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利用神经网络基于Fokker-Planck方程学习随机Hamilton系统

  • 陈格格 ,
  • 程旭鹏 ,
  • 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: 2024-10-18

  修回日期: 2025-01-08

  网络出版日期: 2025-03-26

Learning stochastic Hamiltonian systems via neural networks based on associated Fokker-Planck equations*

  • CHEN Gege ,
  • CHENG Xupeng ,
  • WANG Lijin
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  • School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2024-10-18

  Revised date: 2025-01-08

  Online published: 2025-03-26

Supported by

*National Natural Science Foundation of China (No. 11971458)

摘要

本文中我们提出一种利用神经网络从观测数据学习随机Hamilton系统的方法,该方法基于与系统相关联的Fokker-Planck方程的时间半离散,以及随机Hamilton系统的解的期望。我们学习的目标是系统的漂移和扩散Hamilton函数,这使得通过学习可以获得系统的辛结构,进而实现具有较好精度的辛预测。数值实验展示了所提出的方法的有效性。

本文引用格式

陈格格 , 程旭鹏 , 王丽瑾 . 利用神经网络基于Fokker-Planck方程学习随机Hamilton系统[J]. 中国科学院大学学报, 0 : 250326 . DOI: 10.7523/j.ucas.2025.001

Abstract

In this paper we propose a method of learning stochastic Hamiltonian systems (SHSs) from observational data via neural networks, based on the temporal semi-discretization of the Fokker-Planck equations associated to the systems, as well as the expectations of the SHSs’ solutions. Our learning targets are the drift and diffusion Hamiltonian functions of the systems, which enables capturing the symplectic structure of the systems by the learning, and consequently ensures symplectic prediction that possesses good accuracy. Numerical experiments demonstrate effectiveness of the proposed method.

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