Directed differential equation discovery using modified mutation and cross-over operators

TL;DR

This paper introduces a directed evolutionary approach for differential equation discovery, enhancing convergence accuracy by modifying mutation and crossover operators inspired by biological evolution techniques.

Contribution

It proposes a novel directed evolution-based method for equation discovery, improving convergence over traditional gradient-based and standard evolutionary methods.

Findings

Enhanced convergence towards accurate solutions

Successful application to Burgers', wave, and Korteweg--de Vries equations

Demonstrated superiority over conventional methods

Abstract

The discovery of equations with knowledge of the process origin is a tempting prospect. However, most equation discovery tools rely on gradient methods, which offer limited control over parameters. An alternative approach is the evolutionary equation discovery, which allows modification of almost every optimization stage. In this paper, we examine the modifications that can be introduced into the evolutionary operators of the equation discovery algorithm, taking inspiration from directed evolution techniques employed in fields such as chemistry and biology. The resulting approach, dubbed directed equation discovery, demonstrates a greater ability to converge towards accurate solutions than the conventional method. To support our findings, we present experiments based on Burgers', wave, and Korteweg--de Vries equations.