Deep Neural Network Modeling of Unknown System Dynamics

Speaker: Zhen Chen (Dartmouth)

Dates: 2023/02/17

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Abstract: There are numerous observational, experimental, or simulation data for problems in science and engineering. Differential equations governing the underlying dynamics are often unknown for some systems. The ability to model the underlying dynamics from data is essential for a quantitative understanding of the system. My research focuses on developing data-driven modeling methods using machine learning techniques to learn underlying system dynamics. This talk will discuss my work on deep learning of unknown partial differential equations (PDEs) using observation data. A particular focus will be on designing deep neural networks for hyperbolic systems of conservation laws. We proposed a conservative form neural network and showed that our method consistently captures the correct shock propagating speed and is robust to noise and sparse observation. I will also discuss work where we proposed a mathematical framework for modeling general unknown PDEs from observation data. The method is shown to be able to work with mesh-free data.

About speaker: Zhen Chen is a postdoctoral research associate at the Department of Mathematics at Dartmouth College, working with Anne Gelb. Before joining Dartmouth, he finished his Ph.D. in Mathematics under the supervision of Dongbin Xiu at the Ohio State University in 2021. His research interests are in scientific machine learning and data-driven modeling. He is interested in combining machine learning techniques with scientific computing knowledge to extract insights from scientific datasets. He has worked on research projects using deep neural networks to model unknown physical laws and governing equations from observation data.