Novel Deep neural networks for solving Bayesian statistical inverse
This work aims to reduce the computational burden for researchers and practitioners working on Bayesian statistical inverse problems involving large-scale PDEs, representing an incremental improvement in computational efficiency.
This paper addresses the computational challenge of Bayesian statistical inverse problems governed by large-scale PDEs, which typically require thousands of forward PDE solves using MCMC. The authors propose a fractional deep neural network approach to accelerate these forward solves within the MCMC routine, demonstrating its efficiency through numerical examples.
We consider the simulation of Bayesian statistical inverse problems governed by large-scale linear and nonlinear partial differential equations (PDEs). Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solve such problems. However, MCMC techniques are computationally challenging as they require several thousands of forward PDE solves. The goal of this paper is to introduce a fractional deep neural network based approach for the forward solves within an MCMC routine. Moreover, we discuss some approximation error estimates and illustrate the efficiency of our approach via several numerical examples.