Free 264-Page Guide Teaches AI to Follow the Laws of Physics

A researcher named Alessandro Bombini has posted a complete set of lecture notes from a PhD course he taught at the University of Bozen/Bolzano in Italy. The 264-page document covers two related ideas: "Physics Informed Neural Networks" and "Neural Operators." Both are ways of building AI that doesn't just memorize examples, but actually understands the physical rules behind them — gravity, heat flow, fluid dynamics, and so on.

Think of the difference between a student who memorizes exam answers and one who understands the underlying science. The first student fails the moment a question changes slightly. AI trained the old way has the same problem: show it a bridge design it hasn't seen before and it may guess nonsense. Physics-informed AI is given the laws of physics as part of its training, so its predictions stay believable even in unfamiliar situations. That matters for simulating things that are too expensive or dangerous to test in real life — oil reservoirs, engines, weather, materials.

The notes walk through how to build these systems from scratch using PyTorch, a popular free AI toolkit, and an open-source Nvidia library called PhysicsNeMo. They also cover newer techniques with intimidating names: Fourier Neural Operators (AI that learns whole functions, not single answers), Mixture-of-Models (several AI models voting together), and Physics-Informed Kolmogorov-Arnold Networks, or PIKANs (a newer, more flexible type of AI brain).

The honest catch: this is a university-level textbook, full of equations, and it assumes you already code. It is not a product you can use tomorrow, and no company is launching anything here. But it is free, published openly, and it gives a clear picture of where engineering AI is heading — which is exactly the kind of work that quietly upgrades the tools used to design the physical world.