Adaptive Deep Density Approximation for Stochastic Dynamical Systems

doi:10.1007/s10915-025-02791-7

	Adaptive Deep Density Approximation for Stochastic Dynamical Systems
	He, Junjie1 ; Liao, Qifeng1 ; Wan, Xiaoliang 2,3
	2025-03-01
发表期刊	JOURNAL OF SCIENTIFIC COMPUTING (IF:2.8[JCR-2023],2.7[5-Year])
ISSN	0885-7474
EISSN	1573-7691
卷号	102 期号:3
发表状态	已发表
DOI	10.1007/s10915-025-02791-7
摘要	In this paper we consider adaptive deep neural network approximation for stochastic dynamical systems. Based on the continuity equation associated with the stochastic dynamical systems, a new temporal KRnet (tKRnet) is proposed to approximate the probability density functions (PDFs) of the state variables. The tKRnet provides an explicit density model for the solution of the continuity equation, which alleviates the curse of dimensionality issue that limits the application of traditional grid-based numerical methods. To efficiently train the tKRnet, an adaptive procedure is developed to generate collocation points for the corresponding residual loss function, where samples are generated iteratively using the approximate density function at each iteration. A temporal decomposition technique is also employed to improve the long-time integration. Theoretical analysis of our proposed method is provided, and numerical examples are presented to demonstrate its performance.
关键词	Stochastic dynamical systems Continuity equation Deep neural networks Normalizing flows
URL	查看原文
收录类别	SCI ; EI
语种	英语
资助项目	National Natural Science Foundation of China[1207129112071291] ; Model Reduction Theory and Algorithms for Complex Systems Program of Institute of Mathematical Sciences, Shanghai Tech University[2024X0303-902-01] ; NSF[DMS1913163]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:001400883400002
出版者	SPRINGER/PLENUM PUBLISHERS
EI入藏号	20250717882536
EI主题词	Stochastic systems
EI分类号	1101.2.1 Deep Learning ; 1201.9 Numerical Methods ; 1202.1 Probability Theory ; 1301.1.2 Physical Properties of Gases, Liquids and Solids
原始文献类型	Journal article (JA)
文献类型	期刊论文
条目标识符	https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/398570
专题	信息科学与技术学院信息科学与技术学院_PI研究组_廖奇峰组信息科学与技术学院_博士生
通讯作者	Liao, Qifeng
作者单位	1.ShanghaiTech Univ, Sch Informat Sci & Technol, Shanghai 201210, Peoples R China 2.Louisiana State Univ, Dept Math, Baton Rouge, LA 70803, USA 3.Louisiana State Univ, Ctr Computat & Technol, Baton Rouge, LA 70803, USA
第一作者单位	信息科学与技术学院
通讯作者单位	信息科学与技术学院
第一作者的第一单位	信息科学与技术学院
推荐引用方式 GB/T 7714	He, Junjie,Liao, Qifeng,Wan, Xiaoliang. Adaptive Deep Density Approximation for Stochastic Dynamical Systems[J]. JOURNAL OF SCIENTIFIC COMPUTING,2025,102(3).
APA	He, Junjie,Liao, Qifeng,&Wan, Xiaoliang.(2025).Adaptive Deep Density Approximation for Stochastic Dynamical Systems.JOURNAL OF SCIENTIFIC COMPUTING,102(3).
MLA	He, Junjie,et al."Adaptive Deep Density Approximation for Stochastic Dynamical Systems".JOURNAL OF SCIENTIFIC COMPUTING 102.3(2025).