Data-efficient Kernel Methods for Learning Hamiltonian Systems

• URL: http://arxiv.org/abs/2509.17154v1
• Date: Sun, 21 Sep 2025 16:50:17 GMT
• Title: Data-efficient Kernel Methods for Learning Hamiltonian Systems
• Authors: Yasamin Jalalian, Mostafa Samir, Boumediene Hamzi, Peyman Tavallali, Houman Owhadi,
• Abstract summary: We propose kernel-based methods for identifying and forecasting Hamiltonian systems directly from data.<n>We present two approaches: a two-step method that reconstructs trajectories before learning the Hamiltonian, and a one-step method that jointly infers both.<n>Our framework achieves accurate, data-efficient predictions and outperforms two-step kernel-based baselines.
• Score: 1.8757823231879849
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 data. We present two approaches: a two-step method that reconstructs trajectories before learning the Hamiltonian, and a one-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 two-step kernel-based baselines, particularly in scarce-data regimes, while preserving the conservation properties of Hamiltonian dynamics. Moreover, our methodology provides theoretical 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.

Related papers

• Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics [0.0]
  We introduce a data-driven method for learning the equations of motion of mechanical systems directly from position measurements.<n>This is particularly relevant in system identification tasks where only positional information is available, such as motion capture, pixel data or low-resolution tracking.
  arXiv  Detail & Related papers  (2025-05-26T12:13:00Z)
• Coarse-Graining Hamiltonian Systems Using WSINDy [0.0]
  We show that WSINDy can successfully identify a reduced Hamiltonian system in the presence of large intrinsics. WSINDy naturally preserves the Hamiltonian structure by restricting to a trial basis of Hamiltonian vector fields. We also provide a contribution to averaging theory by proving that first-order averaging at the level of vector fields preserves Hamiltonian structure in nearly-periodic Hamiltonian systems.
  arXiv  Detail & Related papers  (2023-10-09T17:20:04Z)
• Capturing dynamical correlations using implicit neural representations [85.66456606776552]
  We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data. In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
  arXiv  Detail & Related papers  (2023-04-08T07:55:36Z)
• Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processes [9.581740983484472]
  We present a process model for Hamiltonian systems with efficient decoupled parameterisation. We introduce an energy-conserving shooting method that allows robust inference from both short and long trajectories. We demonstrate the method's success in learning Hamiltonian systems in various data settings.
  arXiv  Detail & Related papers  (2023-03-03T13:51:04Z)
• Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Control [22.549914935697366]
  We present a method to incorporate priori knowledge into data-driven control algorithms using kernel embeddings. Our proposed approach incorporates prior knowledge of the system dynamics as a bias term in the kernel learning problem. We demonstrate the improved sample efficiency and out-of-sample generalization of our approach over a purely data-driven baseline.
  arXiv  Detail & Related papers  (2023-01-09T18:35:32Z)
• Learning Neural Hamiltonian Dynamics: A Methodological Overview [109.40968389896639]
  Hamiltonian dynamics endows neural networks with accurate long-term prediction, interpretability, and data-efficient learning. We systematically survey recently proposed Hamiltonian neural network models, with a special emphasis on methodologies.
  arXiv  Detail & Related papers  (2022-02-28T22:54:39Z)
• Learning Hamiltonians of constrained mechanical systems [0.0]
  Hamiltonian systems are an elegant and compact formalism in classical mechanics. We propose new approaches for the accurate approximation of the Hamiltonian function of constrained mechanical systems.
  arXiv  Detail & Related papers  (2022-01-31T14:03:17Z)
• SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Vision [73.26414295633846]
  A recently proposed class of models attempts to learn latent dynamics from high-dimensional observations. Existing methods rely on image reconstruction quality, which does not always reflect the quality of the learnt latent dynamics. We develop a set of new measures, including a binary indicator of whether the underlying Hamiltonian dynamics have been faithfully captured.
  arXiv  Detail & Related papers  (2021-11-10T23:26:58Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• Supervised DKRC with Images for Offline System Identification [77.34726150561087]
  Modern dynamical systems are becoming increasingly non-linear and complex. There is a need for a framework to model these systems in a compact and comprehensive representation for prediction and control. Our approach learns these basis functions using a supervised learning approach.
  arXiv  Detail & Related papers  (2021-09-06T04:39:06Z)
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components [52.77024349608834]
  We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is noisy partial measurements. We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.
  arXiv  Detail & Related papers  (2021-02-15T19:56:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.