Model Based and Physics Informed Deep Learning Neural Network Structures

Abstract: Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm (Training). Then, the trained model can be used for the prediction or inference step (Testing). As there are also many hyperparameters, related to the optimization criteria and optimization algorithms, a validation step is necessary before its final use. One of the great difficulties is the choice of the NN's structure. Even if there are many "on the shelf" networks, selecting or proposing a new appropriate network for a given data, signal or image processing, is still an open problem. In this work, we consider this problem using model based signal and image processing and inverse problems methods. We classify the methods in five classes, based on: i) Explicit analytical solutions, ii) Transform domain decomposition, iii) Operator Decomposition, iv) Optimization algorithms unfolding, and v) Physics Informed NN methods (PINN). Few examples in each category are explained.