Separable Hamiltonian Neural Networks

• URL: http://arxiv.org/abs/2309.01069v3
• Date: Mon, 25 Mar 2024 17:39:18 GMT
• Title: Separable Hamiltonian Neural Networks
• Authors: Zi-Yu Khoo, Dawen Wu, Jonathan Sze Choong Low, Stéphane Bressan,
• Abstract summary: Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. We propose separable HNNs that embed additive separability within HNNs using observational, learning, and inductive biases.
• Score: 1.8674308456443722
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive separability of the Hamiltonian reduces the regression complexity and improves regression performance. We propose separable HNNs that embed additive separability within HNNs using observational, learning, and inductive biases. We show that the proposed models are more effective than the HNN at regressing the Hamiltonian and the vector field, and have the capability to interpret the kinetic and potential energy of the system.

Related papers

• Learning Generalized Hamiltonians using fully Symplectic Mappings [0.32985979395737786]
  Hamiltonian systems have the important property of being conservative, that is, energy is conserved throughout the evolution. In particular Hamiltonian Neural Networks have emerged as a mechanism to incorporate structural inductive bias into the NN model. We show that symplectic schemes are robust to noise and provide a good approximation of the system Hamiltonian when the state variables are sampled from a noisy observation.
  arXiv  Detail & Related papers  (2024-09-17T12:45:49Z)
• 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)
• Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Study [55.12108376616355]
  The study on NTK has been devoted to typical neural network architectures, but is incomplete for neural networks with Hadamard products (NNs-Hp) In this work, we derive the finite-width-K formulation for a special class of NNs-Hp, i.e., neural networks. We prove their equivalence to the kernel regression predictor with the associated NTK, which expands the application scope of NTK.
  arXiv  Detail & Related papers  (2022-09-16T06:36:06Z)
• 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)
• 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)
• 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)
• A unified framework for Hamiltonian deep neural networks [3.0934684265555052]
  Training deep neural networks (DNNs) can be difficult due to vanishing/exploding gradients during weight optimization. We propose a class of DNNs stemming from the time discretization of Hamiltonian systems. The proposed Hamiltonian framework, besides encompassing existing networks inspired by marginally stable ODEs, allows one to derive new and more expressive architectures.
  arXiv  Detail & Related papers  (2021-04-27T13:20:24Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)
• Sparse Symplectically Integrated Neural Networks [15.191984347149667]
  We introduce Sparselectically Integrated Neural Networks (SSINNs) SSINNs are a novel model for learning Hamiltonian dynamical systems from data. We evaluate SSINNs on four classical Hamiltonian dynamical problems.
  arXiv  Detail & Related papers  (2020-06-10T03:33:37Z)

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.