ShanghaiTech University Knowledge Management System
| An adaptive Gaussian process method for multi-modal Bayesian inverse problems | |
| 2024-09-05 | |
| 状态 | 已发表 |
| 摘要 | Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution is particularly challenging when the forward models are computationally expensive. This challenge escalates further when the posterior distribution is multimodal. To address this, we propose a Gaussian process (GP) based method to indirectly build surrogates for the forward model. Specifically, the unnormalized posterior density is expressed as a product of an auxiliary density and an exponential GP surrogate. In an iterative way, the auxiliary density will converge to the posterior distribution starting from an arbitrary initial density. However, the e ffi ciency of the GP regression is highly influenced by the quality of the training data. Therefore, we utilize the iterative local updating ensemble smoother (ILUES) to generate high-quality samples that are concentrated in regions with high posterior probability. Subsequently, based on the surrogate model and the mode information that is extracted by using a clustering method, MCMC with a Gaussian mixed (GM) proposal is used to draw samples from the auxiliary density. Through numerical examples, we demonstrate that the proposed method can accurately and e ffi ciently represent the posterior with a limited number of forward simulations. |
| 关键词 | Bayesian inverse problems Multimodal Gaussian process Surrogate ILUES |
| 语种 | 英语 |
| DOI | arXiv:2409.15307 |
| 相关网址 | 查看原文 |
| 出处 | Arxiv |
| 收录类别 | PPRN.PPRN |
| WOS记录号 | PPRN:98863926 |
| WOS类目 | Computer Science, Interdisciplinary Applications ; Statistics& Probability |
| 文献类型 | 预印本 |
| 条目标识符 | https://kms.shanghaitech.edu.cn/handle/2MSLDSTB/433542 |
| 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_硕士生 |
| 通讯作者 | Liao, Qifeng |
| 作者单位 | 1.Univ Houston, Dept Math, Houston, TX 77204, USA 2.ShanghaiTech Univ, Sch Informat Sci & Technol, Shanghai 201210, Peoples R China 3.Calif State Univ, Dept Informat Syst & Decis Sci, Fullerton, CA 92831, USA |
| 推荐引用方式 GB/T 7714 | Xu, Zhihang,Zhu, Xiaoyu,Li, Daoji,et al. An adaptive Gaussian process method for multi-modal Bayesian inverse problems. 2024. |
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