# Deep Neural Networks with Symplectic Preservation Properties

arXiv: https://arxiv.org/abs/2407.00294 · HTML: https://mlsanity.com/paper/2407.00294/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 4 references that are in the map.
- First posted on arXiv 29 Jun 2024.

## Builds on (most cited first, 1 of 1)

- [Universal approximation property of invertible neural networks](https://mlsanity.com/paper/2204.07415/) (2022)

## Built on by (most cited first, 1 of 1)

- [The limits of exactness: On the failure of automatic differentiation in physics-informed machine learning](https://mlsanity.com/paper/2609.33078/) (2026)

## Abstract (arXiv)

We propose a deep neural network architecture designed such that its output forms an invertible symplectomorphism of the input. This design draws an analogy to the real-valued non-volume-preserving (real NVP) method used in normalizing flow techniques. Utilizing this neural network type allows for learning tasks on unknown Hamiltonian systems without breaking the inherent symplectic structure of the phase space.