DETERMINATING APPROXIMATION SOLUTION OF PARTIAL DIFFERENTIAL EQUATION USING PHYSICS-INFORMED NEURAL NETWORK (PINN)

• Main Author: Agnes Priscilla, Cyntia
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/82343
• Institution: Institut Teknologi Bandung

We discuss the implementation of physics-informed neural network (abbreviated as PINN), which is neural networks that are trained to solve supervised learning problems, with the additional requirement of obeying certain physical laws expressed as partial differential equations. This is a relatively new approach to obtaining approximate solutions to a partial differential equations. The neural network model first needs to be trained using data solution of the differential equation, in the form of analytical or numerical solutions, which must be obtained first. In this final project, the neural network (PINN) approach is implemented through several partial differential equations, including the transport equation, the nonlinear Burger equation, and the solitary wave propagation from the KdV equation. We also discuss the influence of computational parameters on the quality of the approximation solution. Experimental results show that PINN method effectively provides predictions of partial differential equation solutions that closely approximate the exact solutions. Furthermore, increasing the number of iterations, training data, and collocation points leads to more accurate solution predictions.