Artificial intelligence empowering materials and processes | Francisco Chinesta
There are three contexts in which modelling driven or empowered by data becomes an especially appealing route:
- When the models based on the models reflecting the existing knowledge are not accurate enough.
- When existing models are accurate enough, but it is difficult to access to the parameters that they involve, in order to ensure the right accuracy of their predictions.
- When both of the scenarios just described do not apply, but the time needed for using the models makes their use in service difficult or when exploration of the parametric space is needed for optimizing designs or making reliability or robustness analyses.
Model Order Reduction techniques allow circumventing the last difficulty to a certain extent. The use of reduced approximation bases, representing the design or systems under consideration, enables real-time analyses and real-time decision-making. Different techniques exist, e.g. POD, RB, PGD, that permit operating inside or outside existing software (with different degrees of intrusiveness).
The external solutions minimizing the intrusiveness define sparse DoEs (Design of Experiments), in an active or passive learning way, to cover the parametric space best, before computing at the sampling points high-fidelity solutions with state-of-the-art software. Then, the computed solutions are interpolated or approximated in the whole parametric space to define the so-called meta-models, surrogate models, vademecums, virtual charts, response surfaces, etc. (all these terms refer to the same object approximately, namely the parametric solution of the parametrized problem).
The main challenge continues to be the technologies enabling optimal (active) sampling for maximizing the accuracy while minimizing the sampling set, so they can address many parameters (several tens), while keeping as reduced as possible the number of required high-fidelity solutions (extremely expensive from the computational viewpoint), representing rich behaviors such as nonlinear dependences, and couplings with respect to the model parameters, while asserting the redoubtable overfitting. All these constraints apply differently, depending on the available time for providing responses and availability of data for the training that determine the most appropriate regression technique to be employed.
As soon as the replacement model has been constructed, the so-called virtual twin, simulation, optimization, inverse analysis, uncertainty propagation and control can be performed very accurately and under severe real-time constraints. However, many times, computing fast state-of-the-art models is not enough, and significant differences are noticed between the prediction and the measurements. This is the case when addressing large systems, exhibiting complex behaviors and couplings, involving variability and even intrinsic uncertainty. It is in these scenarios that data can empower and enhance physics-based predictions.
In the context of the modelling and simulation driven by data, different methodologies meet and allow mutual enrichment:
- Data analysis and data reduction. In engineering the big-data paradigm must be transformed into a smart-data one, where some questions must be answered before any action can be undertaken: What data? At which scale? Where and when to collect them? Then, other questions follow: Are these data uncorrelated? Are all them useful with respect to the goal? Is some important data missing or inaccessible? What is the intrinsic dimensionality of the data? In this context the use of manifold learning (linear and nonlinear dimensionality reduction), auto-encoders, etc. are especially pertinent. Special attention must be paid to providing an accurate and concise description of data involving huge topological content: time series or images of rich microstructures involving morphological and topological information. In other cases, data involving images needs to be transformed (e.g. by using convolutions). Graphs are also a very valuable way of using the intrinsic structure of data.
- As soon as the right data is available, clustering, classification and regression can be employed. The former creating groups with the idea that a member in a group shares some qualities of the group and allows for inferring the behavior of a new individual as soon as the group to which it belongs is known. The last, the regression, allows creating the relation between features (inputs) and responses (outputs) in a quantitative manner. Here, the challenge is how to perform accurate predictions, in the multiparametric case and in the low-data limit. With the aim of reducing the amount of data needed while increasing numerical performances, the usual neural network-based regressions can be enriched by incorporating the available knowledge (such as EDP, constraints, properties) in the same way the so-called physics informed neural networks successfully perform. Other times, the hybrid paradigm, that can be viewed as a sort of transfer learning or an augmented learning, as opposed to the informed learning just mentioned, allows the definition of the so-called hybrid-twins, also referred to as physics-informed digital twins.
- New advanced techniques are expected which will enable extracting knowledge and intelligence from collected data. Among the most promising methodologies we can cite transfer learning, multi-modal learning, self-supervised or semi-supervised learning, among others.
- Data-assimilation techniques are also of major relevance. They must address the variability existing in the models, in the parameters and also in the data itself.
Refs
F. Chinesta, A. Huerta, G. Rozza, K. Willcox. Model Order Reduction. In the Encyclopedia of Computational Mechanics, Second Edition, Erwin Stein, Rene de Borst, Tom Hughes, Eds, John Wiley & Sons, Ltd., 2015.
F. Chinesta, E. Cueto, E. Abisset-Chavanne, J.L. Duval, F. El Khaldi, Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data, Archives of Computational Methods in Engineering, 27, 105-134, 2020.
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Francisco Chinesta is the Editor in Chief of the International Journal of Material Forming. www.springer.com/journal/12289 which is the official Journal of the European Scientific Association for material FORMing (ESAFORM) (www.esaform.org).
Chinesta is currently full Professor of computational physics at ENSAM Institute of Technology (Paris, France), Honorary Fellow of the “Institut Universitaire de France” – IUF- and Fellow of the Spanish Royal Academy of Engineering. He is the president of the ESI Group scientific committee and director of its scientific department. He was (2008-2012) AIRBUS Group chair professor and since 2013 he is ESI Group chair professor on advanced modeling and simulation of materials, structures, processes and systems. His research concerns computational mechanics, with major contributions in Model Order Reduction and Engineered Artificial Intelligence, both integrated in the so-called Hybrid paradigm of Simulation Based Engineering. He received many distinctions, among them the Academic Palms, the French Order of Merit, a Doctorate Honoris Causa at the University of Zaragoza (Spain) in 2018 and the Silver medal from the French CNRS in 2019.