Solving Non Linear Partial Differential Equations Using Physics Informed Deep Neural Network

Abstract

In This Study, We Studied On Solving Non Linear Partial Differential Equations Using The Pro Posed Physics Informed Deep Neural Network (Pidnn). Physics-Informed Deep Neural Networks(Pidnns) Use Automatic Differentiation To Solve Non Linear Partial Differential Equations (Pdes)By Penalizing The Pdes In The Loss Function At Random Set Of Points In The Domain Of Boundary And Initial Conditions. In This Study, We Have Used The Supervised Learning And Multi-Layer Architecture To Obtain Approximate Solutions Of Non Linear Partial Differential Equations. Fur The More, We Compared The Pidnn Results And The Exact. Two Implementations (Schr??Dinger Equation And Burgers Equation) Took To Show The Accuracy And The Power Of This Developed Model With Plotted Graphs Using Python Code.