PHYSICS-INFORMED NEURAL NETWORK (PINN) AND ITS APPLICATION TO HEAT DISTRIBUTION - Alfarino B. P., Michael
Distribution of heat is described by the heat equation which is an example of a partial differential equation. There are several methods for obtaining solutions of partial differential equations, namely analytic methods, finite difference methods with the Forward-Time Centered-Space (FTCS) scheme, and Physics-Informed Neural Network (PINN). Heat equation simulation has been done using finite difference method (FTCS scheme) and PINN. Based on the results of the FTCS and PINN simulations, the solution to the heat equation was visualized and the mean-squared error (MSE) value was determined for each method. Solution to the heat equation using PINN has a small mean-squared error when compared to the analytical method. It is concluded that PINN can generally be an alternative for solving partial differential equations, the heat equation in particular. One of the advantages of PINN is that the solution is continuous and not bound by a grid. After comparing the performance of PINN against analytical and FTCS methods, 2-dimensional heat equation with a heat source was studied using Physics-Informed Neural Network (PINN). Two variations of the heat source location were studied, in the middle of the domain and at the edge of the domain. After simulating these two variations, it was concluded that temperatures on a point with a certain distance from the heat source will increase and saturate towards a limit. Points closer to the heat source will experience saturation at a higher temperature.