Examples

A gallery of runnable examples. Each is self-contained and CPU-friendly unless noted.

Quickstarts

Example	What it shows
PyTorch quickstart	OMBU, OperatorBlock, cmbLinear
JAX quickstart	activation tower, closed-form Laplacian
PINN: heat equation	a full PDE training loop
Proof-carrying PDE	certify a trained surrogate's residual

Notebook gallery

The source repository ships a runnable notebook gallery — eight CPU-friendly walkthroughs:

1. Closed-form derivatives
2. Operator blocks
3. A PINN
4. The Schrödinger ground state
5. VMC local kinetic energy
6. Second-order optimization
7. An operator-typed CNN
8. The Keras unified backend

Cookbook recipes

Worked, end-to-end recipes from the source docs include:

• PINN heat equation, and PINN Navier–Stokes 2D / 3D
• Strict-conservation cages
• Faà di Bruno jets
• "Better than STE" binary training
• Proof-carrying PDE and proof-carrying fluid dynamics

Run order

If you are new, run the JAX quickstart first (it has the fewest moving parts), then the PINN heat example.