Learning Stochastic Hamiltonian Systems via Stochastic Generating Function Neural Network

TL;DR

This paper introduces SGFNN, a neural network that learns stochastic Hamiltonian systems from data while preserving their symplectic structure, leading to more accurate long-term predictions.

Contribution

The paper presents a novel neural network model, SGFNN, that effectively learns stochastic Hamiltonian systems and maintains their symplectic structure, improving prediction accuracy.

Findings

SGFNN outperforms benchmark models in accuracy.

SGFNN maintains symplectic structure in predictions.

Effective across various types of stochastic Hamiltonian systems.

Abstract

In this paper we propose a novel neural network model for learning stochastic Hamiltonian systems (SHSs) from observational data, termed the stochastic generating function neural network (SGFNN). SGFNN preserves symplectic structure of the underlying stochastic Hamiltonian system and produces symplectic predictions. Our model utilizes the autoencoder framework to identify the randomness of the latent system by the encoder network, and detects the stochastic generating function of the system through the decoder network based on the random variables extracted from the encoder. Symplectic predictions can then be generated by the stochastic generating function. Numerical experiments are performed on several stochastic Hamiltonian systems, varying from additive to multiplicative, and from separable to non-separable SHSs with single or multiple noises. Compared with the benchmark stochastic flow map learning (sFML) neural network, our SGFNN model exhibits higher accuracy across various prediction metrics, especially in long-term predictions, with the property of maintaining the symplectic structure of the underlying SHSs.