Autoencoders as continuous-time optimal control problems solved with rank-adaptive tensor compression, yielding memory savings and automatic layer-width profiles on MNIST denoising and deblurring.
Novel Deep neural networks for solving Bayesian statistical inverse
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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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OCTANE -- Optimal Control for Tensor-based Autoencoder Network Emergence: Explicit Case
Autoencoders as continuous-time optimal control problems solved with rank-adaptive tensor compression, yielding memory savings and automatic layer-width profiles on MNIST denoising and deblurring.