Robust Identification of Differential Equations from Noisy Data

Virtual Conference: 2022 SIAM Conference on Parallel Processing for Scientific Computing

Abstract. Identifying unknown differential equations from given discrete time dependent data is a challenging problem. Noisy data make such identification particularly challenging. In this talk, we present robust methods against a high level of noise which approximate the underlying noise-free dynamics well. This approach is fundamentally based on numerical PDE techniques, and we introduce successively denoised differentiation and utilize subspace pursuit time evolution error for PDE identification.

Authors

Yuchen He, Georgia Institute of Technology, U.S., yuchenroy@sjtu.edu.cn

Sung Ha Kang, Georgia Institute of Technology, U.S., kang@math.gatech.edu

Wenjing Liao, Georgia Institute of Technology, U.S., wliao60@gatech.edu

Hao Liu, Hong Kong Baptist University, Hong Kong, haoliu@hkbu.edu.hk

Yingjie Liu, Georgia Institute of Technology, U.S., yingjie@math.gatech.edu