Predicting symbolic ODEs from multiple trajectories
This work addresses the challenge of learning symbolic ODEs from data for researchers in dynamical systems and machine learning, but it is incremental as it builds on existing transformer and symbolic regression methods.
The authors tackled the problem of inferring symbolic ordinary differential equations from multiple observed trajectories of a dynamical system, and the result was that their transformer-based model MIO consistently outperformed existing baselines across systems of one to four dimensions and varying noise levels.
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.