Predicting symbolic ODEs from multiple trajectories

TL;DR

This paper presents MIO, a transformer-based model that infers symbolic ODEs from multiple trajectories, improving accuracy and robustness over existing methods by leveraging multiple observations and instance aggregation strategies.

Contribution

The paper introduces MIO, a novel transformer-based approach that combines multiple instance learning with symbolic regression for better ODE inference from multiple trajectories.

Findings

MIO outperforms existing baselines across various systems.

Simple mean aggregation enhances model performance.

MIO is effective under different noise levels.

Abstract

We introduce MIO, a transformer-based model for inferring symbolic ordinary differential equations (ODEs) from multiple observed trajectories of a dynamical system. By combining multiple instance learning with transformer-based symbolic regression, the model effectively leverages repeated observations of the same system to learn more generalizable representations of the underlying dynamics. We investigate different instance aggregation strategies and show that even simple mean aggregation can substantially boost performance. MIO is evaluated on systems ranging from one to four dimensions and under varying noise levels, consistently outperforming existing baselines.