Model Based and Physics Informed Deep Learning Neural Network Structures

TL;DR

This paper explores the integration of model-based signal processing, inverse problems, and physics-informed neural networks to improve neural network structure selection and design.

Contribution

It classifies and discusses five categories of methods, including physics-informed neural networks, for designing neural network structures in signal and image processing.

Findings

Classified methods into five categories including PINNs.

Provided examples for each method category.

Highlighted open problems in NN structure selection.

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.