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Mathematics Colloquium

Zhongjian Wang
University of Chicago

Title: Deep Learning of Multi-Scale PDEs Based on Data Generated from Particle Methods
Date: Friday, January 20, 2023
Place and Time: fsu.zoom.us/s/97976878227, 3:05-3:55 pm


Solving multi-scale PDEs is difficult in high-dimensional and/or convection- dominant cases. The interacting particle methods (IPM) are shown to outperform solving PDEs directly. Examples include computing effective diffusivities, KPP front speed, and asymptotic transport properties in topological insulators. However, the particle simulation takes a long time before convergence and is lack of surrogate models for physical parameters. In this regard, we introduce the DeepParticle methods, which learn the pushforward map from arbitrary distribution to IPM-generated distribution by minimizing the Wasserstein distance. In particular, we formulate an iterative scheme to find the transport map and prove the convergence. On the application side, in addition to KPP invariant measures, our method also applies to investigate the blow-up behavior in chemotaxis models.