Knowledge-aware equation discovery with automated background knowledge extraction

TL;DR

This paper introduces a novel algorithm for discovering unknown differential equations by leveraging automatically or manually extracted background knowledge, improving search stability and robustness over existing methods.

Contribution

It presents a new approach that incorporates background knowledge into the structure search space, enabling the discovery of unknown equations rather than just coefficients.

Findings

Outperforms SINDy in stability and robustness

Successfully discovers Burgers, wave, and Korteweg--De Vries equations

Enhances differential equation discovery with knowledge extraction

Abstract

In differential equation discovery algorithms, a priori expert knowledge is mainly used implicitly to constrain the form of the expected equation, making it impossible for the algorithm to truly discover equations. Instead, most differential equation discovery algorithms try to recover the coefficients for a known structure. In this paper, we describe an algorithm that allows the discovery of unknown equations using automatically or manually extracted background knowledge. Instead of imposing rigid constraints, we modify the structure space so that certain terms are likely to appear within the crossover and mutation operators. In this way, we mimic expertly chosen terms while preserving the possibility of obtaining any equation form. The paper shows that the extraction and use of knowledge allows 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.