---

name: periodic_pde_benchmark description: Build deterministic periodic PDE benchmarks for PINN failure-mode recovery experiments.

Periodic PDE Benchmark

Use this skill when a recovery or evaluation task needs a small synthetic PDE benchmark matching the PINN failure-mode paper. Do not use it for unrelated PDE families or as evidence of full paper-scale reproduction.

Inputs

• PDE system and coefficients, currently convection for deterministic reduced recovery.
• Grid sizes, collocation count, and random seed.
• Periodic spatial domain and time horizon assumptions.

Outputs

• A JSON-compatible benchmark with evaluation grid, exact target values, collocation points, boundary pairs, and initial-condition samples.
• Metadata identifying coefficient values and exact/proxy target type.

Workflow

1. Choose the smallest system that tests the paper mechanism, usually periodic convection.
2. Build x and t grids on [0, 2π] × [0, 1].
3. Compute u(x,t)=sin(x-beta*t) for exact convection targets.
4. Generate seeded collocation points and periodic boundary pairs.
5. Save the benchmark or pass it directly to residual-objective and diagnostics skills.

Validation

Run python scripts/benchmark.py --beta 30 --x-points 8 --t-points 4 --collocation-count 5 and run the tests in tests/.

Limitations

This skill provides a reduced exact convection benchmark. Full reaction-diffusion data generation should extend the same contract and declare numerical target provenance.