Conference ID: 667-703-88409
PIN Code: 463299
Machine learning methods (and more broadly deep learning and artificial intelligence) are giving rise to a new practice of scientific computation.
Their mathematical understanding and their use for the discretization of hyperbolic or parabolic partial differential equations (see for example Hesthaven 2018, Zaleski 2019) require an evaluation or re-evaluation of the foundations of these methods.
A review will be made:
a) a mathematical framework based on adaptive numerical approximation
b) goods and bads about the power of depth assessed from the Takagi function (Yarotsky 2017, Daubechies-DeVore et al. 2019)
c) a recent application to the transport of indicatrix functions with a new numerical scheme VOF-ML.
Bruno Després is Professor in Applied Mathematics at Sorbonne University. After a PhD thesis on domain decomposition methods at Inria, he started his scientific carrier at CEA. Since then, he is interested by numerous aspects of PDEs and numerical approximation of PDEs with application in physical sciences and plasma physics.
He received the national Blaise Pascal prize in 2002. Recently he was a John Von Neumann Visiting at the Munich Technical University (TUM) in 2019 and visiting scholar at Brown university 2020.