用有噪声和不完全数据的平摊无似然推理求解高维逆问题

IF 6.9 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Jice Zeng , Yuanzhe Wang , Alexandre M. Tartakovsky , David A. Barajas-Solano
{"title":"用有噪声和不完全数据的平摊无似然推理求解高维逆问题","authors":"Jice Zeng ,&nbsp;Yuanzhe Wang ,&nbsp;Alexandre M. Tartakovsky ,&nbsp;David A. Barajas-Solano","doi":"10.1016/j.cma.2025.118064","DOIUrl":null,"url":null,"abstract":"<div><div>We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates samples of the approximate posterior distribution of the model parameters based on these summary features. The posterior samples are produced in a deep generative fashion by sampling from a latent Gaussian distribution and passing these samples through an invertible transformation. We construct this invertible transformation by sequentially alternating conditional invertible neural network and conditional neural spline flow layers. The summary and inference networks are trained simultaneously.</div><div>We apply the proposed method to an inversion problem in groundwater hydrology to estimate the posterior distribution of the log-conductivity field conditioned on spatially sparse time-series observations of the system’s hydraulic head responses. The conductivity field is represented with 706 degrees of freedom in the considered problem. Comparison with the likelihood-based iterative ensemble smoother PEST-IES method demonstrates that the proposed method accurately estimates the parameter posterior distribution and the observations’ predictive posterior distribution at a fraction of the inference time of PEST-IES.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"443 ","pages":"Article 118064"},"PeriodicalIF":6.9000,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solving high-dimensional inverse problems using amortized likelihood-free inference with noisy and incomplete data\",\"authors\":\"Jice Zeng ,&nbsp;Yuanzhe Wang ,&nbsp;Alexandre M. Tartakovsky ,&nbsp;David A. Barajas-Solano\",\"doi\":\"10.1016/j.cma.2025.118064\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates samples of the approximate posterior distribution of the model parameters based on these summary features. The posterior samples are produced in a deep generative fashion by sampling from a latent Gaussian distribution and passing these samples through an invertible transformation. We construct this invertible transformation by sequentially alternating conditional invertible neural network and conditional neural spline flow layers. The summary and inference networks are trained simultaneously.</div><div>We apply the proposed method to an inversion problem in groundwater hydrology to estimate the posterior distribution of the log-conductivity field conditioned on spatially sparse time-series observations of the system’s hydraulic head responses. The conductivity field is represented with 706 degrees of freedom in the considered problem. Comparison with the likelihood-based iterative ensemble smoother PEST-IES method demonstrates that the proposed method accurately estimates the parameter posterior distribution and the observations’ predictive posterior distribution at a fraction of the inference time of PEST-IES.</div></div>\",\"PeriodicalId\":55222,\"journal\":{\"name\":\"Computer Methods in Applied Mechanics and Engineering\",\"volume\":\"443 \",\"pages\":\"Article 118064\"},\"PeriodicalIF\":6.9000,\"publicationDate\":\"2025-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Methods in Applied Mechanics and Engineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0045782525003366\",\"RegionNum\":1,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Methods in Applied Mechanics and Engineering","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0045782525003366","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

摘要

针对高维反问题,提出了一种基于归一化流的无似然概率反演方法。该方法由两个互补网络组成:用于数据压缩的汇总网络和用于参数估计的推理网络。摘要网络将原始观测值编码为固定大小的摘要特征向量,而推理网络则根据这些摘要特征生成模型参数近似后验分布的样本。后验样本以深度生成的方式产生,从潜在高斯分布中采样,并通过可逆变换传递这些样本。我们通过顺序交替的条件可逆神经网络和条件神经样条流层来构造这种可逆变换。摘要网络和推理网络同时训练。我们将提出的方法应用于地下水水文学反演问题,以系统水头响应的空间稀疏时间序列观测为条件,估计测井电导率场的后验分布。在考虑的问题中,电导率场用706个自由度表示。与基于似然的迭代集成平滑PEST-IES方法的比较表明,该方法在一小部分的PEST-IES推理时间内准确地估计了参数后验分布和观测值的预测后验分布。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Solving high-dimensional inverse problems using amortized likelihood-free inference with noisy and incomplete data
We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates samples of the approximate posterior distribution of the model parameters based on these summary features. The posterior samples are produced in a deep generative fashion by sampling from a latent Gaussian distribution and passing these samples through an invertible transformation. We construct this invertible transformation by sequentially alternating conditional invertible neural network and conditional neural spline flow layers. The summary and inference networks are trained simultaneously.
We apply the proposed method to an inversion problem in groundwater hydrology to estimate the posterior distribution of the log-conductivity field conditioned on spatially sparse time-series observations of the system’s hydraulic head responses. The conductivity field is represented with 706 degrees of freedom in the considered problem. Comparison with the likelihood-based iterative ensemble smoother PEST-IES method demonstrates that the proposed method accurately estimates the parameter posterior distribution and the observations’ predictive posterior distribution at a fraction of the inference time of PEST-IES.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
CiteScore
12.70
自引率
15.30%
发文量
719
审稿时长
44 days
期刊介绍: Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信