PINNs You Can Defend — POLYMATHICA Edition

A falling neural-network loss curve is not proof that a physics-informed neural network has learned the correct physics.

PINNs You Can Defend is a 32-page specialist POLYMATHICA edition grounded in the real VortX PhysicsNeMo heated-channel PINN workflow.

It goes far beyond generic PINN theory. You will work through the governing continuity, momentum and energy equations; collocation and boundary sampling; training configuration; PDE residual losses; field-level validation; independent finite-difference reference comparison; provenance; failure diagnosis and experiment design.

The book includes the real bounded heated_channel_2d request structure, the validated 1,000-epoch reference configuration, real validation metrics, a controlled ten-experiment improvement matrix, seed-robustness studies and a practical 15-minute PINN audit.

Built for scientific-ML engineers, PhysicsNeMo users, CFD researchers and serious PINN practitioners.