Novel Deep neural networks for solving Bayesian statistical inverse

Harbir Antil; Howard C Elman; Akwum Onwunta; Deepanshu Verma

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arXiv · 2102.03974

Novel Deep neural networks for solving Bayesian statistical inverse

Harbir Antil·Howard C Elman·Akwum Onwunta·Deepanshu Verma

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Abstract

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.

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Harbir Antil, Howard C Elman, Akwum Onwunta, Deepanshu Verma. 2021-02-08. Novel Deep neural networks for solving Bayesian statistical inverse. https://arxiv.org/abs/2102.03974

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