A0726
Title: Scaling up Bayesian uncertainty quantification for inverse problems using deep neural networks
Authors: Shiwei Lan - Arizona State University (United States) [presenting]
Abstract: Due to the importance of uncertainty quantification (UQ), the 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, a surrogate-based method, calibration-emulation-sampling (CES), has recently been proposed for large dimensional UQ problems. We propose a novel CES approach for Bayesian inference based on deep neural network models for the emulation phase. The resulting algorithm is computationally more efficient and more robust against variations in 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 Dimension-Reduced Emulative Autoencoder Monte Carlo (DREAMC) algorithm, is able to scale Bayesian UQ up to thousands of dimensions for inverse problems. Using two low-dimensional (linear and nonlinear) inverse problems we illustrate the validity of this approach. Next, we apply our method to two high-dimensional numerical examples (elliptic and advection-diffusion) to demonstrate its computational advantages over existing algorithms.
