Physics Informed Neural Networks to Solve the 2-D Heat Diffusion Equation

This paper introduces Physics-Informed Neural Networks (PINNs) to model heat distribution in a two-dimensional domain governed by the heat equation. Unlike traditional numerical solvers, PINNs incorporate the physical laws directly into the neural network’s loss function, allowing us to solve the equation. A time-dependent heat source is used to demonstrate the model’s ability to learn both spatial and temporal patterns of temperature evolution. The results show that the PINN accurately captures the dynamic behavior of the system, even with complex boundary conditions. And the simulation time of the PINN is considerably shorter than classical simulation methods.