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name: gated_pinn_architecture description: Build a lightweight gated PINN-style scalar model that exposes trainable parameters and gradient paths for reduced recovery experiments.

Gated PINN Architecture

Use this skill when a PINN recovery wants to exercise the paper's improved architecture idea or compare it with a plain parameterization. The standard-library implementation is intentionally small for bounded recovery; full experiments may replace it with a neural-network library implementation.

Inputs

• Basis feature count or hidden width.
• Initialization seed.
• Whether to use gated feature mixing.

Outputs

• Trainable model parameters.
• Forward predictions for coordinate points.
• Parameter count and serializable state.

Workflow

1. Create sinusoidal Helmholtz-like basis functions.
2. Add trainable weights and optional gate scalars that mix coordinate transforms.
3. Expose prediction and finite-difference/free analytic derivatives needed by the loss module.
4. Return parameter snapshots before and after optimization.

Validation

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