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name: pinn_residual_objective description: Compute PINN data, boundary, and PDE residual losses for reduced failure-mode experiments.

PINN Residual Objective

Use this skill when a recovery harness must exercise the paper's soft PDE-constraint mechanism. Do not replace it with plain supervised error; the residual term is the central object being tested.

Inputs

• A benchmark object from periodic_pde_benchmark.
• A parametric prediction surrogate or model interface.
• PDE coefficient values and residual weight.

Outputs

• Loss decomposition containing initial-condition, periodic-boundary, residual, and total losses.
• Residual metadata identifying the coefficient used for the PDE operator.

Workflow

1. Evaluate initial-condition fit against benchmark targets.
2. Evaluate periodic boundary consistency at paired boundary points.
3. Compute convection residual u_t + beta*u_x for the chosen surrogate.
4. Combine losses as initial + boundary + residual_weight * residual.
5. Return the full decomposition for diagnostics and training traces.

Validation

Run python scripts/objective.py <benchmark.json> --speed 1 --beta 30 after creating a benchmark JSON, then run the tests in tests/.

Limitations

The included deterministic script supports analytic sinusoidal convection surrogates. Larger neural PINN implementations should preserve the same loss-field names and residual semantics.