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Predicting Symbolic ODEs From Multiple Trajectories

MCML Authors

Niki Kilbertus

Prof. Dr.

Principal Investigator

Ethics in Systems Design and Machine Learning

Sören Becker

→ Group Niki Kilbertus
Ethics in Systems Design and Machine Learning

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.

inproceedings SKB25b

ML4PS @NeurIPS 2025

Workshop on Machine Learning and the Physical Sciences at the 39th Conference on Neural Information Processing Systems. San Diego, CA, USA, Nov 30-Dec 07, 2025. To be published. Preprint available.