
Markov Chain Generative Adversarial Neural Networks for Solving Bayesian Inverse Problems in Physics Applications
In the context of solving inverse problems for physics applications with...
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Denoising ScoreMatching for Uncertainty Quantification in Inverse Problems
Deep neural networks have proven extremely efficient at solving a wide r...
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SplineBased Bayesian Emulators for Large Scale Spatial Inverse Problems
A Bayesian approach to nonlinear inverse problems is considered where th...
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Adaptive Dimension Reduction to Accelerate InfiniteDimensional Geometric Markov Chain Monte Carlo
Bayesian inverse problems highly rely on efficient and effective inferen...
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LRGLM: HighDimensional Bayesian Inference Using LowRank Data Approximations
Due to the ease of modern data collection, applied statisticians often h...
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Randomized multilevel Monte Carlo for embarrassingly parallel inference
This position paper summarizes a recently developed research program foc...
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Novel Deep neural networks for solving Bayesian statistical inverse
We consider the simulation of Bayesian statistical inverse problems gove...
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Scaling Up Bayesian Uncertainty Quantification for Inverse Problems using Deep Neural Networks
Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov Chain Monte Carlo (MCMC) tend to be computationally intensive and inefficient for such high dimensional problems. To address this issue, several methods based on surrogate models have been proposed to speed up the inference process. More specifically, the calibrationemulationsampling (CES) scheme has been proven to be successful in large dimensional UQ problems. In this work, we propose a novel CES approach for Bayesian inference based on deep neural network (DNN) models for the emulation phase. The resulting algorithm is not only computationally more efficient, but also less sensitive to the training set. Further, by using an Autoencoder (AE) for dimension reduction, we have been able to speed up our Bayesian inference method up to three orders of magnitude. Overall, our method, henceforth called DimensionReduced Emulative Autoencoder Monte Carlo (DREAM) algorithm, is able to scale Bayesian UQ up to thousands of dimensions in physicsconstrained inverse problems. Using two lowdimensional (linear and nonlinear) inverse problems we illustrate the validity this approach. Next, we apply our method to two highdimensional numerical examples (elliptic and advectiondiffussion) to demonstrate its computational advantage over existing algorithms.
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