New trends in computational mechanics: model order reduction, manifold learning and data-driven
Résumé
Engineering sciences and technology is experiencing the data revolution. In the past models were more abundant than data, too expensive to be collected and analyzed at that time. However, nowadays, the situation is radically different, data is much more abundant (and accurate sometimes) than existing models, and a new paradigm is emerging in engineering sciences and technology. This paper retraces some incipient applications based on data within the framework of computational mechanics. Three main topics are addressed in the present work: (i) construction of solution manifolds and its use for interpolating new solutions on the man-ifold; (ii) constructing parametric solutions on the just extracted manifold; and (iii) defining behavior manifolds to perform data-driven simulation while avoiding the use of usual constitu-tive equations.
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