Evaluate the computation you will train

A useful evaluation separates implementation correctness, numerical accuracy, model approximation, and optimization behavior.

1. Compare a small operator example with an independent reference.
2. Assert shapes, dtype, and parameter-gradient availability.
3. Test representative and difficult inputs, including boundaries and singular regions.
4. Measure derivative evaluation and end-to-end training separately.
5. Evaluate the trained model on independent points and appropriate physical constraints.

Certificates and formal checks require their own domains and assumptions. Runtime speed alone does not validate a scientific conclusion. See benchmark methodology and numerical scope.