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name: pinn_loss_decomposition description: Compute separated Helmholtz PINN residual and boundary losses so gradient imbalance can be diagnosed and corrected.

PINN Loss Decomposition

Use this skill when recovery needs separate PDE residual and boundary/data-fit loss terms. Do not collapse losses before gradient-statistic annealing.

Inputs

• A trainable model with coordinate predictions.
• Interior collocation points and forcing values.
• Boundary points and exact boundary values.
• Helmholtz parameters and current lambda values.

Outputs

• Residual loss.
• Boundary loss.
• Weighted total loss.
• Per-parameter gradients for residual and boundary losses when a compatible reduced model is used.

Workflow

1. Predict the solution on interior and boundary samples.
2. Compute the Helmholtz residual or a reduced residual proxy for the selected model family.
3. Compute mean-squared residual and boundary errors separately.
4. Combine them with current lambda weights only after logging the individual terms.

Validation

Run python scripts/losses.py --self-test or the skill tests.