areas (MPAS) in a fisheries management context[END_REF][START_REF] Ehler | Marine Spatial Planning: a step-by-step approach toward ecosystem-based management[END_REF][START_REF] Jupiter | Locally-managed marine areas: Multiple objectives and diverse strategies[END_REF][START_REF] Sterling | Culturally Grounded Indicators of Resilience in Social-Ecological Systems[END_REF] . Planning and management can address single-sector needs, like achieving specific fisheries objectives [START_REF] Palmer | Getting to good enough: Performance of a suite of methods for spatially allocating fishing effort to management areas[END_REF] , or multiple objectives in the wider seascape, as with comprehensive ocean zoning or marine spatial planning [START_REF] Agardy | Mind the gap: Addressing the shortcomings of marine protected areas through large scale marine spatial planning[END_REF][START_REF] Frazão Santos | Integrating climate change in ocean planning[END_REF] . Both single-and multi-sector spatial plans tend to rely on the implementation of spatial or areabased management tools (ABMTs). ABMTs are geographically defined areas where human activities are regulated for one or more purposes, delivering one or more social and ecological outcomes to achieve objectives for biodiversity conservation, sustainable resource use, or both [START_REF] Molenaar | Area-based management tools[END_REF][START_REF] Johnson | Climate change is likely to severely limit the effectiveness of deep-sea ABMTs in the North Atlantic[END_REF] . Since ABMTs are common across ocean sectors, management objectives, and socialecological contexts [START_REF] Ehler | Marine Spatial Planning: a step-by-step approach toward ecosystem-based management[END_REF] , and given their recommended use for achieving conservation and sustainability goals [START_REF]Biodiversity and the 2030 Agenda for Sustainable Development Biodiversity Is Essential for Sustainable Development[END_REF][START_REF] De Santo | Implementation challenges of area-based management tools (ABMTs) for biodiversity beyond national jurisdiction (BBNJ)[END_REF] , a clearer understanding of the contributions of ABMTs to SDG 14 targets may enable strategic planning toward achieving this goal. Here, we assess evidence of ecological, social, and economic ABMT outcomes, ranging from increasing organism size to maintaining ecosystem resilience to preserving access to resources and cultural traditions. We use this evidence to determine the potential contributions of prominent ABMTs to SDG 14 targets, guiding countries and practitioners in selecting the best interventions to deliver SDG 14.

Assessing evidence of outcomes and contributions to SDG 14

To provide management-level guidance on the use of ABMTs for achieving SDG 14, we conducted a two-step approach, including a rapid systematic review of the scientific literature followed by an expert survey to identify evidence, and gaps in evidence, of 17 ecological, social, and economic outcomes from seven types of ABMTs (Figure 1 and Supplementary Table 1). The selected ABMTs have objectives in biodiversity conservation, sustainable resource use, particularly fisheries, or both (Supplementary Table 2). These ABMTs regulate the activities of single sectors, as is typical of gear restriction areas (GRAs), fishery closures (FCs), territorial user right fisheries (TURFs), and particularly sensitive sea areas (PSSAs), or multiple sectors, as is typical of fully protected areas (FPAs), partially protected areas (PPAs), and locally managed marine areas (LMMAs). Many of these tools may be considered 'other effective area-based conservation measures' (OECMs) in some contexts and these tools may overlap in their application or the types of regulations they use.

Using evidence from the literature and expert opinions, we conducted a confidence assessment of the ability of selected ABMTs to deliver selected outcomes. Confidence level was determined based on "quantity and quality of evidence" and the "level of agreement among evidence", following a similar approach to the Intergovernmental Panel on Biodiversity and Ecosystem Services [START_REF]Intergovernmental Panel on Biodiversity and Ecosystem Services[END_REF] (Figure 2, Supplementary Table 6, Supplementary Figure 3). Finally, we developed a scoring system to link ABMTs to SDG 14 targets based on the relative contributions of outcomes to the targets (see Equation 1 in Methods).

Evidence of ABMT outcomes

We identified 276 records of ABMT outcomes from 177 studies (Table 1 and Supplementary References). Of these studies, 31 reported evidence through synthesis-based literature, including meta-analyses, systematic reviews, or literature reviews. Although we found evidence of fully protected areas (FPAs), partially protected areas (PPAs), gear restriction areas (GRAs), fishery closures (FCs), and territorial user right fisheries (TURFs) in these 31 studies, most reported only ecological outcomes. The majority of records from both synthesis-based evidence and evidence from individual studies reported on outcomes from FPAs and PPAs (25% and 29%, respectively). The proportion of all literature-based evidence records across outcomes was comparable for locally managed marine areas (LMMAs), GRAs, FCs, and TURFs (8%, 14%, 12%, 12%, respectively); however, no synthesis-based evidence was identified for outcomes of LMMAs. Individual studies reported 204 records of evidence for ABMT outcomes, including 95 records of positive effects, 68 records of negative effects, and 41 records documenting no effect of ABMTs on outcomes. No literature-based evidence was identified for outcomes of particularly sensitive sea areas (PSSAs).

Expert opinions collected using survey questionnaires (n=75) exhibited greater agreement on the ecological outcomes of most ABMTs than social and economic outcomes (Figure 3). Experts agreed that for most ABMTs, positive effects would occur for the majority of ecological outcomes. More than 60% of experts agreed that FPAs, PPAs, LMMAs, and FCs would have positive effects on organism size (96%, 87%, 60%, and 87%, respectively), organism abundance (89%, 91%, 67%, and 89%, respectively), maintaining habitat (96%, 92%, 67%, and 65%, respectively), ecosystem function (93%, 84%, 63%, and 61%, respectively), ecosystem resilience (92%, 81%, 61%, and 63%, respectively), and on reducing threats to species (93%, 84%, 72%, and 87%, respectively). More than 60% of experts also agreed that GRAs would have positive effects on organism size (68%), organism abundance (73%), maintaining habitat (76%), and reducing threats to species (79%).

In contrast, at least 25% of experts agreed that FPAs, PPAs, LMMAs, GRAs, and FCs would have negative effects on harvest earnings (43%, 25%, 37%, and 43%, respectively), maintaining access to resources (72%, 53%, 43%, and 59%, respectively), equitable access to resources (47%, 37%, 28%, and 37%, respectively), and preserving traditions and customs (47%, 32%, 31%, and 40%, respectively). Experts were less certain about outcomes of TURFs and PSSAs, as more than 20% of experts indicated either "do not know" or "prefer not to answer" for all outcomes of these tools (see Methods). Several experts commented on the difficulty of providing general information on expected effects of ABMTs, especially those pertaining to social and economic outcomes, given the context-dependency of these outcomes relative to local ABMT objectives, monitoring capacity, and social groups.

Confidence assessment

Based on evidence provided by the literature and by experts, we found generally greater confidence in the delivery of ecological outcomes than social and economic outcomes from the assessed ABMTs (Figure 4). We found high confidence, assigned to "well-established" and "established but incomplete" categories (Figure 2), that multi-sector ABMTs, including FPAs, PPAs, and LMMAs, would have positive effects on organism size and abundance, species diversity, habitat, ecosystem function and resilience, and reducing threats to species. Most single sector ABMTs, including GRAs, FCs, and TURFs, were found to have positive effects on fewer ecological outcomes, including organism size and abundance, ecosystem function, and reducing threats to species, with high confidence. We also found high confidence that the seven ABMTs would have no effect on reducing impacts of acidification. While we found no literature-based evidence (Table 1), there was medium or high agreement among experts that ABMTs would have no effect on this outcome (Figure 3). Similarly, though to a lesser extent, there was agreement that none of the ABMTs studied are likely to reduce pollution, though confidence assessment was "incomplete" for LMMAs and PSSAs. Further, we found that FPAs may have the potential to reduce pollution, though evidence of this outcome was "established but unresolved". Low confidence persisted for all outcomes of PSSAs, except the shared result of no effect of ABMTs on reducing impacts of acidification.

Across ABMTs, low confidence, assigned to "established but unresolved", "unresolved", and "incomplete" categories (Figure 2), was found for 43% of all assessed outcomes; however, these were assigned to only 25% of ecological outcomes compared to 63% of social and economic outcomes. There is an apparent lack of evidence of social and economic outcomes and, where evidence does exist, it agrees less often than that for ecological outcomes, resulting in low confidence (Figure 4). For ecological outcomes, 25% exhibited high quantity and quality evidence and 44% showed a high level of agreement among evidence (see data provided with Supplementary Information). In contrast, no social or economic outcome exhibited high quantity and quality evidence and only 21% showed a high level of agreement among evidence.

Further, where high confidence was determined for social and economic outcomes, the effect direction on outcomes across ABMTs was not always consistent. While we found high confidence that some ABMTs have positive effects on increasing non-harvest earnings, alternative livelihood activities, maintaining access to resources, and preserving traditions, others were found to have no effect or negative effects on the same outcome. The direction of effects on social and economic outcomes were generally less consistent across tools than was found for ecological outcomes.

Linking ABMTs to SDG 14 targets

We found that the assessed ABMTs could potentially contribute to five of the seven SDG 14 targets (Figure 5): SDG 14.2 (marine ecosystems), SDG 14.4 (sustainable fisheries), SDG 14.5 (conservation), SDG 14.6 (harmful subsidies), and SDG 14.7 (Small Island Developing States) based on qualitatively determined ABMT scores (see Methods). Since we determined with high confidence that most or all of the assessed ABMTs have no effect on reducing pollution or the impacts of ocean acidification (Figure 4), we found no strong evidence that these tools contribute to SDG 14.1 (marine pollution) or SDG 14.3 (ocean acidification). Based on the confidence assessments presented here, there is currently no evidence that PSSAs on their own contribute to SDG 14 targets. We found that multi-sector ABMTs (i.e., FPAs, PPAs, and LMMAs) make greater potential contributions to targets that focus on ecological objectives, including SDG 14.2, 14.4, and 14.5, than single-sector ABMTs (i.e., GRAs, FCs, and TURFs). This reflects the high confidence identified for positive effects of multi-sector ABMTs on more ecological outcomes than single-sector ABMTs (Figure 4). For all ABMTs, except PSSAs, the potential contributions made to these targets were greater than potential contributions to targets with social and economic objectives, including SDG 14.6 and 14.7.

While multi-sector ABMTs might make similar contributions to ecologically focused SDG 14 targets, they differ in their potential to contribute to socially and economically focused targets (Figure 5). FPAs emerged as the tool with the greatest potential to contribute to SDGs 14.2, 14.4, and 14.5; however, this tool had lower ABMT scores than LMMAs for contributing to SDG 14.6 and 14.7. PPAs had the lowest ABMT scores for contributing to SDG 14.6 and 14.7 of all assessed ABMTs, with the exception of FCs and PSSAs, which were not found to make contributions to these targets based on current evidence. We identified LMMAs as the ABMT with the greatest potential to contribute to SDG 14.6 and 14.7. Second to LMMAs, TURFS presented higher ABMT scores for these targets than other tools. Both LMMAs and TURFs were the only tools found to increase harvest earnings and maintain access to resources with high confidence (Figure 4), thus supporting their greater potential to contribute to these targets. FCs were the only single-sector ABMT found to make no contribution to SDG 14.6 and 14.7. This is likely due to the negative effect of FCs on maintaining access to resources (Figure 4), an outcome that supports these targets (see data provided with Supplementary Information).

DISCUSSION

We found that, based on current evidence, FPAs hold the greatest potential to contribute to ecologically focused SDG 14 targets (i.e., SDG 14.2, 14.4, and 14.5), aiming to preserve or restore ocean ecosystems and biodiversity, followed by PPAs and LMMAs (Figure 5). Those three tools typically regulate multiple sectors and activities, while the remaining tools target activities of single sectors, particularly fisheries via GRAs, FCs, and TURFS and shipping activities via PSSAs. Our results indicate that these multi-sector ABMTs, which may involve the use of multiple single-sector ABMTs, will be important for achieving SDG 14, given their strong potential to contribute to multiple targets. Since no single ABMT assessed was found to potentially contribute to all targets, nor was a single ABMT identified as holding the greatest potential to contribute to both ecologically and socially and economically focused targets, our findings highlight the need for a combination of tools to meet SDG 14. This resonates with a preliminary analysis by the United Nations of spatial management strategies, including marine spatial planning and integrated coastal zone management, for achieving ocean-related SDGs [START_REF]Preliminary analysis of area-based management measures to support SDG implementation[END_REF] .

Our results also highlight the potential role of these ABMTs in contributing to conservation targets as OECMs. While we determined similar ABMT scores for multi-sector tools, an important distinction between FPAs, PPAs, and LMMAs lies in their overarching objectives: biodiversity conservation is the key goal of FPAs and PPAs 21 , while LMMAs prioritize sustainable resource use over conservation per se [START_REF] Burke | Reefs at Risk Revisited[END_REF] .

LMMAs, a tool that has been favoured in Small Island Developing States [START_REF]Island Voices Global Choices. In-depth analysis of partnerships for Small Island Developing States[END_REF] , are unique in their application of a suite of ABMTs under a shared management strategy that is collaborative across communities, partner organizations, and governments at the local level [START_REF] Govan | Status and potential of locally-managed marine areas in the Pacific Island Region: meeting nature conservation and sustainable livelihood targets through widespread implementation of LMMAs[END_REF] . These characteristics are likely reflected in the ABMT scores we present here (Figure 5), particularly due to their ability to deliver ecological, social, and economic outcomes with high confidence (Figure 4). Despite the relatively limited evidence of LMMA outcomes in the primary literature (Table 1), this ABMT scored similarly to FPAs and PPAs that are well-documented. It is clear from our results that experts agree on generally positive expected effects of LMMAs on outcomes (Figure 3). Given these findings, LMMAs represent an opportunity for management as a potential pathway and a research priority to support the achievement of SDG 14. As a tool for ensuring a healthy and resilient ocean for sustainability [START_REF] Giakoumi | Ecological effects of full and partial protection in the crowded Mediterranean Sea: a regional meta-analysis[END_REF][START_REF]Marine Protected Areas: Economics, Management and Effective Policy Mixese[END_REF] , FPAs undoubtedly have a central role in achieving SDG 14.2, 14.4, and 14.5; however, the overarching aim of LMMAs may enable greater delivery of outcomes contributing to SDG 14 targets that seek to sustain the social and economic systems affecting oceans and ocean resources.

While our results show how the assessed ABMTs can potentially contribute SDG 14 targets, they also highlight limitations of ABMTs. We found "incomplete" evidence for all assessed outcomes of PSSAs (Figure 4), hence, no potential for PSSAs to contribute to SDG 14 (Figure 5).

PSSAs may make other important contributions to conservation and sustainability by reducing impacts from international shipping activities. This tool has been suggested for use in areas beyond national jurisdiction for conservation [START_REF] Rochette | Delivering the Aichi target 11: Challenges and opportunities for marine areas beyond national jurisdiction[END_REF][START_REF] Roberts | Area-based Management on the High Seas: Possible Application of the IMO's Particularly Sensitive Sea Area Concept[END_REF] , where threats to biodiversity are growing [START_REF] Warner | Conserving marine biodiversity in areas beyond national jurisdiction: Coevolution and interaction with the law of the sea[END_REF][START_REF] Gjerde | Protecting Earth's last conservation frontier: scientific, management and legal priorities for MPAs beyond national boundaries[END_REF] .

We highlight a need for more research on PSSA outcomes to support this tool as a potential pathway to SDG 14 in the high seas and suggest that ABMTs contributing to conservation outcomes should be used until the role of PSSAs can be clarified, such as FPAs. Our results also demonstrate the inability of the assessed ABMTs to effectively reduce marine pollution (SDG 14.1) and impacts of ocean acidification (SDG 14.3) (Figure 5). Other ABMTs not assessed here, such Special Areas designed under the MARPOL Convention [START_REF]Special Areas Under MARPOL[END_REF] , may better support these targets. Our results may reflect the broader and more systemic changes required for addressing these issues; for example, regulating the consumption and disposal of plastic or large-scale actions for reducing carbon emissions and decarbonizing economies [START_REF] Stafford | Viewpoint -Ocean plastic pollution: A convenient but distracting truth?[END_REF][START_REF] Blythe | The Dark Side of Transformation: Latent Risks in Contemporary Sustainability Discourse[END_REF][START_REF] Geels | Sociotechnical transitions for deep decarbonization: Accelerating innovation is as important as climate policy[END_REF] . Such systemic transformations may be necessary precursors to effectively achieving SDG 14.1 and 14.3, for which little progress has been made [START_REF]The sustainable development goals report 2019[END_REF] . It will be important to consider both non-spatial and spatial management tools, including and beyond the ABMTs assessed here, to achieve all SDG 14 targets. Holistic approaches to planning and management across the land-sea interface, like integrated coastal zone management [START_REF] Pittman | Governance across the land-sea interface: A systematic review[END_REF] and ridge-to-reef management [START_REF] Delevaux | A linked land-sea modeling framework to inform ridge-to-reef management in high oceanic islands[END_REF] , will likely be important for incorporating land-based regulations with ABMTs to achieve SDGs, including SDG 14 [START_REF]Preliminary analysis of area-based management measures to support SDG implementation[END_REF] .

Through this work, we have identified several evidence gaps pertaining to ABMTs and their outcomes. We highlight low confidence and a lack of evidence pertaining to the social and economic outcomes of ABMTs (Table 1, Figure 3, Figure 4). Low confidence was found for 61% of social and economic outcomes assessed, compared to only 25% of ecological outcomes.

These findings indicate a need for research to better assess social and economic outcomes of ABMTs at varying scales and for diverse stakeholders, which may first require the development of measurable indicators for targets that are presently without [START_REF] Virto | A preliminary assessment of the indicators for Sustainable Development Goal (SDG) 14 "Conserve and sustainably use the oceans, seas and marine resources for sustainable development[END_REF] . This evidence gap is again highlighted by the ABMT scores presented here, which indicate the low potential of these tools to contribute to SDG 14.6 and 14.7 that are socially and economically focused. While recent work helped to identify social and economic outcomes of marine protected areas [START_REF] Ban | Well-being outcomes of marine protected areas[END_REF] , an apparent evidence gap persists in identifying these outcomes for single-sector ABMTs, including FCs, GRAs, TURFs, and PSSAs.

We recognize the inherent limitations of our study imposed by the rapid systematic review method. While efforts were made to ensure that this method captured all relevant information, it cannot be truly comprehensive as would a full systematic review capturing both primary and grey literature. Our focus on primary, peer-reviewed literature provided a common filter, ensuring a consistent rigour across the collected evidence. This method was used to conduct a high-level confidence assessment that relied on a qualitative ranking system to assess the quantity and quality of evidence (Supplementary Table 6). To compensate for differences in the availability of literature-based evidence, we surveyed experts to identify the expected effects of ABMTs. Through the selection of survey participants in primarily research institutions and government, expertise from industry, Indigenous Peoples, and communities are not present in our confidence assessments. As with any scientific synthesis, our work may be affected by publication bias with some ABMTs more represented in the literature than others, as well as a tendency for literature to report positive outcomes. As more evidence becomes available, the confidence assessments and potential contributions of tools to SDG 14 targets presented here may be refined. Our results demonstrate the qualitative potential of ABMTs to contribute to SDG 14 and their use in practice should appropriately reflect this. Further, while we did select prominent ABMTs for assessment, other tools are available to practitioners and may also prove useful for achieving SDG 14. Our study does not assess the efficacy of ABMTs, nor does it quantify the extent of outcomes. While ABMTs may deliver similar outcomes, one tool may have a stronger effect than others and our study does not account for this. Delivery of these outcomes is dependent on local social-ecological systems and may vary by target species, ecosystems, and management regimes. To reach their fullest potential, ABMTs must be appropriately designed with attention given to local needs, actively managed, and wellenforced to consistently deliver outcomes contributing to SDG 14 [START_REF] Bennett | Why local people do not support conservation: Community perceptions of marine protected area livelihood impacts, governance and management in Thailand[END_REF][START_REF] Devillers | Reinventing residual reserves in the sea: Are we favouring ease of establishment over need for protection?[END_REF][START_REF] Gill | Capacity shortfalls hinder the performance of marine protected areas globally[END_REF] .

ABMTs are one type of management tool in a suite of tools and approaches available to decision-makers for achieving conservation and sustainability objectives. Our results confirm that no single ABMT can be used to reach all SDG 14 targets, but that a combination of tools, especially those regulating multiple sectors, will likely be necessary for achieving this goal.

When multiple ABMTs are used synergistically, multiple and more diverse outcomes may occur, potentially making stronger contributions to SDG 14. Placing ABMTs into the wider picture of integrated land-sea management, including both spatial and non-spatial approaches, will be important for achieving ocean conservation and sustainability goals [START_REF] Álvarez-Romero | Integrated cross-realm planning: A decision-makers' perspective[END_REF][START_REF] Reuter | Integrated land-sea management: Recommendations for planning, implementation and management[END_REF] . This is especially true for SDG 14 targets that may not be met using ABMTs, including SDG 14.1 to reduce marine pollution and SDG 14.3 to reduce ocean acidification as our results indicate. Our findings highlight important evidence gaps related to social and economic outcomes of ABMTs, especially single-sector ABMTs, providing a research agenda for future work. Through our assessment, we demonstrate which ABMTs may be most useful for achieving specific SDG 14 targets, allowing ocean planners and practitioners to make strategic decisions when selecting management tools. By linking ABMTs to SDG 14 targets, our work may support future research to assess potential contributions of existing or planned ABMTs to SDG 14 at a regional, national, and international scale.

METHODS

Selecting ABMTs and outcomes

The ABMTs assessed in this study were identified from a list of spatial management tools provided by Ehler and Douvere 10 , which included marine protected areas (MPAs), fishery closures (FCs), gear restriction areas (GRAs), and particularly sensitive sea areas (PSSAs). Here, we separated the broad category of MPAs into two distinct tools: fully protected areas (FPAs) and partially protected areas (PPAs) due to their documented differences in outcomes [START_REF] Zupan | Marine partially protected areas: drivers of ecological effectiveness[END_REF] . Locally managed marine areas (LMMAs) and territorial user right fisheries (TURFs) were added, as they have emerged prominently in the literature in recent years [START_REF] Rocliffe | Towards a network of locally managed marine areas (LMMAs) in the Western Indian Ocean[END_REF][START_REF] Lester | Impacts of TURFs and marine reserves on fisheries and conservation goals: Theory, empirical evidence, and modeling[END_REF] . In total, we identified seven ABMTs with distinct objectives, regulations, and outcomes, though these definitions may vary or overlap in their application (Figure 1 and Supplementary Table 2). Some ABMTs may overlay tools, for example an ABMT regulating multiple sectors, like an FPA, may make use of multiple single-sector tools, like FCs, GRAs, or PSSAs.

We assessed 17 ecological, social, and economic outcomes identified from previous reviews reporting observed and expected ABMT outcomes, particularly in the context of MPAs [START_REF] Bennett | From measuring outcomes to providing inputs: Governance, management, and local development for more effective marine protected areas[END_REF] and LMMAs [START_REF] Jupiter | Locally-managed marine areas: Multiple objectives and diverse strategies[END_REF] (Figure 1). Outcomes were assigned distinct definitions (Supplementary Table 1), and evidence of outcomes reported in literature needed to fit these definitions to be included in review. Some of these outcomes have direct links to SDG 14 targets (e.g., maintaining ecosystem resilience and SDG 14.2 on ecosystem restoration), while others are indirect (e.g., maintaining equitable access to resources and SDG 14.4 on sustainable fisheries). Since the primary aim of this research is to provide guidance on the use of ABMTs to achieve SDG 14 targets, additional outcomes not previously identified from existing reviews but with direct links to targets, such as reducing pollution and SDG 14.1, were added. Many of the assessed outcomes may be considered as indicators for monitoring and evaluation of ABMTs [START_REF] Biedenweg | A holistic framework for identifying human wellbeing indicators for marine policy[END_REF][START_REF] Kincaid | How fisher-influenced marine closed areas contribute to ecosystem-based management: A review and performance indicator scorecard[END_REF][START_REF] Pomeroy | How Is Your MPA Doing? A Guidebook of Natural and Social i=Indicators for Evaluating Marine Protected Area Management Effectiveness[END_REF] , which may inform or align with SDG 14 indicators.

Rapid systematic review

Rapid systematic reviews identify all studies meeting specific criteria, such as publication year, article type, geographic region, language, database, data type, or data extraction method [START_REF] Ganann | Expediting systematic reviews: Methods and implications of rapid reviews[END_REF] . We used a rapid review method to overcome challenges introduced by the number of ABMTs and outcomes assessed and the vastness of literature in this field of study. The review was conducted using the Web of Science between July and October 2019, and was limited to primary literature, including only articles and reviews published in English in 2002 or later.

While the grey literature could have provided additional information relevant to this study, including this information would not have permitted a systematic review due to the diversity of access restriction and languages that can be found in the grey literature. Since this method excludes publications from governments, non-governmental organizations, and other research organizations, we also conducted an expert opinion survey to compensate for evidence not found in the primary literature. The constraint on publication year was used to identify studies listing author email addresses, which were later used as contact information to invite participants for this survey [START_REF] Sinclair | The use, and usefulness, of spatial conservation prioritizations[END_REF] . We conducted two phases of rapid systematic review.

The first phase of rapid review was intended to capture synthesis-based evidence, including meta-analyses, systematic reviews, and standard literature reviews, and thus it was assumed that publications earlier than 2002 would have been included in these studies. Where synthesis-based evidence was identified, further review of individual studies in the second phase was not required, reducing the risk of double counting outcomes from individual studies that may have been captured by reviews. In addition to these limitations, search terms were designed to return the most relevant literature from titles, abstracts, and keywords (Supplementary Tables 3 and4). The efficacy of search terms was tested using pilot searches to ensure that 10 pre-determined studies were returned by the selected search terms in Web of Science (Supplementary Table 5).

Search terms were designed for the seven ABMTs, for ABMT outcomes in general, for metaanalyses and reviews, and for the 17 outcomes assessed in this study. All returned literature was screened first by reviewing titles and abstracts and then by reviewing full articles where an inclusion decision could not be made confidently from the title and abstract. Literature was screened based on the following criteria:  Population: studies must observe the marine environment  Intervention: studies must observe at least one of the seven ABMTs, aligning with the assigned definitions (Supplementary Table 2), though evidence of any assessed ABMT was recorded  Time and place: studies must be published after 2001 in any geographic location  Outcomes: studies must report evidence of positive, negative, or no effect on at least one of the 17 selected outcomes (Supplementary Table 1), excluding studies using strictly theoretical methods or theoretical modelling In the second phase of the review, additional searches were conducted to identify studies reporting evidence of individual ABMT outcomes for any case where synthesis-based evidence was not identified in the first phase of review. Returned literature for each outcome per ABMT was sorted using the "Relevance" feature on Web of Science, which ranks studies based on search term frequency in titles, abstracts, and keywords. Then, the first 25 records were screened using the same method and inclusion criteria as the first review phase. In cases where fewer than 10 records met all inclusion criteria, the next 25 records available in Web of Science were screened. We used this method to ensure that the most relevant literature and best available evidence was captured.

In the first phase, when studies met all inclusion criteria, the following data were extracted: study type (i.e., meta-analysis, systematic review, or standard literature review), number of studies reviewed or included in the meta-analysis, geographical scope, ABMT type, outcome type (i.e., ecological, social, economic, or multiple), evidence of outcomes, and effect directions (e.g., positive effect on organism size). Additional information related to study quality, including the reporting and rigour of methods, was recorded and informed distinctions made between study type where necessary. Systematic literature reviews were distinguished from standard literature reviews such that the former reported a search strategy, including search terms, and inclusion/exclusion criteria. For each study included, the reported ABMT was classified according to the definitions used in this study (Supplementary Table 2), which in some cases differed from the ABMT that was searched in Web of Science. For example, if a study was returned by a search for FC outcomes, but the described ABMT fit this study's definition of a GRA, the ABMT was classified as a GRA. Where it was unclear whether an MPA was fully or partially protected, MPAtlas (http://www.mpatlas.org/) was used to determine the appropriate ABMT type. If an MPA was reported as being entirely no-take on MPAtlas, it was classified as an FPA. All other MPAs, including those with some no-take zones according to MPAtlas, were classified as PPAs. In the second phase, data on study location, ABMT type, evidence of outcomes, and effect direction were extracted and qualitative information that clarified the nature of reported outcomes was recorded.

 Established but incomplete: general agreement among evidence, although limited evidence exists  Established but unresolved: moderate evidence exists, although conclusions do not consistently agree or disagree  Unresolved: comprehensive evidence exists, and conclusions do not agree  Incomplete: limited evidence exists, recognizing major knowledge gaps We used a qualitative ranking system to determine the quantity and quality of evidence and the level of agreement to be either "high", "medium", or "low" based on the criteria presented in Supplementary Table 6, applied in a decision tree presented in Supplementary Figure 3. High quantity and quality evidence included one or more meta-analysis or systematic review or more than one standard literature review or five or more individual studies and more than 75% of experts reporting one expected effect. High agreement required the majority of studies to agree on an ABMT outcome, the majority of experts to agree on an outcome, and for the studies and experts to agree on that same outcome. Each ABMT outcome was assessed according to these criteria and assigned a confidence category (Supplementary Figure 3). Wellestablished and established but incomplete categories were considered to be of high confidence, reflecting high certainty that a particular ABMT would deliver a particular outcome, and were assigned confidence scores of 2 and 1, respectively. All other confidence categories were not assigned a confidence score, as these categories were considered to be of low confidence.

Linking ABMTs to SDG 14 targets

ABMT outcomes assessed in this study do not all make equivalent contributions to SDG 14 targets. To account for this, each outcome was assigned a contribution score per target. Scores ranged from one to three, depending on the type of contribution. A direct contribution (score= 3) has a central role in meeting the objectives of the target; a supporting contribution (score= 2) aids the delivery of a direct contribution; and an indirect contribution (score= 1) enables the delivery of supporting or direct contributions to a lesser extent (see data provided with and2. This figure presents positive effects on outcomes given their potential contributions to SDG 14, though positive, negative, and neutral effects were collected as evidence in this study.

FPA, fully protected area; PPA, partially protected area; LMMA, locally managed marine area; GRA, gear restriction area; FC, fishery closure; TURF, territorial user right fishery; PSSA, particularly sensitive sea area. Icons are attributed to Becris (LMMA), Freepik (FPA, PPA), Mavadee (PSSA), Smashicons (FC), Surang (GRA), Wichai.wi (TURF) from www.flaticon.com. 6 and detailed in Supplementary Figure 3. "Well-established" and "established but incomplete" categories were considered to be high confidence categories, while remaining categories were considered to be low confidence, for the purpose of linking ABMTs to Sustainable Development Goal 14 targets (see Methods). Icons are attributed to Becris (LMMA), Freepik (FPA, PPA), Mavadee (PSSA), Smashicons (FC), Surang (GRA), Wichai.wi (TURF) from www.flaticon.com. There is highest confidence in the delivery of "well-established" outcomes (green) and lowest confidence in the delivery of "incomplete" outcomes (dark orange). The effect direction for each outcome is indicated within each circle. For some "established but unresolved" and "unresolved" outcomes, more than one effect direction is indicated due to a lack of agreement among evidence. "Incomplete" outcomes do not indicate an effect direction. FPA, fully protected area; PPA, partially protected area; LMMA, locally managed marine area; GRA, gear restriction area; FC, fishery closure; TURF, territorial user right fishery; PSSA, particularly sensitive sea area. Icons are attributed to Becris (LMMA), Freepik (FPA, PPA), Mavadee (PSSA), Smashicons (FC), Surang (GRA), Wichai.wi (TURF) from www.flaticon.com.

Figure 1 .

 1 Figure 1. Area-based management tools and their potential ecological, social, and economic outcomes assessed in this study. The selected tools have objectives for biodiversity conservation, sustainable resource use, or both and regulate activities of single or multiple sectors. Complete definitions of tools and outcomes are provided in Supplementary Tables 1

Figure 2 .

 2 Figure 2. Confidence assessment framework, adapted from IPBES 20 , used to determine confidence in the delivery of area-based management tool (ABMT) outcomes based on evidence from rapid systematic review and expert opinions. Criteria for determining quantity and quality of evidence and level of agreement among evidence are defined in Supplementary Table6and detailed in Supplementary Figure3. "Well-established" and "established but

Figure 3 .

 3 Figure 3. Expert opinions (n= 75) on the expected effects of area-based management tools (ABMTs) on ecological, social, and economic outcomes. See Supplementary Tables1 and 2for definitions of ABMTs and outcomes. FPA, fully protected area; PPA, partially protected area; LMMA, locally managed marine area; GRA, gear restriction area; FC, fishery closure; TURF, territorial user right fishery; PSSA, particularly sensitive sea area.

Figure 4 .

 4 Figure 4. Confidence assessment of literature-based and expert opinion evidence for the delivery of ecological, social, and economic outcomes from area-based management tools (ABMTs). There is highest confidence in the delivery of "well-established" outcomes (green) and

Figure 5 .TABLESTable 1 .

 51 Figure 5. Potential contributions of area-based management tools (ABMTs) to Sustainable Development Goal 14 (SDG 14) targets based on confidence assessments of ABMT outcomes and the potential contributions of outcomes to SDG 14 targets (see data supplied with Supplementary Information). Circle size is proportional to ABMT scores indicated in each circle (scores range from 0 to 102, see Equation 1 in Methods). Crosses indicate an ABMT score of zero, meaning no potential contribution of a tool to a target, based on current evidence and the relative contribution of an outcome to a target. FPA, fully protected area; PPA, partially protected area; LMMA, locally managed marine area; GRA, gear restriction area; FC, fishery closure; TURF, territorial user right fishery; PSSA, particularly sensitive sea area. Icons are attributed to Becris (LMMA), Freepik (FPA, PPA), Mavadee (PSSA), Smashicons (FC), Surang (GRA), Wichai.wi (TURF) from www.flaticon.com.

ACKNOWLEDGEMENTS

We thank Dr. Natalie Ban for her support in this work, including survey development, and useful comments on an earlier version of this manuscript. This work was supported by the Mitacs Globalink Research Award and a Discovery Grant of the Natural Sciences and Engineering Research Council (NSERC) of Canada awarded to R.D. JC was supported by BiodivERsA (METRODIVER) and Agence Nationale de la Recherche (ANR-14-CE03-0001-01).

DATA AVAILABILITY

Data supporting the analyses and results of this study are available in the Supplementary Information. Correspondence regarding this data should be addressed to J.M.R.

Expert opinion survey

An expert opinion survey was designed to capture knowledge of ABMT outcomes that could fill gaps from the rapid systematic review. Using Qualtrics® software, the online survey asked participants to identify their familiarity with the assessed ABMTs, the expected effect of ABMTs on each outcome, and to provide demographic information relating to their professional experience. When identifying the expected effects of ABMTs on outcomes, participants were asked to assume that ABMTs were appropriately designed, actively managed, and wellenforced. We identified potential participants using two methods: (1) authors of studies included in the first phase of review and (2) known experts in the ABMTs identified from our collective professional networks, including representatives of academia, governments, nongovernmental organizations, and independent experts. Invitations to participate were extended to these individuals via direct email with an anonymous link to the survey. In addition, we invited participants to share the survey with colleagues or to provide contact information of colleagues to receive an individual invitation. To conduct the confidence assessment, responses on the expected effects of ABMTs were grouped into positive effects from "Strong Positive" and "Positive" responses, negative effects from "Strong Negative" and "Negative" responses, and uncertain effects from "Do Not Know" and "Prefer Not to Answer" responses.

This research was approved by the Interdisciplinary Committee on Ethics in Human Research

(ICEHR) at the Memorial University of Newfoundland, ICEHR No. 20200294-AR.

Confidence assessment

To determine the level of confidence in the delivery of ABMT outcomes, we used an assessment method modified from the IPBES assessment process [START_REF]Intergovernmental Panel on Biodiversity and Ecosystem Services[END_REF] (Figure 2, Supplementary Table 6, Supplementary Figure 3). We defined five confidence categories based on the quantity and quality of evidence and level of agreement among evidence collected via rapid systematic review and expert opinion survey. These categories are:  Well-established: comprehensive evidence exists, and conclusions agree Supplementary Information). We considered contributions to the targets broadly based on their description and, where feasible, their indicators. While some indicators were used to inform contribution scores for ABMT outcomes, others were not relevant to the outcomes assessed.

For example, a study reporting an ABMT outcome of healthy ocean acidity (pH), the indicator for SDG 14.3, would be considered as evidence of a direct contribution to this target. Similarly, a study reporting improved ecosystem resilience as an ABMT outcome would be considered as evidence of an indirect contribution to this target (see data provided with Supplementary Information). In contrast, the indicator for SDG 14.5, protected area coverage, is not an outcome of ABMTs and is therefore not relevant to this study. To link ABMTs to SDG 14 targets, an ABMT score was calculated according to the following equation:

Possible ABMT scores ranged between 0 and 102, depending on the assigned confidence and contribution scores for the 17 assessed outcomes (see data provided with Supplementary Information). ABMT scores were qualitatively compared to determine the relative contributions of ABMTs to SDG 14 targets (Supplementary Figure 4).

AUTHOR CONTRIBUTIONS

All authors contributed to the conception of this research, to study design, and to editing the manuscript. J.M.R. reviewed the literature, conducted the expert opinion survey, carried out analyses, and drafted the manuscript.

COMPETING INTERESTS

The authors declare no competing interests.


domain: spi phys math info

text:
Célestin Ott

Charles Pivot

Pierre Dubois

Quentin Gallas

Jérôme Delva

Marc Lippert

Laurent Keirsbulck
email: laurent.keirsbulck@uphf.fr

Céletin Ott

C Ott

Pulsed jet phase-averaged flow field estimation based on neural network approach

Keywords: Neural Network, Deep Learning, Actuators, Dynamic Characterization, Flow Control

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Multidimensional flow field database development has become more and more important for a large number of applications (understanding of the physical phenomena involved [START_REF] Callaham | Robust flow reconstruction from limited measurements via sparse representation[END_REF], active flow control configuration optimisation [START_REF] Williams | Brief History of Flow Control[END_REF], parametric study for the prediction of specific phenomena occurrence [START_REF] Li | Flow field reconstruction and prediction of the supersonic cascade channel based on a symmetry neural network under complex and variable conditions[END_REF]...) The main objective of flow field reconstruction consists in estimating the space-and time-resolved flow fields with the associated coherent structures. Experimentally, such a task is however challenging especially because of the technical complexity associated to the acquisition of experimental data directly resolved in space and time. To address these challenges, efforts can be made in the metrology process to capture the flow field and in the methodology to process experimental data. In the topic of flow field measurements, the stake is to capture the physics and the coherent structures in the flow field. Beyond the temporal resolution, the deployed metrology technique must also have a sufficient spatial resolution. Only a few metrology techniques allow to measure directly and vectorially a volumic velocity field, such as V3V or HPIV (space-time resolved particle tracking techniques on a thick laser sheet [START_REF] Soria | Towards 3C-3D digital holographic fluid velocity vector field measurement -Tomographic digital holographic PIV (Tomo-HPIV)[END_REF]). These methods are particularly suitable for fluidic actuator's dynamic characterization as shown by [START_REF] Cambonie | Experimental study of counter-rotating vortex pair trajectories induced by a round jet in cross-flow at low velocity ratios[END_REF] and [START_REF] Cambonie | Transition scenario of the round jet in crossflow topology at low velocity ratios[END_REF]. Such approaches however require a complex experimental setup, which is not necessarily compatible with standard geometric configurations for various reasons (obstruction, intrusiveness, high-speed laser power, seeding issues, optical access, near-wall resolution...) [START_REF] Poelma | 3D Flow reconstruction using ultrasound PIV[END_REF], [START_REF] Haack | Characterization of a high-speed flow control actuator using digital speckle tomography and PIV[END_REF]. In this case, other methods with a trade-off on the nature of the recovered information can be implemented:

• local time-resolved measurements, such as hot-wire sensor [START_REF] Fernandez | Experimental Measurement Benchmark for Compressible Fluidic Unsteady Jet[END_REF]) or Laser Doppler Anemometry [START_REF] Bisgaard | Velocity fields around spheres and bubbles investigated by laser-doppler anemometry[END_REF]) which allow to capture velocity signals at high frequency (20 kHz) • space-resolved flow field, such as 2D PIV (or Stereo-PIV on a laser sheet [START_REF] Foucaut | Unsteady characteristics of near-wall turbulence using high repetition stereoscopic particle image velocimetry (PIV)[END_REF], [START_REF] Béra | Flow analysis of two-dimensional pulsed jets by particle image velocimetry[END_REF]) which make possible to obtain velocity fields space-resolved but at a lower frequency (conventionally 2 kHz for high-speed PIV) and only in a two dimensions plan, or refractive index gradient-based methods (shadowgraphy [START_REF] Emerick | SparkJet actuator characterization in supersonic crossflow[END_REF], Schlieren or holography [START_REF] Olchewsky | Vertical digital holographic bench for underexpanded jet gas density reconstruction[END_REF]) which enable the capture of pressure fields (or pressure gradient fields) but not velocity fields.

Since the goal of the dynamic characterization process is to obtain a volumic space-time resolved velocity field, the experimental data have to be manipulated (when Holographic-PIV (3D space-time-resolved) can not be used), flow field can be estimated using reconstruction methods (based on incomplete experimental data, supplemented or not with stochastic estimations). in particular, [START_REF] Kovasznay | Hot-wire investigation of the wake behind cylinders at low Reynolds numbers[END_REF] has developed a method to extract a velocity field resolved in space and time. This method can be adapted to be based on a one-, twoor three-dimensional measurement grid on where local time-resolved signals are successively captured and synchronized using a noticeable trigger representative of the studied phenomenon period [START_REF] Ostermann | Sweeping jet from a fluidic oscillator in crossflow[END_REF]. In the context of periodic fluidic actuators, this approach is particularly tailored and was adapted for various applications, mainly to convert local hot-wire measurements into:

• instantaneous velocity profiles Ott et al. (2019b), or to estimate a 3D velocity field based on multiple parallel 2D velocity fields, synchronized with each other. The conditional approach shows good results when coupled with a phase-average process, acting as filtering [START_REF] Schaeffler | Overview of active flow control actuator development at NASA Langley research center[END_REF][START_REF] Hardy | Plasma synthetic jet for flow control[END_REF][START_REF] Ostermann | Phase-Averaging Methods for the Natural Flowfield of a Fluidic Oscillator[END_REF]. Estimation methods are preferred when the temporal or spatial resolution of the experimental rough data needs to be improved. Stochastic estimations, such as LSE / QSE methods (linear / quadratic stochastic estimation) [START_REF] Hudy | Stochastic estimation of a separated-flow field using wallpressure-array measurements[END_REF] can then be implemented. The purpose is to use a local time-resolved conditioner signal to estimate a velocity field [START_REF] Fadla | Electrochemical Measurements for Real-Time Stochastic Reconstruction of Large-Scale Dynamics of a Separated Flow[END_REF] [START_REF] Chovet | Dynamical aspects of a backward-facing step flow at large Reynolds numbers[END_REF]. This method shows good results in a wide range of application (isotropic turbulence [START_REF] Adrian | Conditional eddies in isotropic turbulence[END_REF], turbulent boundary layers [START_REF] Guezennec | Stochastic estimation of coherent structures in turbulent boundary layers[END_REF], axisymmetric jets [START_REF] Bonnet | Stochastic estimation and proper orthogonal decomposition: Complementary techniques for identifying structure[END_REF], descending steps [START_REF] Cole | Applications of stochastic estimation in the axisymmetric sudden expansion[END_REF], open cavities [START_REF] Murray | Estimation of the flowfield from surface pressure measurements in an open cavity[END_REF]...). Deep learning methods, based on the emerging field of machine learning [START_REF] Turing | Computing Machinery and Intelligence. Parsing the Turing Test: Philosophical and Methodological Issues in the Quest for the Thinking Computer[END_REF], also begin to find their applications to flow field estimation, thanks to their ability to assimilate a large number of data and extract inter-correlations or paradigms. Supervised learning methods have shown their effectiveness in reconstructing 2D velocity and pressure fields around a cylinder, based on local pressure measurements [START_REF] Bright | Compressive sensing based machine learning strategy for characterizing the flow around a cylinder with limited pressure measurements[END_REF]. More recently, neural network learning has been used to greatly improve the spatial and temporal resolution of low-resolution 2D velocity fields in the wake of a cylinder [START_REF] Jin | Prediction model of velocity field around circular cylinder over various Reynolds numbers by fusion convolutional neural networks based on pressure on the cylinder[END_REF][START_REF] Jin | Time-resolved reconstruction of flow field around a circular cylinder by recurrent neural networks based on non-timeresolved particle image velocimetry measurements[END_REF].

Indeed, this kind of deep learning tools have benefited large developments thanks, mainly, to computer capabilities in the past years while being known from decades. Sophisticated neural networks based on physicsconstrained deep learning strategies have been recently proposed: [START_REF] Raissi | Physicsinformed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations[END_REF], [START_REF] Li | Flow field reconstruction and prediction of the supersonic cascade channel based on a symmetry neural network under complex and variable conditions[END_REF], [START_REF] Sun | Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data[END_REF], [START_REF] Sun | Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data[END_REF]. However large-area flow field measurements with both high spatial and temporal resolution remain a real challenge [START_REF] Lee | Data-driven prediction of unsteady flow over a circular cylinder using deep learning[END_REF]. These estimation methods have a common objective: to obtain space-and time-resolved flow field when only restricted data are available (low spatial or temporal resolution). In this framework, a slotted pulsed jet blowing at 100 Hz with a peak velocity of 90 m/s through a 0.5 × 30 mm slot inclined at 45°is used in order to test the present flow field estimation method. Previous studies [START_REF] Ott | Space-time resolved fluidic actuators characterization, and experimental identification of the physical mechanisms involved in their interaction with a boundary layer[END_REF]) shown that particle seeding is not compatible with this configuration to characterize the flow dynamics, but 20kHz hot-wire measurements have been successfully conducted along a 3D space-resolved measurement grid. In order to obtain a 3D space-time-resolved velocity field based on these local measurements, we propose in the present study a Neural Network-based flow field estimation method able to give a 3D spacetime-resolved velocity field using local time-resolved velocity signals captured with a hot-wire traveling along a 3D measurement grid. To validate this method, the same experimental data set is processed using a previouslyvalidated conditional-based approach Ott et al. (2019b), which allows to obtain a 3D space-time-resolved baseline flow field. The paper is outlined as follows. The experimental setup and the two estimation methods are detailed in section 2. The neural network approach is validated in section 3 in two steps: firstly with a quantitative study of the learning and test losses for different sampling rates, and secondly with an in-depth comparison of the results obtained by the neural network with the results of the conditional approach. The use of neural network based methods as flow field estimation is discussed in section 4, and its benefits and perspectives are clarified. Section 5 briefly concludes this study.

Apparatus and estimation methodologies

Experimental setup

The experimental setup used to capture the reference data set, consists in a 45°inclined slotted pulsed jet, blowing in a confined space, without crossflow. The present experiment was performed in the onera-lmfl boundary layer wind tunnel, which has a cross-sectional area of 30×30 cm 2 . The pulsed jet is generated by a Festo valve, with a working frequency of 100 Hz (using a duty-cycle of 50%). An inlet pressure of 5 bars regulated with 0.01 bar accuracy is used (Centronics pressure valve). The outlet of the valve is connected to a diffuser and a nozzle. The goal is to obtain a homogeneous jet (in terms of velocity amplitude) at the outlet of the nozzle. The nozzle is 45°inclined, and has a cross-sectional area of 30×0.5 mm 2 . The simple hotwire is mounted on a traveling system, motorized with stepping motors enabling the hot-wire to move with an accuracy of 0.1 mm in all directions. Dantec Dynamics single-hot-wire probe, type 55P15 (5 µm diameter and 1.25 mm long plated tungsten wire sensor), operating at constant temperature connected to a Dantec Dynamics conditioner (featuring a Wheatstone bridge) are employed to acquire the velocity induced by the actuator at the nozzle outlet. The sensor is calibrated on a Dantec calibration bench before each wind tunnel tests, and a verification calibration is performed after each test to monitor the polynomial calibration law evolution. The velocity measurements are sampled at 20kHz and are low pass filtered with a cutting frequency of 10 kHz. The test duration is chosen to be equal to 2s. The 5049 cells measurement grid has a size of 40 mm in the Z-direction, with a 5 mm resolution, and are centered with the nozzle. In the X-direction, the grid has a size of 80 mm with a 5 mm resolution and is placed so that the nozzle is centered at X=5 mm from the left border of the grid. In the Y-direction, the grid is 30 mm high and begins at a distance of 0.3 mm from the wall. The resolution of the measurement grid along the Y-axis is variable (from 0.2 mm close to the wall, and up to 2 mm far from the wall). In this framework, for the results layout, a dimensionless orthonormal coordinate system is defined, whose origin is the center of the actuator slot. The dimensions along X-and Y-axis are normalized by the slot width:

Estimation methodologies

In this sub-section, we introduce the two different estimation methods used in the present paper. The goal of these methods is to express 3D time-resolved phaseaveraged velocity fields based on the local time-resolved velocity data-set obtained with the moving hot-wire. In the following sections, U (t) denotes the rough velocity in physical time captured by the hot-wire sensor in m/s, U ϕ (t * ) is the phase-averaged velocity in dimensionless time (t * = t /T with T the actuator period), and U RM S is the root mean square of the phase-averaged velocity. For a given spatial location k a (defined by a X,Y and Z), and at a given dimensionless time t * a , the phaseaveraged velocity U ϕ is defined by:

U ϕ (k a ; t * a ) = 1 N N -1 i=0 U (k a ; t * a + iT ) (1)
and the phase-averaged root mean square velocity U RM S by:

U RM S = 1 N N -1 i=0 (U (k a ; t * a + iT )) 2 -(U ϕ (k a ; t * a )) (2)
where T denotes the actuator period and N is the number of periods used in the phase-average process.

Conditional approach

The conditional approach used in this paper is based on a method already used and validated on 2D cases Ott et al. (2019a[START_REF] Chovet | Dynamic characterization of piezoelectric microblowers for separation flow control[END_REF], and extrapolated to the 3D cases Ott et al. (2019b[START_REF] Ott | Space-time resolved fluidic actuators characterization, and experimental identification of the physical mechanisms involved in their interaction with a boundary layer[END_REF]. This approach is implemented through a Python program, and processed using eight core processors (10240 Kb each). The local hot-wire measurements acquired simultaneously with the synchronization signal are processed in four steps. The first step is the synchronization of all local time-resolved measurements with each other. The second step consists in performing a classical phase-average U ϕ over these periods. The third step is the distribution of the data into a three-dimensions tensor, and the fourth and last step is the extraction of the instantaneous velocity snapshots for each time step. These four steps are described in detail in Appendix A1 and shown in Fig. 8.

Neural network

Neural networks are nonlinear regression tools that have extensively been used in image recognition and language processing [START_REF] Kotu | Deep Learning[END_REF]. According to the universal approximation theorem, any function can be approximated by a sufficiently large and deep network [START_REF] Hornik | Approximation capabilities of multilayer feedforward networks[END_REF]. In this paper, a neural network is used to express the complete phase-averaged velocity field as a nonlinear function of spatial coordinates and time. A general introduction to the neural network (including terminology, functioning of a neuron and a neural network), is detailed in Appendix A2.

In this paper, training data are phase-averaged local velocity signals based on hot-wire measurements and the objective is to learn optimal weights and biases to express the phase-averaged velocity field and turbulent statistics as a function of spatial coordinates and dimensionless time. In terms of neural network, input neurons are X, Y, Z, t * and output neurons are U ϕ (X, Y, Z, t * ) and U RM S (X, Y, Z, t * ). Since the goal of this paper is to validate the use of a neural network for flow field estimation based on local hot-wire measurements, the neural network architecture is not subject to in-depth optimization. [START_REF] Goodfellow | Explaining and Harnessing Adversarial Examples[END_REF] showed that the architecture presented by [START_REF] Szegedy | Intriguing properties of neural networks[END_REF] (a three-layer 100-100-10 non-convolutional neural network with a Sigmoid activation function) showed good performance to limit the disturbances existing in the inputs data, in particular for the recognition of linearly noisy images. Furthermore, the work of [START_REF] Goodfellow | Explaining and Harnessing Adversarial Examples[END_REF] and [START_REF] Szegedy | Intriguing properties of neural networks[END_REF] underlines the fact that, in adversarial examples, the higher layers are significantly more useful than those on the lower layers. Following these recommendations and a preliminary trial-error study, the chosen architecture is composed of three hidden layers with respectively 15, 11 and 9 neurons, which allowed to limit the impact of the noise present in the hot-wire measurements used for the training of the neuron network, and thus obtain a more robust estimation. The cost function considers all hotwire locations (superscript i) and all samples (index t), yielding:

E 2 = t,i ||U ϕ (i) t -NN (i) t || 2 (3)
Where U ϕ

(i) t * is a vector containing U ϕ (X i , Y i , Z i , t * ) and U RM S (X i , Y i , Z i , t * ) while NN (i)
t contains the neural network estimate. The gradient descent (evaluated with batches of 1000 samples) is done over 1500 epochs (one epoch beeing one pass over the entire dataset). In order to make sure that the neural network training is converged and not over-fitted after these 1500 epochs, the cost function is monitored for the crossvalidation data and the training data. In this framework, the cross-validation/training ratio is set to 10%. The neural network was implemented under Python, using the Keras library [START_REF] Keras | Guide to the Sequential model -Keras Documentation[END_REF]. The final training procedure is summarized in Fig. 2. Finally, the neural network acts as an optimal nonlinear interpolator. Naturally, the success of such estimation depends on the training data quality (hot-wire locations Lakshminarayanan et al. ( 2016)), the good choice of hyperparameters and the learning procedure.

Results

The experimental setup presented in 2.1 is used to capture the hot-wire database and the space-and timeresolved velocity fields are reconstructed using the 3D conditional approach (2.2.1) and the deep learning approach (2.2.2). However, the raw measurements represent a very large database: 5049 measurement locations, 2 seconds of measurement time for each point with a frequency of 20 kHz, which represents a total of 20 × 10 7 samples. As the neural network structure is chosen in this study to be more versatile and able to be used in a large number of cases and with noisy signals, the learning duration of such a database is estimated at more than 30 hours with the hardware configuration used in Fig. 2: Neural network training this study (8 core CPU with 8 GB of RAM). In comparison, processing the same database using the conditional approach takes 25 minutes. To overcome this high computational cost, a reduction in the quantity of data used for training the neural network is carried out. For this reason, the present section is divided into two sub-section. The first one aims at investigating the effects of the amount of data used for training the neural network on the quality of the results, and select a satisfactory case. The chosen case is then subject to an in-depth study in the second sub-section.

Neural network's reliability study

In this sub-section, the neural network's architecture is tested for different amounts of training data in a range of 10% to 30% (with a 5% increment) of the raw database (corresponding respectively to 10.0 × 10 4 and 30.3 × 10 4 samples). The data are randomly selected over the raw database (10.0 × 10 5 samples), and used as input for the neural network. The results of these data processing are shown on Fig. 3.

In order to quantify the network's reliability, three tools are used (corresponding to the three columns of the Fig. 3). The first one is the monitoring of the learning losses over epochs. It consists in the calculation of the cost-function (MSE) at each epoch over the training set (orange line) and over the test set (dashed green). The second tool are the estimated flow fields of U ϕ and U RM S that can be compared to the reference base flow obtained with the conditional approach. It allows to check the flow field estimations relevance and to visualize the smoothing in space. For these visualizations, a two-dimensions Z plan is extracted from the volume estimations, at the middle of the slot (Z l = 0) for two representative instants (t * = 0.1 and t * = 0.25). On these snapshots, the phase-averaged velocity is colored using the dark end rainbow color scale, and the rms velocity is colored using the blue-red color scale. The third tool is a local time-resolved plotting of the neural network phase-averaged velocity estimation at a strategic location. The location is chosen close to the actuator where the velocity gradient is the highest, at X d =30, Y d =20 and Z l =0 (mid-plan, 15 mm downstream the slot and 10 mm from the wall). The reference phase-averaged velocity obtained with the conditional approach is plotted in dark blue over dimensionless time t * , and the phaseaveraged velocity estimated with the neural network is plotted in light blue over dimensionless time t * .

The local time-resolved phase-averaged velocity signal plotted on Fig. 3 show that the amount of data used in the training process of the neural network has a minor effect on the extremum amplitudes: the velocity peak amplitude are well estimated in every case. However, the temporal reliability and the global shape of the estimated signal (particularly the width of the blowing peak) are drastically improved when the amount of data used increases: the quadratic error between the neural network estimation and the base flow at this specific location decreases from 1.3 at 10% to 0.6 at 30%. The same observation can be done on the 2D-flow fields on both instants chosen: when the amount of data used is low, the jet envelop is smoothed and can be overestimated at some locations in terms of phase-averaged velocity, and is globally smoothed and underestimated Fig. 3: Effect of the data training amount on the accuracy of the phase-averaged flow field estimation in terms of rms velocity. The reliability of these estimations increases with the amount of data used. Learning losses quantification is a really interesting tool to quantify the neural network capability, and monitor the training process over epochs. With 10% of the database, the training error is higher than the test error for the first tens epochs, which means that at this stage the neural network is more efficient to estimate the data already processed than the data set aside for the test. The loss function is at 0.73 at the end of the first epoch for the test error, and 0.71 for the training error. The losses quickly decrease to respectively 0.035 and 0.034 at 600 epochs, and decrease slowly to end up at a plateau of respectively 0.031 and 0.030 from 900 epochs, meaning that the weights and bias of the neural network are converged. Furthermore, the losses curves are superim-posed, which means that there is no over-fitting in this case. The losses curves behave similarly for all percent of data used, except that when the amount of data used increases, the difference between the test and the training errors at the first epoch decreases. The values of the loss function after the convergence of the losses are however almost similar for each case (0.03±0.001). Particular attention must be paid to the fact that this quadratic error is calculated with respect to the data set used as input to the neural network for each case. These quantities therefore can not be compared with each other since the input data set is not the same. In order to quantify and compare the reliability of each model, it is mandatory to evaluate the cost function of each model with respect to the original 10 × 10 5 samples database. This evaluation is therefore performed over all the models presented in Fig. 3, regarding U ϕ . The quadratic errors of the U ϕ estimation using the different percentages of training data are then compared on Fig. 4.

Fig. 4: Quadratic error

This comparison shows that by expanding the input database from 10% to 30%, the MSE (mean squared error) of the U ϕ estimation can be lowered by 39% (from an MSE of 4.5 to 2.7). Thus the estimated flow field is more reliable when 30% of the database is used as input data for the neural network, but the computing time is also higher. The 30% case showing good reliability in terms of quadratic error on U ϕ and good training convergence, it is selected as the best reliability/calculation cost compromise in this framework. It is therefore used in the following subsection to carry out the in-depth study of the flow field estimations and a detailed comparison with the reference base flow obtained with the conditional approach.

In-depth study of the results

This sub-section aims to compare the 3D fields obtained with the conditional approach and the neural network using randomly 30% of the database. The reconstructed velocity-fields using the conditional approach are plotted on Fig. 5 a b andc , corresponding to three different dimensionless time instants t * . The same phaseaveraged velocity-fields are estimated using the neural network approach on Fig. 5 d e andf . On these 3D flow fields, iso-velocity surfaces of U ϕ = 15m/s are plotted and colored by U RM S (m/s) using the blue-red color scale. The domain borders are colored by U ϕ (m/s) using the dark end rainbow color scale. 2D slices are extracted from the 3D reconstructed fields at Z = 20mm. On those proposed planes, the velocity fields are colored by U ϕ (m/s) using the dark end rainbow color scale, and the associated RMS fields are colored by blue-red color scale ( g , h , i for the conditional approach and j , k , l for the neural network approach). The spatial development of the jet reconstituted using the 3D conditional approach is considered as the reference flow thanks to its validation in Ott et al. (2019b) and using comparisons with literature about slotted and pulsed jet development [START_REF] Eroglu | Structure, penetration, and mixing of pulsed jets in crossflow[END_REF], [START_REF] Vernet | Analysis and reconstruction of a pulsed jet in crossflow by multiplane snapshot POD[END_REF], [START_REF] Mahesh | The Interaction of Jets with Crossflow[END_REF], [START_REF] Sau | Optimization of pulsed jets in crossflow[END_REF]. The Fig. 5 gives the results of the conditional approach (left) and those related to the neural network (right). The 3D jet dynamic development corresponds, as expected, to those observed in the literature. The jet is symmetrical with regard to the plane Z l = 0 (mid-slot, with Z l defined by Z/l with l the slot length). The three-dimensional effects of the jet are correctly captured and reconstituted here. The flow features are coherent and continuous in space and time. At the instant t * =0.1 (2 ms after the valve opening), the blowing front coming out of the slot can be discerned. The jet is homogeneous along the slot, and despite the 45 °inclined nozzle, it remains confined close to the wall, as shown on Fig. 5 a andd . At this instant, the jet only modifies a reduced area (1 l wide, 0.5 l long and 0.1 l thick, with l the length of the slot). The slot edges (Z l =± 0.5) are the first areas where structures are produced, inducing two velocity peaks. These peaks are enclosed in cylindrical structures parallel to each other and aligned with Z l =-0.5 and Z l =+0.5. These structures correspond to the formation of a pair of counter-rotating vortices, which are well identifiable on plot a . The corresponding structures obtained by the neural network on plot d can be perceived despite a pronounced smoothing of the iso-surfaces shape. These two vortices then loose their intensity to form a homogeneous blowing front along the Z-axis. From t * = 0.25 ( h for the conditional approach and e for the neural network), a shear layer vortex created at the leading edge of the slot is also formed above the jet core, slightly upstream the blowing front. This structure is centered on X d =34 at t * = 0.25 and on X d =82 at t * = 0.75 (on plot c and f ). At the instant t * = 0.75 (5 ms after the valve closing), it is noticeable that the blowing extinction is not homogeneous. The jet first stops blowing in the middle of the slot but remains at Z l =-0.5 and Z l =+0.5. Thus the two contra-rotating vortices continue to be fed, which induce the generation of conical structures centered on Z l =-0.5 and Z l =+0.5 for X d ∈ [0; 70]. All these topological elements observed in the reference velocity field (obtained with the conditional approach on plot a , b and c ) and in the literature are well estimated using the neural network approach, while ensuring data continuity as shown by the 3D reconstructed fields on plot d , e and f . The velocity fields extracted from the 3D fields at mid-plane perpendicularly to the slot and the wall also show good restitution of the phase-averaged dynamic response of the actuator inside the jet compared to the base flow. Plot g , h and i show that the jet core (defined by U ϕ ≥ 30 m/s) is 45 °inclined at t * =0.1, with a jet core length of 36d (with d the slot width). The jet is then confined close to the wall and is 120d long at t * =0.25 (on h ).

At this time the shear layer vortex is clearly visible. During the blowing half-period, the average core velocity is U ϕ =32 m/s, with an average rms velocity of U RM S =7 m/s. At t * =0.75 ( i ), the actuator is turned off, and the last flow features are advected (mainly the jet core and the shear layer vortex). Plot j , k and l show the flow-fields obtained using the neural network approach. At t * =0.1 ( j ), the jet core is 45 °as expected given the previous results. However, the jet core is only 0.4L long, and the average rms velocity inside the jet core is U RM S =5 m/s. At t * =0.25 ( k ), the mean and rms velocities fields are smoothed (jet core is only 1.5L long) and the shear layer vortex is observable but its boundary is not sharply demarcated. The advection velocity of the main flow features is well modeled (the vortex and jet core are located where they are expected with regard to the conditional approach). At t * =0.75 ( l ) the jet envelop is well estimated despite a slightly smoothed border. The rms field also show a globally underestimated intensity without modifying the shape of the rms field and isolines. Overall the comparison of 2D fields allows to highlight that the standard deviations seem to be globally underestimated by the neural network: on average by 36% in the jet core, and by 12% in its surrounding. Moreover, the outline of the jet core is smoothed and spread out: the jet core surface and the jet length are underestimated. However, the mesh of the neural network estimation plot is not degraded compared to the base flow plot one, which means that the method allows to obtain the same overall phase-averaged flow dynamics as in the base flow by using only 30% of the experimental data. In order to quantitatively study the performance of the neural network method, the signals reconstructed by this method are extracted locally for a phase-averaged period and overlaid with the phase-averaged hot wire experimental data. These comparisons are shown in Fig. 6. The comparison locations are chosen close to the actuator slot, where the velocity gradient is the highest, and thus where the velocity estimation in time is more challenging. These locations are the following: the point 1 is placed at X d =2, Y d =1 and Z l =0 (1 mm downstream the slot and 0.5 mm from the wall). The point 2 is at X d =30, Y d =20 and Z l =0 (15 mm downstream the slot and 10 mm from the wall). Fig. 6 1 and 2 show that the main dynamic of the signal is well estimated by the neural network. Indeed, plot 1 shows that the blowing edge reach this location at t * =0.15 on the reference base flow (Conditional Approach), and at t * =0.17 on the signal given by the neural network, i.e. an error of 13%. The velocity peak occurs at t * =0.31 for the reference signal and is anticipated by the neural network at t * =0.30 (3% error). On plot 2 , this error is reduced to 6% for the blowing edge (t * =0.31 for the reference signal estimated at t * =0.29 by the neural network) and to 2% for the velocity peak (t * =0.38 for the reference signal and t * =0.37 for the neural network).

The dynamics and the average characteristics of the flow are locally well estimated by the neural network (the shapes of the curves are identical and the temporal errors remain low). However, the neural network strongly smooths the velocity variations of low amplitude, filtering out high frequencies.

In terms of amplitude the time-averaged velocity is well estimated by the neural network, with an underestimation of 5% at the location 1 and overestimation of 12% at the location 2 . However, the velocity peaks are both underestimated by the neural network in terms of amplitude, with an error of 13% at 1 and 4.8% at 2 . This local comparison confirms the observations made on 2D and 3D fields: the neural network is able, using only 30% of the original data, to reliably estimate the phase-averaged velocity, especially the mean behavior of the velocity. However, the velocity signals are smoothed (high-frequency features are filtered) and tend to underestimate the velocity amplitude. These limitations of the neural network-based method (underestimated velocity intensity and smoothed outline of the jet core) could result from various roots:

• the removal of 30% of the database • the neural network architecture • a too small number of trained weights in the neural network • the choice of the activation function in the neural network

The method however allows a reliable estimation, since the main flow features are well estimated in space and time. The reconstruction by the neural network is therefore a relevant method for the 3D estimation of space-time-resolved fields, based on the learning of experimental data chosen randomly in space and time.

Global discussion

This section aims to compare the effectiveness and capabilities of both methods presented in this paper. Table 1 gathers the advantages and limitations found in the present study regarding the use of the neural network versus the conditional approaches. The conditional approach is a versatile and quick method that is simple to implement. The neural network, meanwhile, requires more time and preliminary studies to be implemented and validated. Increased attention has to be brought to the analysis of the results in order to validate the consistency of the estimated physics. The conditional approach is quicker than the present neural network in terms of computational time. The complete process (from rough data to reconstructed flow fields) is 70 times higher using the neural network than the conditional approach (30 hours versus 25 minutes). The learning process of the neural network itself is responsible for 99.5% of the computational time, which means that once the model is defined the time needed for the flow field estimation is neglectable. Furthermore, the conditional approach only provides flow fields with a coarser or equal resolution (in space and in time) than the experimental data, while the neural network approach allows refining both spatial and time-resolutions. This comes from the fact that the conditional approach only reconstitutes the flow field based on the experimental measurements, while the neural network can model the complete flow field. This study has shown that it is possible to improve drastically the temporal and spatial resolution of the flow field estimation compared to the resolution of the measurements, without too much flow dynamics losses. The main limitation of the present neural network approach is the processing time, which led in this paper to a randomized reduction of the learning database and therefore a deterioration of the estimation. Furthermore, the neural network method showed smoothed velocity fields and underestimated standard deviations, which could come from the fact that only 30% of the original data were used, or that the architecture of the neural network was not perfectly suited (too low number of weights, activation function choice ...). In order to decrease the computational time of the learning process while increasing the input database size, it would be necessary to look to structural optimization of the neural network and its architecture, as proposed by [START_REF] Dubois | Data-driven predictions of the Lorenz system[END_REF] and [START_REF] Idrissi | Genetic algorithm for neural network architecture optimization[END_REF]. Indeed, a too-small number of trained weights (i.e. not enough hidden layers/neurons) can lead to smoothed results, while too many trained weights (i.e. large number of hidden layers/neurons) can lead to over-fitted results. Parameter studies can provide a more robust neural network with better performances [START_REF] Hamwood | Effect of patch size and network architecture on a convolutional neural network approach for automatic segmentation of OCT retinal layers[END_REF]). In addition, rather than using the classical sigmoid activation function, the literature suggests that using more subtle activation function (e.g. relus functions) could allows to prevent neural network overfittings [START_REF] Ramachandran | Searching for activation functions[END_REF] 1: Advantages and limitations of the estimation approaches mation domain. It could be, for instance, theoretically possible to enhance drastically the estimated area or to investigate boundary conditions that have not been investigated experimentally. This could be achieved for instance by adding the actuation frequency in the input data, and by training the network with random measurements (different positions, instants, and actuation frequencies). It might be then possible to reconstruct the fields for several frequencies, even if these have not been investigated experimentally. Particular attention should then be paid to the distribution of the database used for training, as well as its resolution.

Conclusion

This study proposes a data processing approach to obtain a space-time-resolved velocity field at the exit nozzle of a slotted pulsed jet based on hot-wire local timeresolved velocity data. This method uses the periodic behavior of the flow and the actuator's command signal as a synchronization trigger. It is based on a neuronal network whose entries are the location and the time, and outputs are the mean and rms velocities. This space-time-resolved estimation approach is validated by comparison with the conditional approach (previously validated) performed on the same experimental data set. The neural network approach shows good results in the phase-averaged dynamic restitution of the actuator's behavior, even by degrading the learning database (only 30% of the data are used), which means that this technique can be used to drastically improve the temporal or spatial resolution of a flow field estimation compared to the experimental data resolution. The main coherent structures are well captured and the flow behavior and physics are well estimated. The rms velocity seems however to be underestimated by the neural network and the jet core is smoothed and spread out, due to the intentional degradation of the learning database.

There is no claim of optimality in the network architecture used in this framework, since it is based on the literature without further optimizations. However, the chosen architecture has proven to be robust for the interpolation task and may therefore be considered as a first trial of hyperparameters when post-processing large hot-wire signals database.

Furthermore, without any structural optimization of the neural network, the computational time required to obtain the flow field (which corresponds to the cumulative time of the learning process and the estimation), is about 70 times longer than the conditional approach for the same experimental database size. Since the flow field estimation processing time is about 600 times smaller than the learning time for the neural network method, in the case of single database studies requiring multiple reconstructions, the use neural network method can be of great benefit and save considerable time.

Appendices

A1. Conditional approach details

The four steps of the conditional approach are the following: The first step is the detection of the triggers used to synchronize the data with a common base time. The rising edges of the actuator square control signal are used here. This allows to check the forcing frequency, to determine the first trigger which will become the new time origin and the number of periods available for the processing. The second step consists to perform a classical phase-average U ϕ over these periods. This process is illustrated in Fig. 7, where t * is the dimensionless time t /T (with T the actuation period) and U (t) is the velocity measured by the hot-wire for the instant t. The third step is the definition of the new common time origin stored in a i × j matrix, with i the number of variables (coordinates, velocity, RMS...) and j the number of time steps in a period defined by j = f acquisition (Hz) f actuator (Hz) (4)

These steps are carried out on all of the k measurement points. Each matrix is stored in the i×j ×k tensor, then the instantaneous flow fields can be obtained for each time step by extracting a (ik) matrix. It is then possible to animate these snapshots in dimensionless time (along j) in order to observe the phase-averaged flow field dynamics using time-resolved flow field animations. This process is schematized on Fig. 8. In its simplest formulation, a neural network consists in interconnected units (called neurons) transforming the input information through a feed-forward process.

One neuron and its associated parameters is shown in Fig. 9. This neuron receives a weighted information Σ = Fig. 9: Artificial neuron and its associated connections ω 1 × i and activates according to the σ function. The activation is classically a sigmoid reading:

σ(Σ) = 1 1 + exp(-Σ) (5)
Given a bias b for the neuron and a weight ω 2 for the output, the considered neuron transforms the input i into o = ω 2 × σ(ω 1 × i + b). In a dense network, each connection has a specific weight and each neuron has a specific bias. The Fig. 10 illustrates a simple architecture: one input layer with one neuron, one hidden layer with two neurons and one output layer with two neurons. The input value is x. In the hidden layer, the upper neuron outputs σ(w 1 × x + b 1 ) while the lower neuron outputs σ(w 2 × x + b 2 ). The neuron in the out-

E 2 = m t=1 (y t -NN t ) 2 (7)
Where NN t = NN(x t ). The neural network operator N N is built upon parameters and hyperparameters. Parameters are optimized via a gradient descent on the cost function and hyperparameters (number of layers and number of neurons) are often based on the user experience.

  X d = X d and Y d = Y d with d=0.5mm. Dimensions along Z-axis are normalized by the slot length: Z l = Z l with l=30mm. The experimental setup is shown on Fig. 1. It allows to capture the local time-resolved velocity signals along the present volumic measurement grid. For each measurement, the signal used to control the actuator (square signal at 100 Hz with a DC of 50%) is acquired simultaneously, and the rising edge of this square signal is used as a trigger for the synchronization.

Fig. 1 :

 1 Fig. 1: Experimental setup and hot-wire measurement grid

Fig. 5 :

 5 Fig. 5: Results and methods comparison

FigFig. 8 :

 8 Fig.8: 3D-adaped conditional approachOtt et al. (2019b)

Fig. 10 :

 10 Fig. 10: Interactions between four neurons

  ).Such an optimized neural network could open doors to many interesting applications in the flow field esti-

	Approach	advantages	limitations
		• spatial and temporal resolution enhancement
	Neural Network	• quick reconstruction • great development potential • nonlinear modeling	• high learning computational time • implementation complexity
		• flexibility
	Conditional	• light implementation • quick process • robust method	• restricted spatial and temporal resolution • requires a full process for each flow field esti-mation • absence of modeling
		Table

Acknowledgements This work was carried out within the framework of the CNRS Research Federation on Ground Transports and Mobility, in articulation with the ELSAT2020 project supported by the European Community, the French Ministry of Higher Education and Research, and the Hauts-de-France Regional Council. The authors gratefully acknowledge the support of these institutions.