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利用带辛约束的自编码器学习随机哈密尔顿系统

  • 谌晨 ,
  • 王丽瑾
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  • 中国科学院大学数学科学学院, 北京 100049

收稿日期: 2026-01-05

  修回日期: 2026-05-08

  网络出版日期: 2026-05-09

Learning stochastic Hamiltonian systems via symplectic-constrained autoencoders*

  • CHEN Chen ,
  • WANG Lijin
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  • School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2026-01-05

  Revised date: 2026-05-08

  Online published: 2026-05-09

Supported by

*National Key Research and Development Project of China 2024YFA1013101

摘要

近年来,从观测数据中学习随机哈密顿尔系统(SHSs)的相流映射问题,已在计算物理与机器学习领域引起越来越多的关注。本文提出一种融合辛约束的自编码器方法,将随机流映射学习(sFML)框架拓展至随机哈密尔顿系统相流映射的保结构学习。该方法通过编码器提取服从标准正态分布的隐随机变量,并利用解码器重构系统的状态演化映射;其损失函数创新性地融入辛约束,以保证系统辛结构的保持。基于Kubo振子的数值实验验证了所提出的方法相较于基准sFML模型的优越性。

本文引用格式

谌晨 , 王丽瑾 . 利用带辛约束的自编码器学习随机哈密尔顿系统[J]. 中国科学院大学学报, 0 : 20260509 . DOI: 10.7523/j.ucas.2026.029

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.

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