Scientific models often encode boundary conditions, conservation properties, or admissible regions through their parameterization. A structural construction can enforce a specific property by design; a residual penalty asks training to reduce a violation.
Identify the guarantee
Specify the coordinates, domain, boundary behavior, and mathematical assumptions of the model class. Derivative primitives can evaluate its operators, but they do not automatically establish every physical constraint.
Validate the full problem
Combine operator checks with independent boundary and interior evaluation. Record the optimizer, sampling strategy, and convergence criteria. A small residual at sampled points alone is not a proof of global accuracy.