Inferring the Structure of Ordinary Differential Equations

TL;DR

This paper extends the AIFeynman symbolic regression method to infer the structure of ordinary differential equations from observational data, improving interpretability of dynamical systems compared to black box models.

Contribution

It introduces an extension of AIFeynman for dynamic systems and empirically compares its performance to state-of-the-art symbolic regression methods.

Findings

The extended AIFeynman performs best on benchmark dynamical systems.

All methods struggle with complex systems like Cart-Pole.

The approach enhances interpretability of physical models.

Abstract

Understanding physical phenomena oftentimes means understanding the underlying dynamical system that governs observational measurements. While accurate prediction can be achieved with black box systems, they often lack interpretability and are less amenable for further expert investigation. Alternatively, the dynamics can be analysed via symbolic regression. In this paper, we extend the approach by (Udrescu et al., 2020) called AIFeynman to the dynamic setting to perform symbolic regression on ODE systems based on observations from the resulting trajectories. We compare this extension to state-of-the-art approaches for symbolic regression empirically on several dynamical systems for which the ground truth equations of increasing complexity are available. Although the proposed approach performs best on this benchmark, we observed difficulties of all the compared symbolic regression approaches on more complex systems, such as Cart-Pole.