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name: failure_mode_diagnostics description: Diagnose PINN failure-mode recovery runs with relative errors and optimizer progress checks.

Failure Mode Diagnostics

Use this skill when comparing PINN predictions or reduced proxy outputs to a target field. It is especially useful for deciding whether a run shows high-error soft-constraint failure or improvement from a proposed remedy.

Inputs

• Prediction and target arrays with matching shapes.
• Optional loss traces from vanilla or curriculum optimization.
• Relative-error thresholds for reduced recovery acceptance.

Outputs

• Relative L2 error and absolute L2 error.
• Boolean flags for high relative error, finite loss trace, and loss improvement.
• A concise text summary for recovery and analysis reports.

Workflow

1. Flatten prediction and target arrays while preserving numeric values.
2. Compute relative L2 error using a guarded target norm.
3. Compute root-mean-square absolute L2 error.
4. Check whether recorded losses are finite and improve.
5. Report metrics without claiming full reproduction unless the recovery target says so.

Validation

Run the tests in tests/; they check exact, shifted, and constant predictions.

Limitations

These diagnostics do not explain every loss-landscape property from the paper. They provide bounded executable evidence for recovery gating and refinement decisions.