# Mastering high-dimensional dynamics with Hamiltonian neural networks

arXiv: https://arxiv.org/abs/2008.04214 · HTML: https://mlsanity.com/paper/2008.04214/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2020.

## Built on by (most cited first, 3 of 3)

- [Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems](https://mlsanity.com/paper/2211.01873/) (2022)
- [Thermodynamics of learning physical phenomena](https://mlsanity.com/paper/2207.12749/) (2022)
- [Neuronal diversity can improve machine learning for physics and beyond](https://mlsanity.com/paper/2204.04348/) (2022)

## Abstract (arXiv)

We detail how incorporating physics into neural network design can significantly improve the learning and forecasting of dynamical systems, even nonlinear systems of many dimensions. A map building perspective elucidates the superiority of Hamiltonian neural networks over conventional neural networks. The results clarify the critical relation between data, dimension, and neural network learning performance.