Laboratoire IMATH

Abstract : In recent years, as a representative of data-driven methods, Deep Learning methods that are based on deep neural networks have made breakthrough progress. We see three reasons, among others, why Deep Learning has been the subject of intense research over the last 4 years in all fields of Physics and Mechanics : the power of interpolation, the ability to deal with very large problems, the great richness of this model (in terms of generalization). The presentation is organized as follows. We first present what a Deep Learning problem consists of, from the point of view of computational mechanics, focusing on physics-informed DNNs which allow:to include a priori information (e.g. symmetry groups and equations). Based on the analysis of recent papers, we then analyze some results obtained, some of them extremely spectacular, in the following fields : turbulence and constitutive laws, multi-scale approach and homogenization, boundary value problem solving. We conclude with some perspectives on these topics, which suggest new paradigms in Mechanics once the community has appropriated recent methods.