Physics Informed Cellular Neural Networks for Solving Partial Differential Equations

Physics-Informed Neural Networks (PINNs) are a scientific machine learning technique used to solve a broad class of problems. PINNs approximate problems' solutions by training a neural network to minimize a loss function; it includes terms reflecting the initial and boundary conditions along the space-time domain's boundary. PINNs are deep learning networks that, given an input point in the integration domain, produce an estimated solution in that point of a differential equation after training. The basic concept behind PINN training is that it can be thought of as an unsupervised strategy that does not require labelled data, such as results from prior simulations or experiments. In this paper we generalize the idea of PINNs for solving partial differential equations by introducing physics informed cellular neural networks (PICNNs). We shall present example of the solutions of reaction-diffusion obtained by PICNNs. The advantages of the proposed new method are in the fastest algorithms and real time solutions.