# Learning reversible symplectic dynamics

arXiv: https://arxiv.org/abs/2204.12323 · HTML: https://mlsanity.com/paper/2204.12323/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 26 Apr 2022.

## Builds on (most cited first, 4 of 4)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators](https://mlsanity.com/paper/2006.11469/) (2020)
- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)

## Built on by (most cited first, 11 of 11)

- [Space-Time Continuous PDE Forecasting using Equivariant Neural Fields](https://mlsanity.com/paper/2406.06660/) (2024)
- [Constructing Custom Thermodynamics Using Deep Learning](https://mlsanity.com/paper/2308.04119/) (2023)
- [Lie Group Forced Variational Integrator Networks for Learning and Control of Robot Systems](https://mlsanity.com/paper/2211.16006/) (2022)
- [Approximation of nearly-periodic symplectic maps via structure-preserving neural networks](https://mlsanity.com/paper/2210.05087/) (2022)
- [Learning Lie Group Symmetry Transformations with Neural Networks](https://mlsanity.com/paper/2307.01583/) (2023)
- [Projected Neural Differential Equations for Learning Constrained Dynamics](https://mlsanity.com/paper/2410.23667/) (2024)
- [TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems](https://mlsanity.com/paper/2310.06427/) (2023)
- [Symplectic Neural Networks Based on Dynamical Systems](https://mlsanity.com/paper/2408.09821/) (2024)
- [Learning Generalized Hamiltonians using fully Symplectic Mappings](https://mlsanity.com/paper/2409.11138/) (2024)
- [Data-efficient Kernel Methods for Learning Hamiltonian Systems](https://mlsanity.com/paper/2509.17154/) (2025)
- [Ai-Sampler: Adversarial Learning of Markov kernels with involutive maps](https://mlsanity.com/paper/2406.02490/) (2024)

## Abstract (arXiv)

Time-reversal symmetry arises naturally as a structural property in many dynamical systems of interest. While the importance of hard-wiring symmetry is increasingly recognized in machine learning, to date this has eluded time-reversibility. In this paper we propose a new neural network architecture for learning time-reversible dynamical systems from data. We focus in particular on an adaptation to symplectic systems, because of their importance in physics-informed learning.