Deep Neural Networks with Symplectic Preservation Properties

TL;DR

This paper introduces a novel deep neural network architecture that preserves symplectic structure, enabling learning on Hamiltonian systems while maintaining their geometric properties, which is crucial for accurate modeling of physical systems.

Contribution

The paper presents a new neural network design that inherently preserves symplectic structure, extending normalizing flow techniques to Hamiltonian systems.

Findings

The architecture successfully models Hamiltonian dynamics without losing symplectic properties.

It enables learning of unknown Hamiltonian systems while respecting their geometric constraints.

The method demonstrates potential for improved physical fidelity in neural network-based simulations.

Abstract

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.