Predicting symbolic ODEs from multiple trajectories

2025-10-27

AI Summary

This work addresses the problem of automatically inferring symbolic ordinary differential equations (ODEs) from multiple observed trajectories to enhance generalization in modeling dynamical systems. We propose MIO, a novel framework that integrates multi-instance learning with Transformer-based symbolic regression, where features from multiple trajectory instances are aggregated to strengthen symbolic expression learning. MIO robustly discovers closed-form ODEs across varying noise levels and for systems of dimension one to four. Experiments demonstrate that MIO significantly outperforms existing symbolic regression baselines on multiple benchmark dynamical systems; even with the simplest mean aggregation strategy, performance gains are statistically significant. The core contribution is the first systematic incorporation of the multi-instance learning paradigm into symbolic dynamical modeling—leveraging redundant observations to improve both generalization and robustness.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

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.

Problem

• Predicting symbolic ODEs from multiple observed trajectories
• Leveraging repeated system observations for generalizable dynamics
• Outperforming baselines across varying dimensions and noise levels

Innovation

• Transformer-based model infers symbolic ODEs
• Combines multiple instance learning with symbolic regression
• Uses instance aggregation strategies to boost performance