Physics-Informed Neural Networks (PINNs) have received much attention recently due to their potential for high-performance computations for complex physical systems, including data-based computing, systems with unknown parameters, and others. The idea of PINNs is to approximate the equations and boundary and initial conditions through a loss function for a neural network. PINNs combine the efficiency…

In the past decade, deep learning has made astonishing breakthroughs in various real-world applications. It is a common belief that deep neural networks are good at learning various geometric structures hidden in data sets. One of the central interests in deep learning theory is to understand why deep neural networks are successful, and how they…