Separable Gaussian neural networks for high-dimensional nonlinear stochastic systems

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Probabilistic Engineering Mechanics Pub Date : 2024-03-11 DOI:10.1016/j.probengmech.2024.103594
Xi Wang , Siyuan Xing , Jun Jiang , Ling Hong , Jian-Qiao Sun
{"title":"Separable Gaussian neural networks for high-dimensional nonlinear stochastic systems","authors":"Xi Wang ,&nbsp;Siyuan Xing ,&nbsp;Jun Jiang ,&nbsp;Ling Hong ,&nbsp;Jian-Qiao Sun","doi":"10.1016/j.probengmech.2024.103594","DOIUrl":null,"url":null,"abstract":"<div><p>This paper extends the recently developed method of separable Gaussian neural networks (SGNN) to obtain solutions of the Fokker–Planck–Kolmogorov (FPK) equation in high-dimensional state space. Several challenges when extending SGNN to high-dimensional state space are addressed including proper definition of domain for placing Gaussian neurons and region for data sampling, and numerical integration issue of evaluating marginal probability density functions. Three benchmark nonlinear dynamic systems with increasing complexity and dimension are examined with the SGNN method. In particular, the steady-state probability density of the response is obtained with the SGNN method and compared with the results of extensive Monte Carlo simulations. It should be pointed out that some solutions of high-dimensional FPK equations for nonlinear dynamic systems would be very difficult to obtain without SGNN.</p></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":null,"pages":null},"PeriodicalIF":3.0000,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probabilistic Engineering Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S026689202400016X","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0

Abstract

This paper extends the recently developed method of separable Gaussian neural networks (SGNN) to obtain solutions of the Fokker–Planck–Kolmogorov (FPK) equation in high-dimensional state space. Several challenges when extending SGNN to high-dimensional state space are addressed including proper definition of domain for placing Gaussian neurons and region for data sampling, and numerical integration issue of evaluating marginal probability density functions. Three benchmark nonlinear dynamic systems with increasing complexity and dimension are examined with the SGNN method. In particular, the steady-state probability density of the response is obtained with the SGNN method and compared with the results of extensive Monte Carlo simulations. It should be pointed out that some solutions of high-dimensional FPK equations for nonlinear dynamic systems would be very difficult to obtain without SGNN.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
用于高维非线性随机系统的可分离高斯神经网络
本文扩展了最近开发的可分离高斯神经网络(SGNN)方法,以获得高维状态空间中福克-普朗克-科尔莫戈罗夫(FPK)方程的解。本文探讨了将 SGNN 扩展到高维状态空间时面临的几个挑战,包括高斯神经元放置域和数据采样区域的正确定义,以及评估边际概率密度函数的数值积分问题。利用 SGNN 方法研究了复杂度和维度不断增加的三个基准非线性动态系统。特别是,利用 SGNN 方法获得了响应的稳态概率密度,并与大量蒙特卡罗模拟的结果进行了比较。需要指出的是,如果没有 SGNN,某些非线性动态系统的高维 FPK 方程解将很难获得。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
期刊最新文献
Real-time anomaly detection of the stochastically excited systems on spherical (S2) manifold Nonprobabilistic time-dependent reliability analysis for uncertain structures under interval process loads Fractional-order filter approximations for efficient stochastic response determination of wind-excited linear structural systems Seismic reliability analysis using Subset Simulation enhanced with an explorative adaptive conditional sampling algorithm Efficient optimization-based method for simultaneous calibration of load and resistance factors considering multiple target reliability indices
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1