Towards true discovery of the differential equations

TL;DR

This paper investigates methods for autonomous discovery of differential equations from data, aiming to improve reliability and eliminate the need for prior assumptions about the equation form.

Contribution

It introduces approaches for independent equation discovery without relying on predefined equation forms or expert input, addressing the challenge of assessing discovery adequacy.

Findings

Proposes tools for evaluating the quality of discovered equations

Eliminates the need for prior knowledge of the equation form

Enhances the reliability of data-driven differential equation discovery

Abstract

Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and appropriate differential terms, algorithms can autonomously uncover equations from data. This paper explores the prerequisites and tools for independent equation discovery without expert input, eliminating the need for equation form assumptions. We focus on addressing the challenge of assessing the adequacy of discovered equations when the correct equation is unknown, with the aim of providing insights for reliable equation discovery without prior knowledge of the equation form.