# Predicting symbolic ODEs from multiple trajectories

arXiv: https://arxiv.org/abs/2510.23295 · HTML: https://mlsanity.com/paper/2510.23295/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 20 references that are in the map.
- First posted on arXiv 27 Oct 2025.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Attention-based Deep Multiple Instance Learning](https://mlsanity.com/paper/1802.04712/) (2018)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [ODEFormer: Symbolic Regression of Dynamical Systems with Transformers](https://mlsanity.com/paper/2310.05573/) (2023)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [Probabilistic Grammars for Equation Discovery](https://mlsanity.com/paper/2012.00428/) (2020)
- [Predicting Ordinary Differential Equations with Transformers](https://mlsanity.com/paper/2307.12617/) (2023)
- [TimeMIL: Advancing Multivariate Time Series Classification via a Time-aware Multiple Instance Learning](https://mlsanity.com/paper/2405.03140/) (2024)
- [Identifiability Challenges in Sparse Linear Ordinary Differential Equations](https://mlsanity.com/paper/2506.09816/) (2025)

## Built on by (most cited first, 2 of 2)

- [Foundation Inference Models for Ordinary Differential Equations](https://mlsanity.com/paper/2602.08733/) (2026)
- [Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers](https://mlsanity.com/paper/2608.02662/) (2026)

## Abstract (arXiv)

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.