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The concept of MoDeNa is an interconnected multi-scale modelling-software framework.
Four scales are linked together by this framework namely the nano-, micro-, meso-, and macroscale. This unifying software framework will allow for enhanced product- and process design across these scales. The modelling framework is intimately coupled with the software framework. In this project, the software framework will facilitate and greatly enhance the modelling activities. The orchestrator enables the linking of all scales, which is a necessary condition to obtain an integral approach, in contrast to a series of disconnected phases. The modelling software will usually combine a scale-local, (but generic) model to a solver to form a modelling tool, examples are CULGI, Material Studio, LAMMPS, GROMACS, Fluent, OPENFOAM, OpenMM. Each instance of a model, also called a single event, is established by adding an appropriate set of data, which are given as input. The data may also be requested “real-time” during execution of an instance. The tool will generate results – again - either when completing the computations or during computation. In order to get a concerted computation involving several tools, the data must be passed between instances of tools. Since the data and their format do not match on both sides, one requires adaptors that provide the compatibility between output data of one tool to the input data of the connected tool. A recipe is specific configuration of the computation sequence in the orchestrator and provides the flexibility to define alternative computational procedures. The orchestrator is the backbone of our software suite, which logically links the specific task-solvers. The orchestration software is very much like a workflow generation interface, in which the different task-solvers acting at each single scale are ‘orchestrated’ by the framework. The orchestrator calls the external software and obtains the necessary information, which is analysed, pre-processed and passed to the next task-solver through a suitable protocol. The feasibility of the implementation of such supervisory software has been commercially proven by for example two applications that were equally multidisciplinary and multi-objective though devoted to different markets: ModeFRONTIER (by Esteco) for the mechanical engineering and fluid dynamics and Pipeline Pilot (by Accelrys) for the pharmaceutical sector as well as lacking core features outlined above. The orchestrator-software suite concept tackles a number of challenges, which exist in the production of closed cell PU foams. These are the understanding of the cell growth, coalescence and deformation. Understanding of these challenges is very important in order to improve mechanical and thermal properties. For example, up to now it is not possible to produce closed cell PU foams below a certain minimum bubble size (few hundred microns). This is because Ostwald ripening leads to a disappearance of small bubbles and a further growth of larger bubbles. Since smaller bubbles lead to a decrease of the thermal conductivity of the foam it would be highly desirable to overcome the present minimum bubble size limit by a smart adaptation of recipes and process conditions. Another unsolved problem for closed cell PU foams is the undesired drainage of polymer from the cell membranes into the foam knuckles since a thinning of the membranes leads to a reduction of the mechanical strength of the foam. Because these challenges are connected to each other, an integral approach is required to address all of them. MoDeNa aims to provide such an integral approach. In order to increase the potential for successfully reaching our objective, application-specialised codes (mostly already existing) will be connected across the scales. This coupling will allow for the application to product and process design as well as the integration of the various computational tasks (see Figure below) through linking of models, associated parameters, data, and the production process of a multi-scale material can be accurately simulated. Multi-scale coupling as proposed in MoDeNa requires the exchange of information between software instances developed for specific scales in a consistent way. In order to achieve this, it is necessary to generate consistent representations for models and data that is based on a solid theoretical framework. The information exchange is governed by protocols and may occur in two ways, namely:
- forward mapping (passing information from the fine to the coarse scale, upward direction)
- backward mapping (passing information from the coarse to the fine scale, downward direction)
Forward mapping is relatively straightforward, while backward mapping inevitably requires iteration since changing the operating conditions at the fine level changes the feedback to the coarse level. ‘Backward mapping’ can be realised in two ways: ‘Two-way coupling’ and ‘model fitting’ through a sequence of model based design of experiments and parameter estimation. The first approach usually requires exchange of large amounts of data during runtime that may be expensive either due to the complexity of the data exchange or the computational cost associated with executing the fine scale software. In such cases, surrogate models, which are ‘parameter fitted models’ presents the only viable alternative.
A surrogate model (or a meta-model) is a simple description that captures those characteristics of an intrinsically complex system that are relevant for the application. As an engineering method, surrogate models are used when an outcome of interest cannot be easily directly measured, so a model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the air flow around the wing for different shape variables (length, curvature, material, ..). For many real world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and what-if analysis become impossible since they require thousands or even millions of simulation evaluations. Specifically, in the area of multiscale modeling, a surrogate model is needed to represent the details at a lower scale, in which all the degree s of freedom are equilibrated, by a simpler (and faster) model to able to reproduce the behavior at a larger scale. As an example, at atomistic level all interatomic interactions are consider using e.g. molecular dynamics and the internal energy for the equilibrated system is measured. The resulting interaction energies (binding energies) are estimated and from them the effective Flory Huggins parameter can be estimated and used later on in a surrogate model at upper scale (Flory Huggins equation or Dissipative particle dynamics equation).
The iterative procedures arising from backwards mapping, mainly being "model fitting" will be accommodated within the software suite by interfacing and extending other open source software products (e.g. Dakota, ADMB, OpenOpt). Two-way coupling will be integrated into the orchestrator as it will be capable to deal with complex coupling algorithms allowing for the conditional and/or repeated execution of the coupled (parallel or sequential) components. In addition, the software framework will enable the user to pass information to multiple target codes in a generic and with adequate performance, i.e. through source code (possibly a novel domain-specific programming language) and compiled libraries. The interfacing library will provide this functionality. Model-based design and parameter estimation (as well as some target code implementation) will greatly benefit from the availability of derivatives. This capability will be provided through computer algebra systems (CAS) and/or automatic differentiation (AD) - again by interfacing to existing public domain software products. Consistent handling data, and models, coding and wrapping models automatically will enable us to consequently integrate existing scale-specialized software, which is readily extendable.