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Learning dissipative Hamiltonian dynamics with reproducing kernel Hilbert spaces and random Fourier features

arXiv 2410.18656 ↗First posted 24 Oct 2024cs.LG cs.ROcited by 0

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Abstract (arXiv)

This paper presents a new method for learning dissipative Hamiltonian dynamics from a limited and noisy dataset. The method uses the Helmholtz decomposition to learn a vector field as the sum of a symplectic and a dissipative vector field. The two vector fields are learned using two reproducing kernel Hilbert spaces, defined by a symplectic and a curl-free kernel, where the kernels are specialized to enforce odd symmetry. Random Fourier features are used to approximate the kernels to reduce the dimension of the optimization problem. The performance of the method is validated in simulations for two dissipative Hamiltonian systems, and it is shown that the method improves predictive accuracy significantly compared to a method where a Gaussian separable kernel is used.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 12 of its 30 references that are in the map. First posted on arXiv 24 Oct 2024.

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12 of 30 references.

References · 12

  1. 2019Hamiltonian Neural Networkscited by 702
  2. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 183
  3. 2019Symplectic Recurrent Neural Networkscited by 148
  4. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 77
  5. 2022Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separatelycited by 46
  6. 2019Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularizationcited by 32
  7. 2016Random Fourier Features for Operator-Valued Kernelscited by 22
  8. 2018Learning Contracting Vector Fields For Stable Imitation Learningcited by 20
  9. 2016Operator-Valued Bochner Theorem, Fourier Feature Maps for Operator-Valued Kernels, and Vector-Valued Learningcited by 15
  10. 2021Nonparametric adaptive control and prediction: theory and randomized algorithmscited by 8
  11. 2023Learning of Hamiltonian Dynamics with Reproducing Kernel Hilbert Spacescited by 2
  12. 2024Learning Hamiltonian Dynamics with Reproducing Kernel Hilbert Spaces and Random Featurescited by 2

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