Physics-Informed Neural Networks (PINNs) are transforming the way we solve complex scientific and engineering problems. This book serves as your essential guide to understanding this powerful technique, which elegantly combines the flexibility of neural networks with the fundamental rigor of physical laws. PINNs embed partial differential equations (PDEs), along with their boundary and initial conditions, directly into a neural network’s training process via a custom loss function. This means the neural network learns to obey the laws of physics! The solution function is represented by a...