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name: gradient_stat_annealing description: Update PINN data-loss weights from residual and data-fit gradient statistics using the paper's moving-average annealing rule.

Gradient Statistic Annealing

Use this skill when a composite PINN loss keeps residual and data-fit losses separate and needs the paper's adaptive lambda update. Do not use it when only aggregate loss gradients are available.

Inputs

• Residual-gradient magnitudes or a residual-gradient vector.
• One or more data-fit gradient vectors.
• Current lambda values.
• Smoothing coefficient alpha and numerical epsilon.

Outputs

• Updated lambdas.
• Instantaneous lambda estimates.
• Residual max-gradient statistic and data mean-gradient statistics.
• Balance ratios for recovery mechanism checks.

Workflow

1. Compute max(abs(grad L_r)).
2. Compute mean(abs(grad L_i)) for each data-fit loss.
3. Compute lambda_hat_i = max_grad_r / (mean_grad_i + epsilon).
4. Apply lambda_i = (1 - alpha) * lambda_i + alpha * lambda_hat_i.
5. Log all values in the training trace.

Validation

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