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Numerical Analysis Seminar: Li Wang, University of Minnesota, Neural network based solvers for kinetic equations
March 28 | 3:00 pm - 4:00 pm EDT
Deep learning method has emerged as a competitive mesh-free method for solving partial differential equations (PDEs). The idea is to represent solutions of PDEs by neural networks to take advantage of the rich expressiveness of neural networks representation. In this talk, we will explore the applicability of this powerful framework to the kinetic equation, which is a mesoscopic description of many particle systems. We will emphasize on dealing with multiple scales and obtaining long time stability. The latter is especially useful for uncertainty quantification or inverse problems when repeated applications of the forward model are needed.