Model constrained empirical Bayesian neural networks for inverse prob- lems
Palavras-chave:
variational inference, uncertainty quantification, Bayesian methods, inverse problems, Deep learningResumo
Principled Uncertainty quantification (UQ) in deep learning is still an unsolved problem. Numerous methods have been developed so far, with Bayesian neural networks (BNNs) as the popular approach. BNNs, while inherently UQ-enabled and resistant to over-fitting, suffer from unnatural and artificial priors over their parameters.
This paper develops a model-constrained framework for quantifying the uncertainty in deep neural network inverse solutions. At the heart of our approach is an interpretable and physically-meaningful prior over neural network parameters trained through use of Stein variational gradient descent (SVGD). We provide comprehensive numerical results for a 2D inverse heat conductivity problem and a 2D inverse initial conditions problems for both the time-dependent Burgers’ and Navier-Stokes equations.
