Solving Computational Science Problems with AI: Physics-Informed Neural Networks (PINNs)
This article explores the use of Physics-Informed Neural Networks (PINNs) to solve challenging problems in computational science, particularly partial differential equations (PDEs). PINNs overcome limitations of traditional numerical methods by incorporating physical laws directly into the neural network's loss function. This addresses issues like insufficient data, high computational cost, and poor generalization. The article explains PDEs, partial derivatives, and demonstrates PINNs' implementation using the 2D heat equation, covering network architecture, loss function definition, and training. Results show PINNs accurately and efficiently model heat diffusion, offering a powerful tool for various scientific and engineering challenges.