Knowledge-aware differential equation discovery with automated background knowledge extraction

Abstract

In differential equation discovery algorithms, a priori expert knowledge is mainly used to constrain the form of the expected equation, making it impossible for the algorithm to truly discover equations. As a result, most differential equation discovery algorithms try to recover the coefficients for a known fixed form of the equation. In this paper, we, using the initial guess obtained automatically, modify the structure space instead of imposing rigid constraints so that specific terms appear more likely within the cross-over and mutation operators. In this way, we mimic expertly chosen terms while preserving the possibility of obtaining any form of differential equation. The paper shows that the extraction and use of knowledge allow it to outperform the SINDy algorithm in terms of search stability and robustness. Synthetic examples are given for Burgers, wave, and Korteweg–de Vries equations.