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- W4386346089 abstract "Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based methods have been proposed. As these methods need a great number of forward and backward computations, they become costly in computation, in particular, when the forward or generative models are complex and the evaluation of the likelihood becomes very costly. Using Deep Neural Network surrogate models and approximate computation can become very helpful. However, accounting for the uncertainties, we need first understand the Bayesian Deep Learning and then, we can see how we can use them for inverse problems. In this work, we focus on NN, DL and more specifically the Bayesian DL particularly adapted for inverse problems. We first give details of Bayesian DL approximate computations with exponential families, then we will see how we can use them for inverse problems. We consider two cases: First the case where the forward operator is known and used as physics constraint, the second more general data driven DL methods. keyword: Neural Network, Variational Bayesian inference, Bayesian Deep Learning (DL), Inverse problems, Physics based DL." @default.
- W4386346089 created "2023-09-01" @default.
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- W4386346089 date "2023-08-28" @default.
- W4386346089 modified "2023-10-16" @default.
- W4386346089 title "Deep Learning and Bayesian inference for Inverse Problems" @default.
- W4386346089 doi "https://doi.org/10.48550/arxiv.2308.15492" @default.
- W4386346089 hasPublicationYear "2023" @default.
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