# Robust Learning of Heterogeneous Dynamic Systems

arXiv: https://arxiv.org/abs/2604.05285 · HTML: https://mlsanity.com/paper/2604.05285/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 7 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Coping with Label Shift via Distributionally Robust Optimisation](https://mlsanity.com/paper/2010.12230/) (2020)
- [Federated Adaptive Causal Estimation (FACE) of Target Treatment Effects](https://mlsanity.com/paper/2112.09313/) (2021)
- [Statistical Inference for Maximin Effects: Identifying Stable Associations across Multiple Studies](https://mlsanity.com/paper/2011.07568/) (2020)
- [Learning stable and predictive structures in kinetic systems: Benefits of a causal approach](https://mlsanity.com/paper/1810.11776/) (2018)
- [Network Reconstruction From High Dimensional Ordinary Differential Equations](https://mlsanity.com/paper/1610.03177/) (2016)
- [Robust Inference for Federated Meta-Learning](https://mlsanity.com/paper/2301.00718/) (2023)
- [Kernel Ordinary Differential Equations](https://mlsanity.com/paper/2008.02915/) (2020)
- [Post-Regularization Confidence Bands for Ordinary Differential Equations](https://mlsanity.com/paper/2110.12510/) (2021)

## Abstract (arXiv)

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the problem of learning shared patterns from multiple heterogeneous dynamic systems. In this article, we propose a novel distributionally robust learning approach for modeling heterogeneous ODE systems. Specifically, we construct a robust dynamic system by maximizing a worst-case reward over an uncertainty class formed by convex combinations of the derivatives of trajectories. We show the resulting estimator admits an explicit weighted average representation, where the weights are obtained from a quadratic optimization that balances information across multiple data sources. We further develop a bi-level stabilization procedure to address potential instability in estimation. We establish rigorous theoretical guarantees for the proposed method, including consistency of the stabilized weights, error bound for robust trajectory estimation, and asymptotical validity of pointwise confidence interval. We demonstrate that the proposed method considerably improves the generalization performance compared to the alternative solutions through both extensive simulations and the analysis of an intracranial electroencephalogram data.