Data-efficient Kernel Methods for Learning Hamiltonian Systems
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Abstract (arXiv)
Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems. In this work, we propose kernel-based methods for identifying and forecasting Hamiltonian systems directly from trajectory data. We present two approaches: a 2-step method that reconstructs trajectories before learning the Hamiltonian, and a 1-step method that jointly infers both. Across several benchmark systems, including mass-spring dynamics, a nonlinear pendulum, and the Henon-Heiles system, we demonstrate that our framework achieves accurate, data-efficient predictions and outperforms 2-step kernel-based baselines, particularly in scarce-data regimes, while preserving the Hamiltonian structure. Moreover, we prove a priori error estimates, ensuring reliability of the learned models. We also provide a more general, problem-agnostic numerical framework that goes beyond Hamiltonian systems and can be used for data-driven learning of arbitrary dynamical systems.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 27 of its 71 references that are in the map. First posted on arXiv 21 Sep 2025.
Builds on
27 of 71 references.
References · 27
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15 more
- 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 26
- 2023Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEscited by 21
- 2021Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy datacited by 13
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Citing papers per year: 2025: 1; 2026: 1.
2 papers.