Physics-Informed Machine Learning A Practical Guide: Stage 1 Foundations & Your First PINN

A practical, code-first introduction to Physics-Informed Machine Learning (PIML) — written for scientists and engineers who know the physics but are new to deep learning.

If you have a background in physics, engineering, or applied mathematics, you already understand differential equations. This book teaches you to put that knowledge to work inside a neural network: solving the equations you know, fusing them with sparse data, and tackling the problems where pure machine learning needs too much data and classical solvers need too much specification.

You won't just read about how Physics-Informed Neural Networks (PINNs) work — you'll build one yourself, from scratch, in PyTorch, and measure exactly how accurate it is against an exact solution.

This is Stage 1 — Foundations & Your First PINN. In about 100 pages across five chapters, you will:

• Understand why physics-informed methods matter, and when to choose them over pure ML or classical simulation
• Master the essential mathematics — PDEs, optimization, and automatic differentiation — in one consistent notation
• Set up a clean PyTorch environment, and learn where libraries like DeepXDE help (and where they hide too much)
• Build every component of a PINN by hand: the network, the physics and data losses, and the training pipeline
• Train a complete solver for the heat equation and verify it against the exact solution — with real, reproducible results

Throughout, the book stays honest about what these methods can and cannot do. Physics-informed machine learning is powerful, but it has real, well-documented limitations — and a guide that showed only the happy path would not be practical at all. Where the method struggles, this book says so plainly, and shows you how to recognize the trouble when it arrives.

Who it's for: readers comfortable with calculus and differential equations who can write intermediate Python, but who have not yet worked with a deep learning framework. No prior PyTorch, JAX, or TensorFlow experience required.

Published progressively. This book grows in three stages under the Lean Publishing model. Buy Stage 1 today and receive Stage 2 (Advanced) and Stage 3 (Applications) as free updates when they're released.