Towards true discovery of the differential equations
It addresses a key challenge in interpretable machine learning for scientific applications, but appears incremental in focusing on assessment rather than a new discovery method.
This paper tackles the problem of assessing the reliability of discovered differential equations when the true equation is unknown, aiming to enable independent equation discovery without expert input or assumptions about the equation form.
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.