# Improving Simulations with Symmetry Control Neural Networks

arXiv: https://arxiv.org/abs/2104.14444 · HTML: https://mlsanity.com/paper/2104.14444/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 10 references that are in the map.
- First posted on arXiv 29 Apr 2021.

## Builds on (most cited first, 7 of 7)

- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Hamiltonian Generative Networks](https://mlsanity.com/paper/1909.13789/) (2019)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [Learning Symbolic Physics with Graph Networks](https://mlsanity.com/paper/1909.05862/) (2019)
- [Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks](https://mlsanity.com/paper/2003.04299/) (2020)

## Abstract (arXiv)

The dynamics of physical systems is often constrained to lower dimensional sub-spaces due to the presence of conserved quantities. Here we propose a method to learn and exploit such symmetry constraints building upon Hamiltonian Neural Networks. By enforcing cyclic coordinates with appropriate loss functions, we find that we can achieve improved accuracy on simple classical dynamics tasks. By fitting analytic formulae to the latent variables in our network we recover that our networks are utilizing conserved quantities such as (angular) momentum.