Uncertainty quantification for goal-oriented inverse problems via variational encoder-decoder networks

被引:0
作者
Afkham, Babak Maboudi [1 ]
Chung, Julianne [2 ]
Chung, Matthias [2 ]
机构
[1] Tech Univ Denmark, Dept Appl Math & Comp Sci, DTU Compute, Lyngby, Denmark
[2] Emory Univ, Dept Math, Atlanta, GA 30322 USA
基金
美国国家科学基金会;
关键词
deep learning; regularization; encoder-decoder networks; uncertainty quantification; quantity of interest; hyperparameter selection; REGULARIZATION PARAMETER; NEURAL-NETWORKS; RECONSTRUCTION;
D O I
10.1088/1361-6420/ad5373
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work, we describe a new approach that uses variational encoder-decoder (VED) networks for efficient uncertainty quantification for goal-oriented inverse problems. Contrary to standard inverse problems, these approaches are goal-oriented in that the goal is to estimate some quantities of interest (QoI) that are functions of the solution of an inverse problem, rather than the solution itself. Moreover, we are interested in computing uncertainty metrics associated with the QoI, thus utilizing a Bayesian approach for inverse problems that incorporates the prediction operator and techniques for exploring the posterior. This may be particularly challenging, especially for nonlinear, possibly unknown, operators and nonstandard prior assumptions. We harness recent advances in machine learning, i.e. VED networks, to describe a data-driven approach to large-scale inverse problems. This enables a real-time uncertainty quantification for the QoI. One of the advantages of our approach is that we avoid the need to solve challenging inversion problems by training a network to approximate the mapping from observations to QoI. Another main benefit is that we enable uncertainty quantification for the QoI by leveraging probability distributions in the latent and target spaces. This allows us to efficiently generate QoI samples and circumvent complicated or even unknown forward models and prediction operators. Numerical results from medical tomography reconstruction and nonlinear hydraulic tomography demonstrate the potential and broad applicability of the approach.
引用
收藏
页数:27
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