Learning stochastic Hamiltonian systems via symplectic-constrained autoencoders*

doi:10.7523/j.ucas.2026.029

Abstract

Abstract: Learning the phase flow mapping of stochastic Hamiltonian systems (SHSs) from observed data has been attracting growing attention in computational physics and machine learning fields in recent years. In this paper, we propose a symplectic-constrained autoencoder approach, extending the stochastic flow map learning (sFML) framework to the structure-preserving learning of the flow mapping of SHSs. The proposed method extracts latent random variables following a standard normal distribution via the encoder and reconstructs the state evolution mapping through the decoder, with the loss function integrating symplectic constraint innovatively to ensure the preservation of symplectic structure. Numerical experiments conducted on the Kubo oscillator validate the superiority of our approach in comparison with the benchmark sFML model.

Key words: stochastic Hamiltonian systems, autoencoder neural networks, symplectic integrators

CLC Number:

O241.8

CHEN Chen, WANG Lijin. Learning stochastic Hamiltonian systems via symplectic-constrained autoencoders^*[J]. Journal of University of Chinese Academy of Sciences, DOI: 10.7523/j.ucas.2026.029.

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Learning stochastic Hamiltonian systems via symplectic-constrained autoencoders^*

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