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name: adaptive_ntk_weighting description: Compute Algorithm 1 PINN loss weights from NTK trace ratios with degeneracy checks and diagnostics.

Adaptive NTK Weighting

Use this skill after computing PINN NTK block traces. It implements the trace-ratio weighting rule proposed for calibrating convergence rates of different loss components.

Inputs

• trace_full: trace of the combined boundary-plus-residual NTK.
• trace_kuu: boundary-output kernel trace.
• trace_krr: residual-operator kernel trace.
• Optional epsilon for rejecting degenerate traces.

Outputs

• lambda_b = trace_full / trace_kuu.
• lambda_r = trace_full / trace_krr.
• A diagnostic indicating which component receives the stronger weight.

Workflow

1. Validate traces are finite and nonnegative.
2. Reject component traces below epsilon instead of silently dividing by zero.
3. Compute trace-ratio weights exactly as Algorithm 1 states.
4. Preserve component names so a recovery harness applies weights to the correct losses.

Validation

Run:

python tests/test_adaptive_weights.py

The tests verify the paper's ratio formulas and that the smaller-trace component receives a larger weight.

Limitations

The skill does not tune learning rates or batch sizes. It only computes the NTK-based loss weights used by a downstream training loop.