Standard simulation in classical mechanics is based on the use of two very different types of equations. The first one, of axiomatic character, is related to balance laws (momentum, mass, energy, …), whereas the second one consists of models that scientists have extracted from collected, natural or synthetic data. Even if one can be condent on the first type of equations, the second one contains modeling errors. Moreover, this second type of equations remains too particular and often fails in describing new experimental results. The vast majority existing models lack of universality, and therefore must be constantly adapted or enriched to describe new experimental findings. In this research line we propose a new route, able to directly link data to computers in order to perform numerical simulations. These simulations will employ axiomatic, universal laws while minimizing the need of explicit, often phenomenological, models. These techniques are based on the use of machine learning methodologies, that allow to extract the relevant information from large experimental datasets.
- Data-driven non-linear elasticity. Constitutive manifold construction and problem discretization. R. Ibañez, D. Borzacchiello, J. V. Aguado, E. Abisset-Chavanne, E. Cueto, P. Ladeveze, F. Chinesta. Computational Mechanics, in press, 2017. [Download pdf of draft]
- Model order reduction for real-time data assimilation through Extended Kalman Filters. D. Gonzalez, A. Badias, I. Alfaro, F. Chinesta, E. Cueto. Computer Methods in Applied Mechanics and Engineering, in press, 2017. [Download pdf of draft]
- A Manifold Learning Approach to Data-Driven Computational Elasticity and Inelasticity. R. Ibañez, E. Abisset-Chavanne, J. V. Aguado, D. Gonzalez, E. Cueto, F. Chinesta. Archives of Computational Methods in Engineering, in press, 2016. [Download pdf of draft].
- A manifold learning approach for Integrated Computational Materials Engineering. E. Lopez, D. Gonzalez, J.V. Aguado, E. Abisset-Chavanne, F. Lebel, R. Upadhyay, E. Cueto, C. Binetruy F. Chinesta. Archives of Computational Methods in Engineering, in press, 2016. [Download pdf of draft]
- kPCA-based Parametric Solutions within the PGD Framework. D. Gonzalez, J.V. Aguado, E. Cueto, E. Abisset-Chavanne, F. Chinesta. Archives of Computational Methods in Engineering, in press, 2016. [Download pdf of draft]