Learning Hamiltonian Systems with Mono-Implicit Runge-Kutta Methods
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Abstract (arXiv)
Numerical integrators could be used to form interpolation conditions when training neural networks to approximate the vector field of an ordinary differential equation (ODE) from data. When numerical one-step schemes such as the Runge-Kutta methods are used to approximate the temporal discretization of an ODE with a known vector field, properties such as symmetry and stability are much studied. Here, we show that using mono-implicit Runge-Kutta methods of high order allows for accurate training of Hamiltonian neural networks on small datasets. This is demonstrated by numerical experiments where the Hamiltonian of the chaotic double pendulum in addition to the Fermi-Pasta-Ulam-Tsingou system is learned from data.
Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 8 of its 19 references that are in the map. First posted on arXiv 7 Mar 2023.
Builds on
8 of 19 references.
References · 8
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
- 2018Neural Ordinary Differential Equationscited by 3,779
- 2019Hamiltonian Neural Networkscited by 712
- 2017Stable Architectures for Deep Neural Networkscited by 341
- 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
- 2019Symplectic Recurrent Neural Networkscited by 150
- 2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
- 2022On Numerical Integration in Neural Ordinary Differential Equationscited by 21
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Citing papers per year: 2023: 3.
3 papers.