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We consider the simulation of Bayesian statistical inverse problems governedby large-scale linear and nonlinear partial differential equations (PDEs).Markov chain Monte Carlo (MCMC) algorithms are standard techniques to solvesuch problems. However, MCMC techniques are computationally challenging as theyrequire several thousands of forward PDE solves. The goal of this paper is tointroduce a fractional deep neural network based approach for the forwardsolves within an MCMC routine. Moreover, we discuss some approximation errorestimates and illustrate the efficiency of our approach via several numericalexamples.

Novel Deep neural networks for solving Bayesian statistical inverse