  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.
