Heat-demo accuracy study¶

Results catalogue · Problem/reference · Validation

27 October 2026. CPU, float32, 2500 Adam updates, 144 interior grid points, 24 points per side, tanh 32×32 network. Evaluation: 41×41 coordinates, compared with the explicitly truncated 40-odd-mode rectangular series. No plots were changed.

Method	BC weight	Seed	RMSE	Maximum absolute error
baseline	10	7	0.0204918	0.0796043
baseline	10	17	0.0185791	0.0821636
baseline	10	27	0.0203726	0.0808272
baseline	100	7	0.0139774	0.0637816
baseline	100	17	0.0187275	0.0938645
baseline	100	27	0.014494	0.0599912
hard_dirichlet	1	7	0.00090309	0.00246223
hard_dirichlet	1	17	0.000932801	0.00241451
hard_dirichlet	1	27	0.000898833	0.00212636

The hard-Dirichlet method reduced field RMSE and maximum error for all three tested seeds and enforces the supported boundary values exactly. It is available as an explicit optional variant; the existing heat template remains baseline. Raising only the soft boundary penalty helped two seeds but worsened seed 17's maximum error, so a larger penalty was not made a universal default.

This is a narrow correctness/accuracy study, not a mesh-convergence or broad PDE benchmark. The hard variant still has a non-zero collocation residual (reported in the raw data) and is restricted to equal constant Dirichlet boxes. It does not establish GPU equivalence or accuracy on unrelated physics.

Reproduce with the root environment:

.venv/bin/python -m examples.benchmark_heat_accuracy --output benchmark-results/heat-reproduction.json

Choose a fresh output filename: the heat script permits overwriting. The original record is preserved, not rerun during the documentation update. It records Torch, time, evaluation grid/reference and per-run settings/losses/errors, but not a full environment/source snapshot. The file was introduced in commit 0e37a1e; that identifies artifact provenance rather than an inferred exact execution revision.

Raw per-run losses/errors and limited metadata: heat-accuracy.json.