This book serves as a comprehensive, hands-on guide to Physics-Informed Neural Networks (PINNs) and modern scientific machine learning, systematically walking readers from foundational concepts through advanced applications across three structured stages. It begins by establishing PINNs as powerful tools that embed known physical laws—governing equations, boundary conditions, and initial conditions—directly into neural network training, eliminating the need for large labeled datasets while ensuring solutions adhere to real-world constraints. Coverage progresses from soft and hard constraint enforcement strategies, loss weighting, and efficient training workflows to tackling nonlinear systems including Burgers’ equation and steady two-dimensional Navier–Stokes flows, followed by a practical debugging framework addressing spectral bias, convergence failure, numerical instability, and common implementation pitfalls. The text then expands beyond single-problem solvers to introduce Neural Operators—DeepONet and Fourier Neural Operator—for learning solution families and instantly generalizing across new inputs, before turning to inverse problems where PINNs recover unknown physical parameters, fields, and hidden dynamics from sparse, noisy measurements. Throughout, the material balances clear conceptual explanations, complete runnable PyTorch code, validation against trusted conventional solvers, and honest discussion of limitations, making it an indispensable resource for students, researchers, and practitioners applying physics-informed machine learning to engineering and scientific challenges.
This book serves as a comprehensive, hands-on guide to Physics-Informed Neural Networks (PINNs) and modern scientific machine learning, systematically walking readers from foundational concepts through advanced applications across three structured stages. It begins by establishing PINNs as powerf...
