Magali Mauchand
email: magali.mauchand@metz.ensam.fr

Nicolas Perry
email: nicolas.perry@irccyn.ec-nantes.fr

Alain Bernard
email: alain.bernard@irccyn.ec-nantes.fr

Specification management for the cost constraint optimisation in microelectronic design

Keywords: cost evaluation, microelectronic, software model integration, cost methods

In the preliminary design phase the integration of the economic constraints of a product is a difficult engineering task since there is a real lack of dedicated tools. This paper illustrates a specification software solution method making it possible to meet this need, applied to the microelectronics field.

Introduction

Traditional approaches to product development lead to long product development cycles and difficult cost control. Nowadays the desired approach to product development is a concurrent of an emphasis on cost control. Needs for economic and technical product evaluations are compulsory in the design process for the complete product life cycle [START_REF] Giannopoulos | Embedded systems software cost estimating within the concurrent engineering environment[END_REF][START_REF] Liu | Case study using COM (OLE) to link CAD and manufacturing cost estimation software[END_REF]. However, methods for requirement definition integrated costing methods are poorly developed on the market. A design strategy should minimise cost and time while maximising quality. This paper describes a modelling strategy to assist manufacturers in optimising these objectives.

Information and management systems must be developed in order to support the specification and to analyse the considered solutions [START_REF] Bachelet | DESI: Méthode d'évaluation de l'impact économique des choix techniques[END_REF][START_REF] Perry | Cost objective PLM and CE[END_REF].

The microelectronic field is characteristic of firms called 'fabless IC', the design departments are located outside the production sites and have few links with the latter. They focus on design and contract out the production stages to silicon wafer manufacturers or foundries [START_REF] Lu | Successful factors of the fabless IC industry in Taiwan[END_REF]. This outsourcing phenomenon came from the need of reactivity, to earn more money and to keep competitive skills [START_REF] Helo | Managing agility and productivity in the electronics industry[END_REF]. Moreover outsourcing strategies in general are commonly linked to the product life cycle [START_REF] Hilmola | On the outsourcing dynamics in the electronics sector: the evolving role of the original design manufacturer[END_REF]. Also an operating mode must be set up in order to design circuits that are feasible by the production line recommended for the manufacturing.

The main parameters of the life cycle of an electronic product for the public market are, on the one hand its really short lifespan, and on the other hand, the very fast evolution of technologies (shrinks), and also the work requirements for the research and development phase lead. For instance, product life cycles in the PC industries were approximately one year in the middle of the 1980s but by 1997 they had shrunk to approximately three months [START_REF] Curry | Beating the clock: corporate responses to rapid change in the PC industry[END_REF]. In electronics there are some systems with a long lifespan such as the ones developed for military and aviation applications. In these cases the design problem must include the system maintenance and enable a valorisation of the economic impact of decisions [START_REF] Riedel | Costs Analysis Linking Design, Test & Maintenance[END_REF].

Enterprises face the problem of perpetual innovation with the renewal of technologies and world-wide logistic integration to deliver to customers throughout the world. In the PC market, price and time are closely connected [START_REF] Curry | Beating the clock: corporate responses to rapid change in the PC industry[END_REF]. Consequently subcontracting capacities or competences have become common practices in the microelectronics business. "Companies need to be proactive for uncertainties of the market in a productive way" [START_REF] Helo | Managing agility and productivity in the electronics industry[END_REF]. The general axes of competitiveness are time-based competition, increasing product variety and new technologies. These problems will be illustrated and addressed in the framework of the cost constraint optimisations, within the microelectronic design field. Based on PhD collaboration with System Plus Company, a software developer for electronic product cost or price evaluation, a method will be proposed and analysed for industrial deployment.

Microelectronic field context

The keystone of the global approach is to determine the basic elements on which decision-making tools can be built. Moreover, the actor's knowledge background also has to be well understood. Designers have to face and solve economic problems without sufficient skills.

The first step of this work is the generation of a cost or price estimate model. System Plus is a company that develops and edits cost estimation software (costing) or sale price determination (pricing) in the microelectronics field. Four software solutions were developed and/or sold, which answer various aspects of the costing or pricing targets from the silicon wafer (microchips production) to the finished products (electronic boards or cell phones). The description of a generic economic model used to determine the product industrial value is the goal of the PhD project carried out in collaboration between this company and the IRCCyN laboratory.

The experiment of microelectronic parts, and more precisely the integrated circuits and the electronic boards, were highlighted by the development of software dedicated to these elements. Due to historical independent developments, the expert's knowledge is hidden within the heart of these applications. Moreover, each structure, cost models and specific concepts are independent and not fully documented. To guarantee their reliability, they were specified and tested by experts from the technological field and experts in data processing. As a result, major work is necessary, dealing with the software knowledge extraction, analysis and formalisation to transcribe the infrastructure (basic elements) of each solution and check coherency and consistency [START_REF] Du Preez | Customised high-value document generation[END_REF].

Obviously, this approach cannot be compared to the accounting method where the principal concern is the total result of the company. Here, the designer has to create a realisable (feasible) product and meet all the technical specifications and constraints. Design is "the creative activity which consists in working out a project, or a part of the elements that compose it, on the basis of the expressed needs and means existing and technological possibilities with an aim of creating a product or a service" [START_REF] Gdt | Le Grand Dictionnaire Terminologique[END_REF].

All necessary information is available in order to establish a costing. But it remains to be able to put in accordance their objectives with the costs of the product during its design. The distribution of the data-gathering sites (departments, services, continents) is a key-point approached in several papers such as those by Michael Wahl, who has built a cost model based on information (Wahl et al., 2000a,b). charge of cost control

Statement: a new product life cycle management, new costing approaches

Manufacturing industries (having a great number of operating human resources) have gradually moved towards engineering industries (requiring more and more thinking resources). The distribution of the realisation costs of a product (direct and indirect costs) have moved in parallel, being reversed compared to the economic model of the last few years. One of the principal reasons comes from the fact that studies delay are longer for a batch production with weak dimensions within a context where the environment tends towards short life cycles of product. Consequently, the methods (e.g. cost accounting or analogical approaches), developed when the distribution of the costs resulting primarily from direct costs are no longer relevant. Over the last few years there have been significant improvements on the level of concepts, methods and general approaches of cost determination of a manufactured product. It proves that the methods which emerged from it, have not yet reached a sufficient level of maturity [START_REF] Berliner | Cost Management for Today's Advanced Manufacturing, the CAM-I Conceptual Design[END_REF]. Problems persist, such as implementation steps that are very little specified and global, and that are not able to provide relevant solutions. None of these approaches propose a deployment methodology of already well established and well controlled (e.g. allowing the extraction of cost drivers).

Result: a lack of tools for cost estimation dedicated to engineering

In the preliminary phases of the product life cycle, the cost control is a major performance criterion of a firm's competitiveness. Consequently, the cost (and the cost management throughout the product and process life cycle) is as crucial and dominant as the technical requirements defined in the phase of product specifications (Mevellec and Lebas, 1998). The appropriate tools that the engineers require to assist them in the integration of these economic aspects during the design phase are hard to find. From now on, the control of the costs is the indispensable condition of success, since the technical decisions made in phase of design engage on average more than 70% or even 80% of the final cost of the product according to the type of production [START_REF] Perrin | Cohérence, pertinence et évaluation économique des activités de conception[END_REF]. We should define a methodology of specification management which corresponds only to the technical specifications and other elements defined in the schedule of conditions of the product to support the cost estimation of the design alternative solutions under consideration by the designer.

Costing approaches

Cost estimation methods

This paper does not aim to describe in detail the methods of cost calculation or of cost estimation, so only a short review of the three main and most used approaches is presented.

• the analogical methods are based on the experiment of similar projects/products/functions already developed

• the parametric methods incorporate cost information relevant to the functions of the products

• the analytical methods detailed by part and by operation the cost of the products/process.

Necessary measurements

These various methods impact differently the various stages of the project life cycle and thus have applications dependent very largely on the maturity of design/industrialisation of the concerned product.

In addition, the choices made at the initial stages of the project impose technical solutions in terms of materials, realisation means, solution architectures, etc.

It is obvious that any modification will become increasingly expensive during the progress of the project. The project collaborators track the errors as soon as possible and collaborative working methods try to reduce to the maximum these risks of errors. For each identified error, an indicator of the cost solutions is evaluated in order to see the respect of the global required for the project.

Methods of cost management during the design

Methods of cost management for controlling the design by performance and cost objectives ('Conception à coûts objectifs' (CCO), Design-to-X, etc.) were set.

The Design-To-Cost (DTC): the DTC is thus defined by E.B. Dean:

"Design-to-cost is a method of controlling costs by establishing cost goals at specified levels of a work breakdown structure and then requiring the project to make trades which will ensure that the system built will meet those cost goals.

In design-to-cost, the cost goals are added to the existing requirement set to form an augmented requirement set" [START_REF] Dean | The design-to-cost manifold[END_REF].

'CCO': as the Value Analysis, The expression DTC was first coined in the USA.

The CCO is a French method making it possible to design a product while imposing at first a ceiling cost [START_REF] Delafollie | Analyse de la Valeur[END_REF]. Another more precise definition can be evoked. The 'CCO' can be defined as "a principle of action aiming at establishing rigorous objectives as of the stage of system development and at authorizing cost/performance compromises to allow the respect of these objectives" [START_REF] Petitdemange | La maîtrise de la valeur -La gestion de projet et l'ingénierie simultanée[END_REF].

The standard X 50-150 defines the CCO as a method of project management based on:

• the assignment of an objective ceiling price or cost (predetermined and fixed independently of all references to costs of a technical solution)

• specific procedures and arbitration rules defined at the beginning of the project by the organisation

• the identification and the description of the user's need in open and negotiable form (e.g. the schedule of conditions).

The CCO also called 'Conception pour un Coût Global' (CCG) is a methodological tool which makes it possible to reach industrial competitiveness by the control of the value.

Target costing: the target costing is applied within the framework of a production control mode in Just-In-Time (JIT). In the field of accountancy, the target cost is the cost objective defined by taking into account the market rates and the market conditions. This objective is equal to the difference between the selling price likely to ensure a certain market share and the desirable margin [START_REF] Gdt | Le Grand Dictionnaire Terminologique[END_REF]. It is a cost obtained by withdrawing the desired result of a sales turnover based on an evaluation of the contract prices and production volumes engineering and marketing. The objective cost is not based on the initial cost of the product but rather on the cost which it will reach when at cruising speed [START_REF] Ansari | The CAM-I Target Cost Core Group[END_REF].

Based on four different software application models, we want to concentrate the knowledge they used to process to develop only one model for cost estimation of microelectronic products and/or systems.

Activity-Based Costing (ABC)/Activity-Based Management (ABM) is a cost management method developed by Cooper and Kaplan at the beginning of the 1990s. In the ABC system, accountants work to allocate the cost of each activity (such as purchasing, production, engineering and so on) to the cost object that induces the activity. According to proponents, ABC has two objectives: to provide detailed information that describes the cost and consumption of activities owning to the organisation, and to provide accurate information to managers to improve their decisions (ABM) [START_REF] Sheu | Integrating ABC and TOC for better manufacturing decision making[END_REF].

Theory of Constaints (TOC)/Throughput accounting is based on Goldratt's idea that the main constraints in organisations are often not physical ones but policy constraints. TOC manages three operational performance measures that are throughput, inventory and operating expenses. The focus of TOC is then to maximise throughput while decreasing inventory and operating expenses. The throughput accounting is referred to as the accounting system proposed by TOC, it is seen as the opposite of conventional accounting and ABC [START_REF] Sheu | Integrating ABC and TOC for better manufacturing decision making[END_REF]. TOC could give indicators to decide what the product mix will be (what to produce and how much) or to decide outsourcing [START_REF] Hilmola | Theory of constraints and outsourcing decisions[END_REF]. Sheu et al. show how to use these two last methods to take the decision to make or buy a product. It seems that these approaches can be applied to routine design. Moreover Hilmola emphasises that Throughput accounting can be applied to the evaluation process of new product alternatives [START_REF] Hilmola | Enhancing system-wide profitability with new product introduction and throughput accounting[END_REF].

Steps of unified meta-model/concept construction

A specific approach for creating knowledge-based engineering project is has been developed by our research team and illustrated in Figure 1 [START_REF] Candlot | Réflexion sur une approche systématique pour créer des structures de consolidation de l'information[END_REF]. This figure represents the steps of implementation, formalised in our methodology for the construction of models. This is a three-phased methodology:

• First of all, the fundamental elements of the structure must be identified.

This corresponds to the Infrastructure Definition Phase (identification, extraction, structuring and formalisation).

• Relationships between these elements are then identified, and the elements are deployed in a coherent manner to optimise their efficiency. This is the Architecture Phase (refinement, development, diffusion, maintenance).

• The third phase is a software specification generation by a validated knowledge-based application.

Infrastructure

The goal for defining the infrastructure in the development of applications is to identify the elements (concepts) which make up the application and to define them in terms of attributes, methods and relations between these elements. This definition is summarised by the following stages: Identification: the stage of identification consists in specifying the problem which is posed in order to fix the limits of the applicability, to locate all the concepts handled in this field: key words, knowledge, activities, tasks, constraints, reasoning, etc. It also aims at surrounding and justifying the applications to be set up in terms of deliverable, times, resources to be affected and costs. In other words, this stage enables us to identify the basic elements which will be used to build infrastructure blocks of the application field.

Extraction: the extraction consists in counting the concepts identified in the preceding stage. These concepts being little or badly, not defined, this stage aims at enlightening them, at identifying existing associations between them in order to make sure that all the concepts necessary for the construction of the application are defined. It also aims at specifying the activities in which they get involved.

After the stage of finished structuring the infrastructure of our application field is defined.

Structuring: the structuring focuses on semantically organising the infrastructure of the field. It resides in grouping together the various concepts according to points of view. The latter can be of a functional, geometrical and structural nature. This organisation enables on the one hand a formalisation of the processes, and on the other hand, the construction of an expert reference frame and a reference frame of the field.

The structuring will also relate to the representation of these concepts which can be either textual as certain methods of knowledge management allow it or graph as is the case of Methodology for Knowledge System Management (MKSM) methods.

Formalisation: the goal of the formalisation stage is to syntactically represent the semantic concepts using a standard formalism such as for example, UML, the Petri nets, the logic, etc. It is also composed of data models and sequence diagrams. A semantic and syntaxic systematic questioning is carried out: What does this concept means? Are there similar words or concepts? All this work defines the architecture of the field. This becomes the infrastructure of the final application software.

Architecture

The definition of the application architecture consists in defining how the blocks that compose the infrastructure are articulated and associated between them. This step is illustrated by the following stages:

Refinement: the refinement aims to preserve only the most essential, relevant concepts in comparison with the problem which is posed. During this stage, it is necessary to identify the key concepts which must be shared by all the actors in collaboration. This phase is thus dedicated to the evaluation of the relevance of the concepts and their relationships.

Development specifications: the purpose of this stage is to implement the structures defined in the preceding stages in a computer application. For instance, this implies the translation of the structures in terms of classes and attributes in a computer language. It is also a question of defining the various interfaces of the application and of developing servers of knowledge and procedures of decision-making aids.

Diffusion: the diffusion consists in putting the application at the disposal of the end-user in order to test it. It will be done by an installation of the application on all the stations of the company, by the organisation of training courses and by the installation of a follow-up for the users. A forum of discussion on its starting can also be created.

Maintenance: the last stage of the step aims to define procedures to be put in action to ensure the maintenance of the information inheritances and to evaluate the relevance of the application through experiment feedback on its use by the personnel of the company. This implies the identification of the strong points as well as weak points of the application. The stage of maintenance must also solve the problems of update and the changes of the original specifications.

6 Our case

Industrial tools background

Let us first picture the background of the study. The four software applications developed by System Plus Company, synthesised in Table 1.

• Virtual IC Fab: is based on the simulation of a wafer fabrication plant in order to calculate its costs and its selling price. This software enables the creation of data bases to simulate a clean room. Its principal characteristics are: to be dedicated to the manufacture of wafers and the associated products (integrated circuits), supported by three key-fields in a company which are the knowledge of the production, the system of purchase and the design of the circuits. It carries out a simulation of the outputs and cost variations according to the parameter time, simulations of production costs calculations of the IC, simulations of the selling price according to market fluctuations and creates a virtual wafer fabrication plant and calculates the wafer cost from real data. Moreover, a simulation on several levels of precision is feasible; it depends on the detail level of available information.

• IC purchaser: is a tool for costs and selling price estimation dedicated to integrated circuits. The cost calculations use parametric models extracted from analytical expertise. The passage from the cost to the selling prices is also based on parametric models. Thus, it has cost parameter generators, for example, for the generation of manufacture technology like Wafers, for cases generation.

The database contains the following descriptive elements: technologies of wafer manufacture, encapsulation cases, wafer fabrication plants and component makers. The calculations carried out make it possible the construction of the manufacturing costs and to have an estimate of the selling price.

• SysCost: aims to precisely and rapidly quantify the production cost of an electronic system (compound of complete boards or subsystems), to evaluate and control the costs of a project and to carry out a precise estimate.

• WaCoFo: is used to analyse and predict production costs of semiconductor technologies. It calculates a wafer cost over one defined period, based on the modelling of the manufacturing unit (fabunit, workshop, workcentre description). In order to harmonise all this software under in a unique nutshell, we have tried to tackle this problem with the definition of a global model. It takes into account all the concepts and rules that are used in the existing software applications. Moreover, a method for the conceptual design stage has been developed in order to use the production costs models. This design, the dynamic use of the future tool based on the experience, a methodology implementing expert knowledge at production and design level is presented mixing cased based and rule-based reasoning [START_REF] Rehman | A methodology for modelling manufacturing costs at conceptual design[END_REF]. Moreover, the studies undertaken in the field of the foundry can enrich the development step of the cost estimate model [START_REF] Delplace | L'Ingénierie numérique pour l'amélioration des processus décisionnels et opérationnels en fonderie[END_REF][START_REF] Perry | Costs models in design and manufacturing of sand casting products[END_REF].

Meta-model identification phases

The first stage of the implemented methodology consists in the extraction of the cost estimate models from the tools. Then an abstraction phase leads to the construction of a meta-model common to the various solutions suggested by the company System Plus.

The last phase consists in reinforcing the semantics contained in the meta-model to extend the application fields.

The first methodological phase deals with the infrastructure modelling of System Plus applications; they integrate the very first constraints that were specified by the customer needs (first specification of the tools) and new concepts and models (each specific application makes integrating models whose aims vary from the original) (see Table 2 andFigure 2): • cost calculation models configured within the software are parametric models or analytical models

• models of production flows take into account different degrees of complexity

• different scales of product (of the electronic chart to the chip)

• multi or mono products sites. Thus the field infrastructure consists of all the calculation methods contained in the software solutions and the attributes of the products in their context. Their formalisation and their refinement make it possible to obtain the architecture of a more homogeneous and more complete cost model (see Figure 3). The concepts of activity and process, entity and paper, resources (material and human) and of course cost and selling price are a representative panel of the main extracted concepts. This list is not exhaustive. An interaction exists between the industrial concepts and the prospective scientific tools. Various scientific research projects are concerned with the set of themes implemented here such as the management of production and management control [START_REF] Mevellec | Managing Simultaneously Cost and Value: The Challenge; The Role of Management Accounting in Creating Value[END_REF]Mevellec and Lebas, 1998). In addition, it appears that concepts are employed in several tools without being directly definable. The expert language masks the real semantics of the concepts. It is important to ensure coherence between the latter (as well as the models which represent them) mainly on the aspects of covering the fields, constraints and contexts. It is essential to represent the bonds between the concepts. With this purpose, two aspects have to be approached:

• a static approach (e.g. the concept definition and bond formalisation by a class diagram)

• a dynamic approach (e.g. the use of the concepts through a sequence diagram or a SADT diagram).

The integration phase gives concrete expression to all the models and the concepts including the different tools published by System Plus. It makes it possible to confront the various partial approaches (realised by using a class diagram). It is also necessary to take into account the processes of usage of these concepts and the calculation methods in the System Plus tools (such as, e.g. a SADT diagram identifying the specific needs with each considered stage of the project life cycle). At this level a first methodological approach of deployment and use of the tool is formalised.

Meta-models consolidation phases

In the second phase, the architectural development relies on a semantic analysis that enriches and consolidates the meta-model so as to make it independent of a particular industrial sector. In addition, the methodological step of suggested use is reexamined and enriched to be independent of a specific application (see Figure 4). The definition of a common ontology with [START_REF] Protégé | Ontology Editor and Knowledge-Base Framework[END_REF] will try to ensure coherency and exhaustiveness.

An experiment feedback with the different concepts identification, their global coherency check using ontology and a confrontation with other industrial branches should make it possible to test the robustness of this approach. Interpretations of the final model are preconditioned by the fact that various methods and software tools have already been developed. However, they do not presuppose the final development that remains to be defined. Thus, all the model developments are carried out in interaction with the modelling of these various applications. The implementation of the Architecture is thus closely related to the maturity of the comprehension of the Infrastructure. This becomes the final specification structure and rules for the new costing/pricing software to be developed (Table 3).

Conclusion and outlines

The final model has not yet been attained, but partial area coherency and enrichment have been achieved. A major difficulty is the different initial objects used, without clear definition. Depending on the presence or not of the software developer, the exact 'spirit' of the object can be defined. Moreover, some documented elements (object attributes or calculation rules) do not correspond exactly to the real use or application of the software. The first specifications (when they exist) have been adapted but with no specification modification traceability.

The steps presented in this paper have a double objective:

• To structure the models and the concepts handled by the various tools developed by the System Plus Company, for cost as well as data-processing development.

• To structure the meta-model for cost estimate of industrial products independently of its industrial branch. As this study was begun after the development of the software applications supporting these problems, it benefits from this first generalisation. The suggested methodological step, already tested, guides the construction of the implemented thesis postulate.

The prospects for this work relate to two-fold. On one hand, to continue to confront the general methodology proposed for knowledge-based projects specification with a real case, and improving it if necessary or judging its robustness. In addition, to apply this general approach of modelling recommended in this work to various industrial sectors, identifying any shortcomings and consolidating the generic approach. For the method evaluation, the definition of indicators and their measurement remain to be done. This can take place only by the identification of partners and real applications.

Figure 1

 1 Figure 1 Loop cycle of the integration step

Figure 3

 3 Figure 3 Example of an infrastructure definition of SysCost (see online version for colours)

Figure 4

 4 Figure 4 Example of refinement with the notion of entity in SysCost enriched with the WaCoFo attributes

Table 1

 1 Enters and outputs of the SysCost tool

	Inputs

Table 2

 2 Studied software application characteristics Typology examples: left WaCoFo -right SysCost

		Virtual IC Fab	IC purchaser	SysCost	WaCoFo
	Application	Semi-conductor	Semi-conductor	Electronic	Semi-conductor
	field			board
	Cost method	Analytic	Parametric	Analytic	Analytic
	Product scale	Micro	Micro and multi Macro	Micro
	Enterprise	Multiproducts	Mono-product	Mono-product	Multiproducts
	Flow structure	Complex	Complex	Linear	Complex
	Figure 2

Table 3

 3 Possible and used tools or for each phase

		Phase	Tools
	Infrastructure	1 Identification	Software applications analysis
		2 Extraction	Scientific community
		3 Structuring	Microsoft Office
		4 Formalisation	UML
	Architecture	5 Refinement	Objecteering (UML editor)
		6 Specification	Not defined
		7 Diffusion	Not defined
		8 Maintenance	Not defined

Acknowledgements

The authors would like to thank System Plus partners, who initiated this work, and the French National ANRT association that supports the cross research collaboration between industry and laboratories.


François-Xavier Coudert
email: fx.coudert@chimieparistech.psl.eu

Guillaume Fraux

Siwar Chibani

Modelling of framework materials at multiple scales: current practices and open questions

Keywords: molecular simulation, modelling, framework materials, machine learning, databases

The last decade has seen an explosion of the family of framework materials and their study, both from the experimental and computational point of view. We propose here a short highlight of the current state of methodologies for modelling framework materials at multiple scales, putting together a brief review of new methods and recent endeavours in this area, as well as outlining some of the open challenges in this field. We will detail advances in atomistic simulation methods, the development of materials databases, and the growing use of machine learning for properties prediction.

. . . . . . . . .

Introduction

Nanoporous materials with high specific surface area are extensively used in a wide range of applications, including catalysis, ion exchange, gas storage, gas or liquid separations, sensing and detection, electronics, and drug delivery. The last 15 years have seen the emergence of entire new classes of crystalline nanoporous materials, based on weaker bonds (coordination bonds, π-π stacking, hydrogen bonds, . . . ). The most studied of these new materials are the metal-organic frameworks (MOFs): these nanoporous hybrid organic-inorganic materials, built from metal centers interconnected by organic linkers, have been the subject of an intensive research effort since the pioneering work done by R. Robson in the 90s, with thousands of structures synthesized. Other classes of crystalline nanoporous materials that have emerged in the past decade include covalent organic frameworks, porous molecular organic solids, and other porous molecular framework materials. for a single material, which describe the potential energy surface of the system with high accuracy, but are not transferable to other materials; (ii) generic force fields, whose analytically expressions and parameters are transferable among a large class of material, but that poorly reproduce physical properties. The second approach has been widely used, by relying on generic force-fields such as AMBER [START_REF] Cornell | A second generation force field for the simulation of proteins, nucleic acids, and organic molecules[END_REF] or UFF [START_REF] Rappe | Uff, a full periodic table force field for molecular mechanics and molecular dynamics simulations[END_REF] -possibly with adjustments or extensions -to get a consistent treatment of all frameworks, and therefore to compare different materials when searching the best candidate for a given application in high-throughput studies. [START_REF] Greathouse | Computational screening of metal-organic frameworks for large-molecule chemical sensing[END_REF][START_REF] Ryan | Computational screening of metal-organic frameworks for xenon/krypton separation[END_REF][START_REF] Colón | High-throughput computational screening of metal-organic frameworks[END_REF] One problem arising from this approach is that these force-fields might not contain adequate terms to describe the delicate balance of intraand intermolecular interactions in framework materials. In particular, one can think of the metal coordination bonds, π-π stacking and other soft intermolecular interactions. On the other hand, deriving new force-fields for a specific systems, while useful to investigate the behavior of a given material thanks to higher accuracy of the potential energy surface, fails to allow for comparisons with other systems and is not suitable for large-scale screening.

Another choice of methodology is to use an ab initio description of the interactions in the system, where a quantum chemistry method is used at every time step of the MD simulationthis approach is also called first-principles molecular dynamics (FPMD). This has a much higher computational cost, and thus limits the length and time scales that can be reached, but does not make any assumption on the nature of the interactions. This was used by Chaplais et al. [START_REF] Chaplais | Impacts of the imidazolate linker substitution (CH3, cl or br) on the structural and adsorptive properties of ZIF-8[END_REF] to describe how the adsorbed phase arranges inside a fully flexible ZIF-8, without needing to create a classical force field that would be able to reproduce the full flexibility of ZIF-8. Furthermore, FPMD allows the description of bond breaking and formation, which can be crucial in some dynamic phenomena: as an example, Howe et al. [START_REF] Howe | Understanding structure, metal distribution, and water adsorption in mixed-metal MOF-74[END_REF] used it to analyze the stability of MOFs in presence of water.

We note that the question of the "level of description" applied to the systems (quantum chemistry vs empirical potentials) is relevant not only to molecular dynamics, but also for Monte Carlo simulations, which stochastically generates representative configurations of the system in a given thermodynamic ensemble, by application of random moves weighted by the appropriate Boltzmann probabilities. However, while ab initio Monte Carlo simulations are possible, the large number of energy evaluations necessary make them relatively rare in the literature. [START_REF] Mcgrath | Isobaric-isothermal monte carlo simulations from first principles: Application to liquid water at ambient conditions[END_REF][START_REF] Leiding | An efficient approach to ab initio monte carlo simulation[END_REF] In the context of framework materials, Monte Carlo simulations are used at various scales. First, simulated annealing and biased Monte Carlo simulations are extensively used in the areas of structure solution and to localization of extra-framework ions and adsorbed species. [START_REF] Falcioni | A biased monte carlo scheme for zeolite structure solution[END_REF][START_REF] Maurin | Combining the monte carlo technique with29si nmr spectroscopy: Simulations of cation locations in zeolites with various si/al ratios[END_REF] Secondly, Grand Canonical Monte Carlo is very often used to describe the thermodynamics of adsorption of fluids and fluid mixtures in nanoporous frameworks. [START_REF] Coudert | Computational characterization and prediction of metal-organic framework properties[END_REF] Finally, mesoscale Monte Carlo modelling methods can be used to assess the large-scale ordering (or disorder) in supramolecular frameworks, based on carefully constructed Hamiltonians that describe the local interactions. [START_REF] Paddison | Spin correlations in Ca 3 Co 2 O 6 : Polarized-neutron diffraction and monte carlo study[END_REF][START_REF] Sapnik | Compositional inhomogeneity and tuneable thermal expansion in mixed-metal zif-8 analogues[END_REF][START_REF] Cairns | Encoding complexity within supramolecular analogues of frustrated magnets[END_REF] (b) Make force fields great again Despite the rather strong limitations of force fields described above for their application to framework materials, there have been several recent developments in that area, which we want to highlight here. Deriving a new force-field for a material is a hard and long task, where one need not only to gather or generate reference data, but adapt parameters and check every time that the physical properties predicted by the force-field are right. In the past few years, novel methodologies for force field fitting have been proposed, relying on machine learning algorithms. They aim to make the process more automatic, more reproducible, and also reduce its reliance on human input. Starting from the structure optimized with ab initio calculations and the Hessian at this energy minimum, a machine-learning procedure (for example a genetic algorithm coupled with a least-squares minimization) find the optimal set of parameters matching the structure and the Hessian. Some implementations of this idea are the MOF-FF [START_REF] Bureekaew | MOF-FFa flexible first-principles derived force field for metal-organic frameworks[END_REF] and QuickFF [START_REF] Vanduyfhuys | QuickFF: A program for a quick and easy derivation of force fields for metal-organic frameworks fromab initioinput[END_REF] force-fieldsor maybe more accurately, force field optimization methodologies. While they use slightly different input data and fitting procedures, they share the common goal of parameterizing force fields in a systematic and consistent fashion, from first principles reference data.

f f f f f f X 1 w 1 11 α w 2 11 w 3 11 w 1 13 Y 1 Y 2 X 2 X 3 f f w 1 12 Figure 1.
A representation of a neural network mapping from X i to Y j using three layers. Circles represent neurons using f as the activation function, and lines are adjustable weights w α ij for the input values. In this case, the output of the neuron α would be f ( i w 1 i1 X i ).

To give an example of the use of these new force field methodologies, MOF-FF was recently used to predict the most stable structure and topology for copper paddle-wheel MOFs depending on the linker. [START_REF] Impeng | Computational structure prediction of (4, 4)-connected copper paddle-wheel-based MOFs: Influence of ligand functionalization on the topological preference[END_REF] The authors generated all the structure by combining simple building blocks (linkers and copper paddle-wheel) with different topologies, and where then able to use the same forcefield to optimize and study them all. Finally, we note that these methods were originally developed by relying on reference data gathered on (finite) clusters representative of the MOF structures, and were later extended to periodic input data. The use of periodic structures as a reference was shown to be essential for a correct description of structural, vibrational and thermodynamic properties of soft framework materials like MIL-53(Al) by QuickFF. [START_REF] Vanduyfhuys | Extension of the quickff force field protocol for an improved accuracy of structural, vibrational, mechanical and thermal properties of metal-organic frameworks[END_REF] Despite this progress, classical force-fields remain fundamentally limited by the analytical form they choose to represent interactions, even when parameterized in an optimal fashion. For example, a force-field using a Lennard-Jones dispersion potential will be unable to reproduce any long-range interaction that does not follow this functional form. A promising alternative, in order to be able to reproduce any possible interaction profile coming from the reference data (i.e., quantum chemistry calculations), is the use of neural-networks force-field. Neural networks are algorithms that map a set of input values to a set of output values by associating adjustable weights with each value, and then using a non-linear function (called the activation function) to map the weighted inputs to the outputs. If the outputs are then fed to another neural network, the resulting network is said to have multiple layers -see Fig. 1 for a graphical representation with three layers. One property of neural networks is their ability to reproduce arbitrary multidimensional R n → R m functions with arbitrary accuracy [START_REF] Hornik | Multilayer feedforward networks are universal approximators[END_REF]. This makes them very appealing to reproduce energy or forces from ab initio calculations, using only the atomic position as input -effectively functioning like a force-field, without any assumptions on the nature of the interactions. Before being usable, the network must be "trained" with data representative of the system of interest. During this training, the weights are adapted to ensure a correct mapping from the input (the atomic positions) to the output (forces and energy). Using atomic positions in Cartesian coordinates as the input is not optimal, as the generated network will only be usable with the exact same system used for training. An alternative is to rely solely on the local environment of an atom up to a cutoff distance, represented in a translation and rotation-independent manner. [START_REF] Behler | Generalized neural-network representation of high-dimensional potential-energy surfaces[END_REF] Neural network force-field are a very promising approach to cheap simulation with high accuracy, and they are already used for small organic molecules [START_REF] Smith | ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost[END_REF], water [START_REF] Cho | A polarizable force field for water using an artificial neural network[END_REF][START_REF] Morawietz | A density-functional theory-based neural network potential for water clusters including van der waals corrections[END_REF]; as well as classical dense crystalline materials [START_REF] Hellström | Neural network potentials in materials modeling[END_REF] , and amorphous inorganic materials. [START_REF] Deringer | Machine learning based interatomic potential for amorphous carbon[END_REF][START_REF] Deringer | Realistic atomistic structure of amorphous silicon from machine-learningdriven molecular dynamics[END_REF] They are especially helpful with amorphous materials such as silicon or glasses, where the usual classical potential are complex multi-body potentials. This approach still remains to be extended to porous frameworks materials.

(c) Simulating complex systems

One of the biggest current challenges in the simulation of framework materials lies in the complexity of these systems. The computational cost of our tools imposes limits on the systems we can model, both in terms of length scale (and thus number of atoms) and time scales. For crystalline phases, the use of periodic boundary conditions, where the simulated system is repeated in all spatial dimensions, is a very effective way to describe infinite systems within computers with limited memory and CPUs. However this approach falls short when we want to study phenomena involving large correlation lengths, such as dynamic properties of soft materials. Another difficult area is the computational modelling of disordered phases, where a very large simulation box would be necessary to correctly describe the system. Yet, within the field of framework materials, such disordered systems are attracting a lot of interest due to their properties that differ from their crystalline counterparts. We can here cite as examples systems such as MOF glasses [START_REF] Bennett | Melt-quenched glasses of metal-organic frameworks[END_REF][START_REF] Zhao | Nanoporous transparent mof glasses with accessible internal surface[END_REF][START_REF] Zhou | Metal-organic framework glasses with permanent accessible porosity[END_REF] and liquids, [START_REF] Gaillac | Liquid metal-organic frameworks[END_REF] or framework materials with defects and correlated disorder. [START_REF] Cheetham | Defects and disorder in metal organic frameworks[END_REF] There is thus an important drive to model these materials, because of their properties (e.g., amorphous phases can have more appealing mechanical and optical properties than crystals) or because catalysis, nucleation, or adsorption can occur preferentially around defects. A strategy that can be used in this case -if the brute force approach of using a very large simulation box is not feasible -is to use multiple realizations (or "copies") of the system of interest, and average the measured properties over those replicas. This approach has been extensively used in the past for the study of amorphous systems such as silica glasses or disordered carbons. For example, Van Ginhoven et al. [START_REF] Ginhoven | Silica glass structure generation forab initiocalculations using small samples of amorphous silica[END_REF] used DFT calculations on 18 different configurations of silica glass created using a classical force-field, and were thus able to obtain a good statistical representation of static and dynamic properties with comparable or better accuracy than a longer, bigger simulation (see Fig. 2).

Another strategy to study large-scale systems is to change the level of description, moving closer to mesoscopic methods and using coarse-grained force fields instead of atomistic ones. Dürholt et al. [START_REF] Dürholt | Coarse graining of force fields for metal-organic frameworks[END_REF] have generated such a coarse-grained force field for the HKUST-1 MOF, based on copper paddle-wheels. These authors showed that even a very coarse model is able to reproduce the low energy deformations of the system, with only one coarse-grained bead for 30 atoms. Another mesoscopic approach, in the field of adsorption, is the use of Lattice Boltzmann methods to describe the coupling between fluid flow and adsorption in porous media with complex geometries. Beyond this scale, it can also be useful to turn to macroscopic modelling methods to simulate even larger systems. Indeed, many potential applications of framework materials are based on their use not as single crystals, but are expect to construct nanostructured or composite systems: common examples include monoliths, supported thin films, and mixed-matrix membranes. In order to describe these composite systems, one has to turn to conventional microscopic modelling methods: finite elements for solid mechanics, computational fluid dynamics to describe transport, etc. In this vein, Evans et al. [START_REF] Evans | Macroscopic simulation of deformation in soft microporous composites[END_REF] used a macroscopic description and finite element methods to compute deformation properties of mixed-matrix membrane and other composite of framework materials and polymers. The use of finite element methods allowed them to study sizes up to 400 µm, which is five orders of magnitude bigger than typical atomistic simulations.

Finally, we note that while we are starting to see new techniques and methods that go from one level of description to the next (quantum to classical, micro to meso, meso to macro), the bridging of those various scales of simulations into a coherent multi-scale simulation methodology is still a widely open research question. How can one use data from ab initio simulation to fit atomistic classical force-field? [START_REF] Bureekaew | MOF-FFa flexible first-principles derived force field for metal-organic frameworks[END_REF][START_REF] Vanduyfhuys | Ab initio parametrized force field for the flexible metal-organic framework mil-53[END_REF] Or leverage force-field-based data to create a coarse-grained model? [START_REF] Dürholt | Coarse graining of force fields for metal-organic frameworks[END_REF] Or transfer microscopic properties into input for a finite element methods? [START_REF] Evans | Macroscopic simulation of deformation in soft microporous composites[END_REF][START_REF] Coudert | Adsorption deformation of microporous composites[END_REF] Every time we go up a level of description, we are able to work with bigger systems at longer timescales, at the cost of some accuracy and precision, but we still lack a systematic way to create and validate these novel models for performance and accuracy.

(d) Describing excited states

We note here that a particularly challenging area of the modelling of framework materials is that of the description of their excited states, in order to better understand, e.g., their optical properties and photocatalytic activity. Such phenomena involve transitions between the system's ground state and another state of higher energy (the excited state) upon photon absorption or emission. The energy difference involved in the electronic transitions is directly related to the position of absorption and emission bands. Theoretical models can give insight into the properties of electronically excited states, and are therefore a useful complement to experimental measurements. In that framework, Density Functional Theory (DFT), and more precisely its time-dependent form (TD-DFT) [START_REF] Runge | Density-functional theory for time-dependent systems[END_REF][START_REF] Casida Me | Time-dependent density functional response theory for molecules[END_REF] is the ab initio method of choice for most of the cases, [START_REF] Wilbraham | Modelling photophysical properties of metal-organic frameworks: a density functional theory based approach[END_REF][START_REF] Wu | Cerium metal-organic framework for photocatalysis[END_REF] as it may treat structures containing up to ca. 300 atoms. To study framework materials, Wilbraham et al. have developed a computational protocol in order to simulate the optical signatures of two MOF structures based on the 4,4 -bis((3,5dimethyl-1H-pyrazol-4-yl)methyl)-biphenyl (H 2 DMPMB) linker. The developed protocol was successfully applied to characterize and to rationalize the adsorption and the emission behavior on the interchange of zinc and cadmium as metal cation. [START_REF] Wilbraham | Modelling photophysical properties of metal-organic frameworks: a density functional theory based approach[END_REF] Another important optical properties in hybrid materials is the nature of the electronic excitations that could present ligand-to-metal charge transfer (LMCT) character. Very recently, Wu et al. showed that from different cations, electronic excitations occur in the linker of the UiO-66(Ce) MOF upon light absorption. These authors showed that incorporation of the cerium cation presents an effective way not only to stabilize the LMCT, but also to increase the photocatalytic activity of UiO-66 MOF. [START_REF] Wu | Cerium metal-organic framework for photocatalysis[END_REF] For applications in photocatalysis, the magnitude of the band gap and the absolute positions of the band edges are of high importance. [START_REF] Butler | Electronic chemical potentials of porous metal-organic frameworks[END_REF][START_REF] Grau-Crespo | Modelling a linker mix-and-match approach for controlling the optical excitation gaps and band alignment of zeolitic imidazolate frameworks[END_REF] As an example, based on the mixing of organic linkers, Ricardo et al. have designed new ZIF materials with a narrower band gaps in order to allow the absorption of the visible range solar spectrum. They showed that introducing a transition metal (copper) in the tetrahedral position of the mixed-linker ZIFs, it is possible to increase photo-adsorption. [START_REF] Grau-Crespo | Modelling a linker mix-and-match approach for controlling the optical excitation gaps and band alignment of zeolitic imidazolate frameworks[END_REF]

Materials databases

As stated in the introduction, the last decade has seen an important increase in the number of studies on various families of framework materials, with the goal of discovering or designing novel materials with targeted properties. Given the large number of materials synthesized, characterized and reported, three important series of questions arise:

(i) Where and how is stored the information on these materials? What is the available data? (ii) Under what form is it stored, how can it be queried, retrieved, and interpreted? That is, issues of Application Programming Interface (API), format, and interoperability. (iii) What is the extent of information and properties provided for each structure? How were they determined? Those are questions about the metadata associated with each structure.

In this section, we will briefly review the current state of the art and describe some of the existing materials databases for framework materials, contrasting the situation with that of inorganic materials.

(a) Zeolites

Let us start with the grandparent of this family of databases, namely the database of zeolites structures from the International Zeolite Association (IZA), which is a freely available on the internet at http://www.iza-structure.org/databases/. Most of the information it is also available in printed form, as the Atlas of zeolite framework types book. [START_REF] Baerlocher | Atlas of Zeolite Framework Types 6th Edition[END_REF] Zeolite belong to the class of nanoporous materials and are composed of oxygen, silicon and aluminium. They have widespread applications at the industrial level in the fields of catalysis, adsorption and separation. [START_REF] Speybroeck | Advances in theory and their application within the field of zeolite chemistry[END_REF][START_REF] Chapman | Radioactive iodine capture in silver-containing mordenites through nanoscale silver iodide formation[END_REF][START_REF] Bučko | Monomolecular cracking of propane over acidic chabazite: An ab initio molecular dynamics and transition path sampling study[END_REF][START_REF] Nenoff | Silver-mordenite for radiologic gas capture from complex streams: Dual catalytic CH3i decomposition and i confinement[END_REF] At the current date, the corresponding database provides structural information for 230 zeolite framework types reported experimentally, among which 67 are natural zeolites. Ten years ago, only 176 zeolite frameworks were known, showing that even among "conventional" porous materials, progress is steady and the synthesis of new zeolites remains a considerable challenge. The IZA database is heavily curated, as all the zeolitic structures it includes have been approved by the Structure Commission of the IZA, to verify that it is unique and that the structure has been satisfactorily proven. The nomenclature for these materials is recognized by IUPAC (the International Union of Pure and Applied Chemistry) and is assigned by a three letter code -such as FAU, for the faujasite framework, or MOR for the mordenite framework. Data associated with each framework type code includes crystallographic data: space group, cell parameters, positions of vertices in the idealized framework, but also topological density, ring size, channel dimensions, maximum diameter of an included sphere, accessible volume and composite building units. Moreover, going beyond idealized framework structure and topological properties, the database features detailed information for building models, and simulated powder diffraction patterns for representative materials, as well as all corresponding literature references.

At this stage, the reader unfamiliar with zeolites may be surprised that only 230 zeolitic structures have been identified experimentally. Indeed, at the molecular scale, zeolites are constituted of TO 4 tetrahedra (where typically T = Al or Si), connected by their corners. It is mathematically possible to create an infinite number of such four-connected nets that have threedimensional periodicity. The question of why only a few structures are experimentally realized, known as "zeolite feasibility", is still wide open. [START_REF] Bushuev | Feasibility of pure silica zeolites[END_REF][START_REF] Blatov | The zeolite conundrum: Why are there so many hypothetical zeolites and so few observed? a possible answer from the zeolite-type frameworks perceived as packings of tiles[END_REF] Nevertheless, researchers have used theoretical and computational tools to develop databases of hypothetical zeolitic structuresbased on four-connected nets, but usually with added constraints such as an upper bound on the lattice energy or topology. Compared to the experimental zeolites, the number of hypothetical zeolitic structures is much larger and rapidly growing. In the first such database published, by Li et al. [START_REF] Li | Design of zeolite frameworks with defined pore geometry through constrained assembly of atoms[END_REF][START_REF] Yu | Rational approaches toward the design and synthesis of zeolitic inorganic open-framework materials[END_REF][START_REF] Li | New stories of zeolite structures: Their descriptions, determinations, predictions, and evaluations[END_REF] and available at http://mezeopor.jlu.edu.cn/hypo/, two sets of hypothetical zeolite structures are provided. [START_REF] Li | New stories of zeolite structures: Their descriptions, determinations, predictions, and evaluations[END_REF][START_REF] Li | Synthesis of new zeolite structures[END_REF] The first set is generated by the FraGen algorithm, which is based on Monte Carlo direct space structure modeling. [START_REF] Li | FraGen: a computer program for real-space structure solution of extended inorganic frameworks[END_REF] The second set is composed of so-called ABC-6 structures, which are enumerated through a materials genome approach. [START_REF] Li | In silico prediction and screening of modular crystal structures via a high-throughput genomic approach[END_REF] The number of all the ABC-6 structures is 84 292. Besides their structures in CIF format, all hypothetical structures are assembled in an Excel spreadsheet listing their properties, such as stacking layers, stacking sequences, space groups, cell dimensions, channel openings, framework energies, framework densities, stacking compactness and the constituent cages. [START_REF] Li | New stories of zeolite structures: Their descriptions, determinations, predictions, and evaluations[END_REF] A second hypothetical zeolite structures database, available at http://www.hypotheticalzeolites. net, was generated by Treacy and Foster [START_REF] Treacy | Enumeration of periodic tetrahedral frameworks[END_REF][START_REF] Treacy | Enumeration of periodic tetrahedral frameworks. ii. polynodal graphs[END_REF]. It contains 5 millions of different frameworks, triaged into "bronze" and "silver" sets, depending on their feasibility based respectively on a specifically-designed cost function and force field energy minimization. The two sets contain 5 389 408 bronze and 1 270 921 silver structures, and have been used as starting point for a series of theoretical surveys of zeolitic frameworks [START_REF] Zwijnenburg | Absence of limitations on the framework density and pore size of high-silica zeolites[END_REF] and related four-connected frameworks. [START_REF] Zwijnenburg | An extensive theoretical survey of low-density allotropy in silicon[END_REF][START_REF] Zwijnenburg | Apparent scarcity of low-density polymorphs of inorganic solids[END_REF] Using Monte Carlo approach, Earl et al. have developed a systematic computational procedure to search through unit cells with different space group symmetries, [START_REF] Earl | Toward a database of hypothetical zeolite structures[END_REF] called the Symmetry-Constrained Intersite Bonding Search (SCIBS) approach. They have used it to generate a third database of 2.6 million zeolite-like materials that have topological, geometrical, and diffraction characteristics that are similar to those of known zeolites. Besides the aluminosilicate zeolites, open-framework aluminophosphates, or AlPOs, constitute an important class of microporous inorganic materials with a variety of structures ranging from neutral zeolites to anionic frameworks. The AlPO framework is not only limited to Al and Si as tetrahedral atoms, the upper limit of pore size can go beyond twelve-membered rings, and the primary building units are not restricted to tetrahedra. This gives the AlPO family a rich variety of structural architectures and physico-chemical properties. There is an AlPO database, available online at http://mezeopor.jlu.edu.cn/alpo/, developed by Y. Li, J. Yu and R. Xu. It contains over 200 experimental AlPO structures reported in the literature. [START_REF] Yu | Insight into the construction of open-framework aluminophosphates[END_REF] In addition to general information, such as formula, space group, cell parameters, and atomic coordinates, this database also includes more detailed structural information, such as coordination environment, Al/P ratio, stacking sequences for 2D structures and coordination sequences. Simulated XRD reflections and references are also included to aid the identification of users' samples.

(b) Metal-Organic Framework

Metal-organic frameworks appeared almost thirty years ago, and designate a class of materials composed of inorganic nodes linked by organic ligands. These materials are a novel generation of materials, with promising applications to follow zeolites in catalysis and adsorption-related applications. Since their discovery, the growth in number of MOFs structures number reported in the Cambridge Structural Database (CSD) has been staggering, as show on Fig. 3. The latter contains more than 900 000 structures of small molecule crystal structures and materials, among which 70 000 MOF materials can be found. Each crystal structure undergoes extensive validation and cross-checking by expert chemists and crystallographers to ensure that the database is maintained to the highest possible standards. Apart from X-ray, neutron diffraction analyses and 3D structure, every entry is enriched with bibliographic, chemical and physical information. Even though all published MOF structures are collected in the CSD, it is not easy to distinguish them from the rest of the structures in the CSD. In this vein, Watanabe et al. have extracted 30 000 extended MOFs compounds from the CSD, among which 1 163 MOF materials were applied for CO 2 /N 2 separation. [START_REF] Watanabe | Accelerating applications of metal-organic frameworks for gas adsorption and separation by computational screening of materials[END_REF] In 2013, Goldsmith et al. published an automated approach for screening 20 000 porous structures in the CSD useful for hydrogen storage. [START_REF] Goldsmith | Theoretical limits of hydrogen storage in metal-organic frameworks: Opportunities and trade-offs[END_REF] This requires the use of algorithms for virtual solvent removal, and relies on an established empirical correlation between excess hydrogen uptake and surface area.

In 2014, Chung et al. have developed a curated database of MOF structures, named "Computation-Ready Experimental MOFs" (CoRE MOF) database; it is available at https:// gregchung.github.io/CoRE-MOFs/. It contains over 6 000 three-dimensional MOFs, with solvents and templating agents cleaned, and with a pore limiting diameter (PLD) larger than 2.4 Å. [START_REF] Chung | Computation-ready, experimental metal-organic frameworks: A tool to enable high-throughput screening of nanoporous crystals[END_REF] The protocol used to generate the database, represented in figure 4, is the following: (i) identify and extract MOFs structures from CSD, based on atomic types and bonds present; (ii) remove solvents molecules and included templates; (iii) in some cases, remove disorder. Several recent studies have used this database as a starting point. [START_REF] Barthel | Distinguishing metal-organic frameworks[END_REF][START_REF] Park | Text mining metal-organic framework papers[END_REF] Additional computational data can also be added to the database, as did the Sholl group by computing and publishing point charges derived from periodic DFT calculations for more than 2 000 structures in the CoRE MOF database. [START_REF] Nazarian | A comprehensive set of high-quality point charges for simulations of metal-organic frameworks[END_REF] This allows for easier reuse by other research groups, as a starting point for adsorption calculations of polar molecules, for example.

Despite the importance of these CSD-derived databases, they are not integrated within the CSD, and thus require manual updates over time, as new entries are added to the CSD. To address this deficiency, Moghadam et al. have recently implemented seven criteria for MOFs embedded within a custom CSD Python Application Programming Interface (API) workflow. [START_REF] Moghadam | Development of a cambridge structural database subset: A collection of metal-organic frameworks for past, present, and future[END_REF] The constructed CSD MOF is currently integrated into the CCDC's (Cambridge Crystallographic Data Centre) structure search program ConQuest, which allows for tailored structural queries and visualization. CSD MOF thus presents the most complete collection of MOFs, and will stay synchronized with the CSD as time goes by. The authors have also developed an array of computational algorithms in order to remove the solvent molecules from the CSD MOF subset, and then to calculate the geometric and physical properties for all the structures in the database.

Finally, we should note here that some effort has also been devoted to design hypothetical MOFs structures. In this quest, Wilmer et al. have generated a database of 137 953 hypothetical MOFs structures from 102 different building blocks, containing secondary building units (SBU) and organic linkers. [START_REF] Wilmer | Large-scale screening of hypothetical metal-organic frameworks[END_REF] The authors then used this dabase as a starting point for computational screening, with the goal of identifying the best candidates for specific applications. This was applied for example to the cases of hydrogen storage, methane storage and adsorption/stability of water. [START_REF] Gomez | Screening of hypothetical metal-organic frameworks for h2 storage[END_REF][START_REF] He | Methane storage in metal-organic frameworks[END_REF][START_REF] Burtch | Water stability and adsorption in metal-organic frameworks[END_REF] However, once a computational screening approach has identified possible targets, the design of synthesis protocol for these hypothetical materials, as well as their feasibility, is still often a complex issue.

Machine learning for properties prediction

While the databases of structures, both experimentally determined and hypothetical, grow at a fast pace, the efforts to add physical and chemical properties of these materials in databases is happening on a longer timescale. The current theoretical chemistry methods, using microscopic (quantum chemistry and classical molecular modeling) and mesoscopic scales, make it possible to predict and understand the physical and chemical behaviour of given materials that already exist. However, these methods are computationally intensive, and their use on a very large scale is somewhat limited. Computational screening studies based on existing databases, as we have described below, are often limited to very simple descriptors of a materials' performance for a given application. They are often used in a multi-stage strategy, where filters of increasing complexity and computational cost are applied successfully. For example, in the case of adsorption, studies will focus first on pore space and accessible area (geometric descriptors), then identify among those best-performing candidates the ones suitable for adsorption based on Grand Canonical Monte Carlo simulations. A similar strategy was applied by Davies et al. for the screening of stoichiometric inorganic materials for water splitting, where low-computational cost filters based on electronegativity, electronic chemical potential, and atomic solid-state energy. [START_REF] Davies | Computational screening of all stoichiometric inorganic materials[END_REF] To go beyond these methods and identify novel materials for targeted applications, there is thus a need to develop active methods for property prediction based on structure and chemical composition, bypassing quantum calculations and classical molecular simulations -at least during an initial high-throughput screening step. In order to develop such methods, databases are useful in two different ways: first, databases of physical and chemical properties are necessary in order to train, benchmark and validate the new prediction methods. Secondly, larger databases of hypothetical structures are needed as a basis for large-scale screening, once the property prediction methods are adequate.

With this goal in mind, machine learning appears as a powerful tool for predicting chemical and physical properties for large number of materials, i.e. at low computational cost. Neural networks -already presented in section 2 -are a class of machine learning algorithms, but many other exist. Machine learning is the generic term used for algorithms that generate another algorithm, in order to progressively improve their performance for a task they have not been explicitly programmed to perform. In the most commonly-used family of machine learning methods, called supervised learning, the algorithm generated is called the predictor. It takes a set of input descriptors, and map them to the required output. This output is usually the numeric value of a physical property in our case, but it can also be the classification of the input in a given class. When using machine learning on chemical systems, the descriptors can take multiple forms: local descriptors such as atomic positions, bond length, angle, or dihedral angles; global descriptors like mass density, largest included sphere in a porous framework, or elastic properties; and topological descriptors such as ring sizes distribution. As we said, machine learning algorithms generate predictor algorithms from a set of reference input and output data. The idea is to train the machine learning algorithm on a subset of the data, and then test the generated predictor on the remaining part of the reference data. This allow to evaluate the accuracy of the predictor. For more information on machine learning and its usage in molecular and materials science, we refer the interested reader to the very pedagogical review by Butler at al. [START_REF] Butler | Machine learning for molecular and materials science[END_REF] Within the fields of physics and chemistry, machine learning has been applied to a large diversity of applications. On the computational side, research is ongoing on the use of machine learning to improve electronic structure calculations by bypassing the Kohn-Sham equations, [START_REF] Brockherde | Bypassing the kohn-sham equations with machine learning[END_REF] developing machine-learned functionals [START_REF] Hollingsworth | Can exact conditions improve machine-learned density functionals?[END_REF] and creating adaptive basis sets. [START_REF] Schütt | Machine learning adaptive basis sets for efficient large scale density functional theory simulation[END_REF] Other applications in chemistry include the extraction of chemical data (structures, reactions, etc.) from published work, [START_REF] Kim | Materials synthesis insights from scientific literature via text extraction and machine learning[END_REF] the prediction of novel synthetic pathways, [START_REF] Gómez-Bombarelli | Automatic chemical design using a data-driven continuous representation of molecules[END_REF] the design of catalysts, [START_REF] Goldsmith | Machine learning for heterogeneous catalyst design and discovery[END_REF] etc. In 2016, Jong et al. used machine learning techniques to predict elastic properties (bulk and shear modulus) for inorganic compounds in order to accelerate materials discovery and design. [START_REF] De Jong | A statistical learning framework for materials science: Application to elastic moduli of k-nary inorganic polycrystalline compounds[END_REF] However, few studies have focused so far on framework materials and their physical properties. Recently, Evans et al. [START_REF] Evans | Predicting the mechanical properties of zeolite frameworks by machine learning[END_REF] as the bulk modulus and shear modulus) of 590 448 hypothetical pure-silica zeolites, using an accurate training set of elastic properties determined with DFT calculations. [START_REF] Coudert | Systematic investigation of the mechanical properties of pure silica zeolites: stiffness, anisotropy, and negative linear compressibility[END_REF] Evans combined the GBR (gradient boosting regressor) approach using regression trees and a set of local, structural and porosity-related descriptors, and their results highlighted several important correlations and trends in terms of stability for zeolitic structures. Romain Gaillac extended this to predict the auxeticity and the Poisson's ratio of more than 1 000 zeolites. [START_REF] Gaillac | Molecular modeling of physico-chemical properties in microporous solids[END_REF] These recent advances, combined with the availability of DFT-computed elastic tensors for a large number of inorganic materials within the Materials Project, creates new opportunities for computationally assisted materials discovery and design. We should also note here, for the sake of completeness, that unsupervised machine learning has also been applied to chemical questions: such techniques take a data set as input and identify hidden structure in the data -e.g., clustering of data points or structures by similarity. [100,101]

Conclusion

We have given here a short overview of the current state of methodologies for modelling framework materials at multiple scales, and tried to highlight some of the common themes as well as differences between this rapidly expanding class of materials and other inorganic solids. It is clear from the examples listed that the diversity of modelling methods is also growing to match the rapid pace of experimental developments, and the increasing complexity of the systems and phenomena studied. However, while modelling strategies develop at all length and time scales, from the microscopic to the macroscopic, the links between these simulation scales are still rather ad hoc, and comprehensive, coherent multi-scale simulation strategies are still the exception, rather than the norm. Just like experimental and computational tools are complementary in providing a large variety of viewpoints on a given material, studies containing multiple simulations strategies at different scales are appearing, which provide a very deep understanding of the macroscopic properties of a material, and their microscopic origins. Data Accessibility. Supporting data is available online in our data repository at https://github.com/ fxcoudert/citable-data

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Figure 2 .

 2 Figure 2. Ring size distribution in silica glass, as computed from 18 small (72 atoms) replicas, or a single big (1497 atoms) simulation. Reprinted with permission from Ref. 40. Copyright 2005 by the American Physical Society.

  [START_REF] Vanson | Unexpected coupling between flow and adsorption in porous media[END_REF] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

[ 71 ]

 71 All three hypothetical zeolites databases are maintained by individual research groups, and are not open to external submissions of new structures.

Figure 3 .

 3 Figure 3. Schematic of the CSD and MOF entries since 1972. The inset shows the MOF self-assembly process from building blocks: metal nodes (red spheres) and organic ligands (blue struts). Reprinted with permission from Ref. 73.Copyright 2017 American Chemical Society.

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  used a machine learning algorithm to predict elastic properties (such . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Acknowledgements. A large part of the work reviewed here requires access of scientists in the field to large supercomputer centers. Although no original calculations were performed in the writing of this review, we acknowledge GENCI for high-performance computing CPU time allocations (grant A0050807069). We sincerely thank colleagues from Université de France (UNIV France) for their support. We thank Cory Simon and Martijn Zwijnenburg for their insightful feedback on a first version of this manuscript which appeared on the chemRxiv preprint server.

(c) The Materials Project

For other crystalline compounds, and for inorganic solids in particular, there have been a large number of databases, often with a specific focus on a particular class of materials. Most -but not all -are dedicated to experimental structures and properties. They are briefly reviewed in Ref. [START_REF] Zakutayev | An open experimental database for exploring inorganic materials[END_REF], for the interested reader. We want to focus here on a recent development, the development of the Materials Project, which provides a materials database as well as an open API (and web portal) to computed information on known and predicted materials. As we are writing this, it includes information about 86 371 inorganic compounds, and it is regularly updated with additional entries. It also aggregates nanoporous structures from several databases, including CoRE MOFs, hypothetical MOFs and zeolites described in the previous sections, as well as computational predicted porous polymeric networks (PPNs). The main goal of this database is to accelerate advanced materials discovery and deployment. [START_REF] Jain | Commentary: The materials project: A materials genome approach to accelerating materials innovation[END_REF] Classes of materials that feature a specific focus include battery materials, intercalation electrodes and conversion electrodes.

The database is open -after registration -and accessible through its own open-source API. A high-quality reference implementation of this API is provided as part of the open-source Python Materials Genomics (pymatgen) materials analysis package, available at http://pymatgen.org/. In addition to the Materials Project API, pymatgen is a generic materials-oriented Python library, with classes for the representation of elements, sites, molecules, and periodic structures, input/output support for several common file formats, analysis tools for electronic structure and physical properties, etc. For non programmers, the Materials Project also includes a web front-end at https://materialsproject.org/, through which one can access the large data set. Properties such as space group, X-Ray diffraction, band structures, elastic properties, etc. can be browsed or searched. This architecture is extensible; for example, our group has recently provided an integration of the online ELATE application for analysis and visualization of elastic tensors. [START_REF] Gaillac | Elate: an open-source online application for analysis and visualization of elastic tensors[END_REF] This ELATE analysis and visualization is linked from every Materials Project entry that contains elastic data, i.e. every crystalline solid for which the elastic stiffness tensor has been computed by DFT calculations. In 2015, Jong et al. reported elastic properties for 1 181 inorganic compounds. [START_REF] De Jong | Charting the complete elastic properties of inorganic crystalline compounds[END_REF] This number has since grown, and the database currently contains elastic information for 13 934 inorganic compounds -and this number is still growing.