Equation discovery framework EPDE: Towards a better equation discovery

TL;DR

This paper introduces an improved evolutionary algorithm framework for discovering physical equations from data, emphasizing reduced prior knowledge dependence and enhanced robustness to noise.

Contribution

It advances the EPDE framework by generating terms from fundamental functions, incorporating multi-objective optimization, and improving noise resilience compared to existing methods.

Findings

Outperforms SINDy in noisy data scenarios

Generates more accurate and robust equations

Reduces reliance on pre-defined term libraries

Abstract

Equation discovery methods hold promise for extracting knowledge from physics-related data. However, existing approaches often require substantial prior information that significantly reduces the amount of knowledge extracted. In this paper, we enhance the EPDE algorithm -- an evolutionary optimization-based discovery framework. In contrast to methods like SINDy, which rely on pre-defined libraries of terms and linearities, our approach generates terms using fundamental building blocks such as elementary functions and individual differentials. Within evolutionary optimization, we may improve the computation of the fitness function as is done in gradient methods and enhance the optimization algorithm itself. By incorporating multi-objective optimization, we effectively explore the search space, yielding more robust equation extraction, even when dealing with complex experimental data. We validate our algorithm's noise resilience and overall performance by comparing its results with those from the state-of-the-art equation discovery framework SINDy.