Artificial neural networks for solving ordinary and partial differential equations

Abstract

In recent years, deep neural networks have shown the impressive results in solving different tasks in computer vision, natural language processing, game theory, etc. Deep Learning has transformed how categorization, pattern recognition, and regression tasks are performed today across various application domains. The use of artificial neural networks to solve ordinary differential equation problems has started in the 1990s [1]. Various algorithms have been proposed since that time for solving ordinary and partial differential equations on regular and irregular domains [2]. The search and selection of suitable neural network architecture is a difficult task. In this talk, we consider Physics-Informed Neural Networks (PINN) [3] that encode the differential model equations as a component of the neural network itself.