# Training Hamiltonian neural networks without backpropagation

arXiv: https://arxiv.org/abs/2411.17511 · HTML: https://mlsanity.com/paper/2411.17511/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 26 Nov 2024.

## Builds on (most cited first, 15 of 15)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [A Compositional Object-Based Approach to Learning Physical Dynamics](https://mlsanity.com/paper/1612.00341/) (2016)
- [Visual Interaction Networks](https://mlsanity.com/paper/1706.01433/) (2017)
- [Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning](https://mlsanity.com/paper/2002.08860/) (2020)
- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)
- [Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately](https://mlsanity.com/paper/2201.10085/) (2022)
- [Symplectic Learning for Hamiltonian Neural Networks](https://mlsanity.com/paper/2106.11753/) (2021)
- [Nonseparable Symplectic Neural Networks](https://mlsanity.com/paper/2010.12636/) (2020)
- [Sampling weights of deep neural networks](https://mlsanity.com/paper/2306.16830/) (2023)
- [Fast training of accurate physics-informed neural networks without gradient descent](https://mlsanity.com/paper/2405.20836/) (2024)
- [Reconstruction of observed mechanical motions with Artificial Intelligence tools](https://mlsanity.com/paper/2202.11447/) (2022)
- [Hamiltonian Neural Networks with Automatic Symmetry Detection](https://mlsanity.com/paper/2301.07928/) (2023)

## Built on by (most cited first, 2 of 2)

- [Rapid training of Hamiltonian graph networks using random features](https://mlsanity.com/paper/2506.06558/) (2025)
- [Extrapolating the emergence of Hamiltonian chaos with random-feature Hamiltonian neural networks](https://mlsanity.com/paper/2607.28977/) (2026)

## Abstract (arXiv)

Neural networks that synergistically integrate data and physical laws offer great promise in modeling dynamical systems. However, iterative gradient-based optimization of network parameters is often computationally expensive and suffers from slow convergence. In this work, we present a backpropagation-free algorithm to accelerate the training of neural networks for approximating Hamiltonian systems through data-agnostic and data-driven algorithms. We empirically show that data-driven sampling of the network parameters outperforms data-agnostic sampling or the traditional gradient-based iterative optimization of the network parameters when approximating functions with steep gradients or wide input domains. We demonstrate that our approach is more than 100 times faster with CPUs than the traditionally trained Hamiltonian Neural Networks using gradient-based iterative optimization and is more than four orders of magnitude accurate in chaotic examples, including the H'enon-Heiles system.