Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processes

• URL: http://arxiv.org/abs/2303.01925v1
• Date: Fri, 3 Mar 2023 13:51:04 GMT
• Title: Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processes
• Authors: Magnus Ross, Markus Heinonen
• Abstract summary: 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.
• Score: 9.581740983484472
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Hamiltonian mechanics is one of the cornerstones of natural sciences. Recently there has been significant interest in learning Hamiltonian systems in a free-form way directly from trajectory data. Previous methods have tackled the problem of learning from many short, low-noise trajectories, but learning from a small number of long, noisy trajectories, whilst accounting for model uncertainty has not been addressed. In this work, we present a Gaussian process model for Hamiltonian systems with efficient decoupled parameterisation, and 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.

Related papers

• Learning minimal representations of stochastic processes with variational autoencoders [52.99137594502433]
  We introduce an unsupervised machine learning approach to determine the minimal set of parameters required to describe a process. Our approach enables for the autonomous discovery of unknown parameters describing processes.
  arXiv  Detail & Related papers  (2023-07-21T14:25:06Z)
• Scalably learning quantum many-body Hamiltonians from dynamical data [1.702884126441962]
  We introduce a highly scalable, data-driven approach to learning families of interacting many-body Hamiltonians from dynamical data. Our approach is highly practical, experimentally friendly, and intrinsically scalable to allow for system sizes of above 100 spins.
  arXiv  Detail & Related papers  (2022-09-28T18:00:57Z)
• Learning Trajectories of Hamiltonian Systems with Neural Networks [81.38804205212425]
  We propose to enhance Hamiltonian neural networks with an estimation of a continuous-time trajectory of the modeled system. We demonstrate that the proposed integration scheme works well for HNNs, especially with low sampling rates, noisy and irregular observations.
  arXiv  Detail & Related papers  (2022-04-11T13:25:45Z)
• Gradient-Based Trajectory Optimization With Learned Dynamics [80.41791191022139]
  We use machine learning techniques to learn a differentiable dynamics model of the system from data. We show that a neural network can model highly nonlinear behaviors accurately for large time horizons. In our hardware experiments, we demonstrate that our learned model can represent complex dynamics for both the Spot and Radio-controlled (RC) car.
  arXiv  Detail & Related papers  (2022-04-09T22:07:34Z)
• 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)
• Robust and Efficient Hamiltonian Learning [2.121963121603413]
  We present a robust and efficient Hamiltonian learning method that circumvents limitations based on mild assumptions. The proposed method can efficiently learn any Hamiltonian that is sparse on the Pauli basis using only short-time dynamics and local operations. We numerically test the scaling and the estimation accuracy of the method for transverse field Ising Hamiltonian with random interaction strengths and molecular Hamiltonians.
  arXiv  Detail & Related papers  (2022-01-01T13:48:15Z)
• 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)
• Symplectic Learning for Hamiltonian Neural Networks [0.0]
  Hamiltonian Neural Networks (HNNs) took a first step towards a unified "gray box" approach. We exploit the symplectic structure of Hamiltonian systems with a different loss function. We mathematically guarantee the existence of an exact Hamiltonian function which the HNN can learn.
  arXiv  Detail & Related papers  (2021-06-22T13:33:12Z)
• Learning Hamiltonian dynamics by reservoir computer [12.09219019124976]
  Reconstructing the KAM dynamics diagram of Hamiltonian system from the time series of a limited number of parameters is an outstanding question in nonlinear science. Here, we demonstrate that this question can be addressed by the machine learning approach knowing as reservoir computer (RC) We show that RC is able to not only predict the short-term evolution of the system state, but also replicate the long-term ergodic properties of the system dynamics.
  arXiv  Detail & Related papers  (2021-04-24T03:08:02Z)
• Learning Unstable Dynamics with One Minute of Data: A Differentiation-based Gaussian Process Approach [47.045588297201434]
  We show how to exploit the differentiability of Gaussian processes to create a state-dependent linearized approximation of the true continuous dynamics. We validate our approach by iteratively learning the system dynamics of an unstable system such as a 9-D segway.
  arXiv  Detail & Related papers  (2021-03-08T05:08:47Z)

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.