AMS Weekly Seminar | Assistant Professor Chunmei Wang

Location: Gilman 132

When: November 9th at 1:30 p.m.

Title: Finite Expression Methods for Discovering Physical Laws from Data

Abstract: Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to model nonlinear dynamics from data remains challenging. In this talk, the speaker will present a novel deep symbolic learning method called the “finite expression method” (FEX) to discover governing equations within a function space containing a finite set of analytic expressions, based on observed dynamic data. The key concept is to employ FEX to generate analytic expressions of the governing equations by learning the derivatives of partial differential equation (PDE) solutions through convolutions. The numerical results demonstrate that our FEX surpasses other existing methods (such as PDE-Net, SINDy, GP, and SPL) in terms of numerical performance across a range of problems, including time-dependent PDE problems and nonlinear dynamical systems with time-varying coefficients. Moreover, the results highlight FEX’s flexibility and expressive power in accurately approximating symbolic governing equations.