Automating the Discovery of Partial Differential Equations in Dynamical Systems

arXiv:2404.16444v1 Announce Type: new
Abstract: Identifying partial differential equations (PDEs) from data is crucial for understanding the governing mechanisms of natural phenomena, yet it remains a challenging task. We present an extension to the ARGOS framework, ARGOS-RAL, which leverages sparse regression with the recurrent adaptive lasso to identify PDEs from limited prior knowledge automatically. Our method automates calculating partial derivatives, constructing a candidate library, and estimating a sparse model. We rigorously evaluate the performance of ARGOS-RAL in identifying canonical PDEs …

abstract arxiv cs.lg data differential discovery extension framework identify lasso math.ds natural regression stat.ap stat.ml systems type understanding