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name: proxy_training_recovery description: Run bounded proxy PINN training comparisons that exercise residual construction, NTK weighting, and optimizer updates.

Proxy Training Recovery

Use this skill to produce executable recovery evidence for the NTK-PINN paper when full large-scale experiments are blocked or out of scope under soft recovery mode. The skill compares equal weighting with adaptive NTK weighting on a deterministic Poisson-style proxy.

Inputs

• Problem item from pinn_residual_problem.
• NTK diagnostics from ntk_block_spectrum.
• Adaptive weights from adaptive_ntk_weighting.
• Initial scalar parameters and optimizer settings.

Outputs

• Training trace with params_before, params_after, loss_before, and loss_after.
• Numeric comparison metric adaptive_loss_ratio_improvement.
• Mechanism checks showing residual loss, boundary loss, NTK traces, adaptive weights, and optimizer updates all ran.

Workflow

1. Use the problem item to define separated boundary and residual losses.
2. Use deterministic Jacobians to compute NTK block traces and Algorithm 1 weights.
3. Run equal-weight and adaptive-weight gradient steps from the same initial parameters.
4. Measure how close the component-loss ratio is to one after training.
5. Save logs that downstream Distiller validators can inspect.

Validation

Run:

python tests/test_proxy_training.py

The tests assert parameter updates, numeric losses, and improved adaptive component balance.

Limitations

This is a soft-mode proxy and must be declared as such. It is not a full reproduction of all paper figures, but it executes the core mechanism in a bounded way.