PINN for Beginners — A Practitioner's Guide to Physics-Informed Neural Networks

This is the guide I wish existed when I started with PINNs: not a survey of the literature, and not a notebook dump — a complete, standalone walkthrough that takes you from "what is a PINN" to a working nonlinear PDE solver, with the actual math shown at every step.Three tutorials along with extra notebook for setup environment and getting started with automatic differentiation, one continuous thread. Each one builds a real PINN from scratch, explains why every design decision was made, and ends with a complete.What's inside: T0 — Background & Setup. Why finite differences are only ever approximate (with the actual Taylor-series math), how automatic differentiation works underneath torch.autograd.grad, and why tanh works for PINNs when ReLU doesn't — derived, not just asserted. T1 — A First-Order ODE. Your first PINN, taken apart line by line: the residual, the loss, the training loop, and what breaks when you remove the initial condition. T2 — A 1D Boundary Value Problem. Second derivatives, two boundary conditions, and where the 1D Poisson equation actually comes from physically. T3 — The Nonlinear Burgers' Equation. A genuinely nonlinear residual, a two-phase Adam → L-BFGS training strategy explained in full, because they're more instructive than a clean example would have been. By end, you'll be able to: Build a PINN from a blank file, for any 1D ODE or BVP Explain why every piece is there Debug a PINN that isn't converging, using the failure-mode patterns in this guide Run every example yourself along with notebook from Github Format: PDF (51 pages), ready to run with just torch, numpy, matplotlib, and scipy. Who this is for: Anyone comfortable with Python who's seen a derivative before. No numerical methods background required.

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