A domain-decomposed VAE method for Bayesian inverse problems

IF 1.5 4区 工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY International Journal for Uncertainty Quantification Pub Date : 2023-12-01 DOI:10.1615/int.j.uncertaintyquantification.2023047236
Zhihang Xu, Yingzhi Xia, Qifeng Liao
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Abstract

Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and high-dimensional parameterization of priors. This paper proposes a domain-decomposed variational auto-encoder Markov chain Monte Carlo (DD-VAE-MCMC) method to tackle these challenges simultaneously. Through partitioning the global physical domain into small subdomains, the proposed method first constructs local deterministic generative models based on local historical data, which provide efficient local prior representations. Gaussian process models with active learning address the domain decomposition interface conditions. Then inversions are conducted on each subdomain independently in parallel and in low-dimensional latent parameter spaces. The local inference solutions are post-processed through the Poisson image blending procedure to result in an efficient global inference result. Numerical examples are provided to demonstrate the performance of the proposed method.
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贝叶斯逆问题的领域分解 VAE 方法
当前瞻模型受复杂偏微分方程(PDEs)支配时,贝叶斯逆问题通常在计算上具有挑战性。这通常是由于昂贵的前向模型评估和高维的前验参数化造成的。本文提出了一种域分解变异自动编码器马尔可夫链蒙特卡罗(DD-VAE-MCMC)方法,以同时应对这些挑战。通过将全局物理域划分为小的子域,本文提出的方法首先基于本地历史数据构建本地确定性生成模型,从而提供高效的本地先验表示。通过泊松图像混合程序对局部推理解进行后处理,从而得到高效的全局推理结果。我们提供了一些数值示例来证明所提议方法的性能。
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来源期刊
International Journal for Uncertainty Quantification
International Journal for Uncertainty Quantification ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
CiteScore
3.60
自引率
5.90%
发文量
28
期刊介绍: The International Journal for Uncertainty Quantification disseminates information of permanent interest in the areas of analysis, modeling, design and control of complex systems in the presence of uncertainty. The journal seeks to emphasize methods that cross stochastic analysis, statistical modeling and scientific computing. Systems of interest are governed by differential equations possibly with multiscale features. Topics of particular interest include representation of uncertainty, propagation of uncertainty across scales, resolving the curse of dimensionality, long-time integration for stochastic PDEs, data-driven approaches for constructing stochastic models, validation, verification and uncertainty quantification for predictive computational science, and visualization of uncertainty in high-dimensional spaces. Bayesian computation and machine learning techniques are also of interest for example in the context of stochastic multiscale systems, for model selection/classification, and decision making. Reports addressing the dynamic coupling of modern experiments and modeling approaches towards predictive science are particularly encouraged. Applications of uncertainty quantification in all areas of physical and biological sciences are appropriate.
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