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This paper introduces a distributionally robust learning approach for modeling heterogeneous ODE systems by maximizing a worst-case reward over an uncertainty class of trajectory derivatives. The resulting estimator is shown to have an explicit weighted average representation, balancing information across multiple data sources via a quadratic optimization. Theoretical guarantees including consistency of stabilized weights and error bounds are provided, and empirical results on simulated and real-world EEG data demonstrate improved generalization performance.
Learning shared dynamics across heterogeneous systems gets a boost from a new distributionally robust approach that balances information via a worst-case reward optimization.
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.
