[2604.05285] Robust Learning of Heterogeneous Dynamic Systems

Statistics > Methodology arXiv:2604.05285 (stat) [Submitted on 7 Apr 2026] Title:Robust Learning of Heterogeneous Dynamic Systems Authors:Shuoxun Xu, Zijian Guo, Brooke R. Staveland, Robert T. Knight, Lexin Li View a PDF of the paper titled Robust Learning of Heterogeneous Dynamic Systems, by Shuoxun Xu and 4 other authors View PDF HTML (experimental) Abstract: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 i...