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autoregressive-neural-pde-solver

Training patterns for autoregressive neural PDE solvers (FNO, DeepONet, CNO). Covers rollout training, noise injection for stability, multi-component loss functions (H1, frequency-sensitive, boundary-aware), per-channel normalization for coupled multi-variable systems, and the PDEBench nRMSE metric. Use when training any neural operator that predicts time-dependent PDE solutions.

76

Quality

95%

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SKILL.md
Quality
Evals
Security

Quality

Content

90%Weight 40%Scale 1-5

Reviews the quality of instructions and guidance provided to agents. Good implementation is clear, handles edge cases, and produces reliable results.

A dense, expert-level pattern reference: executable code for every technique, a symptom→fix pitfalls table, and genuine validation checkpoints (val/test discipline, dual-metric reporting). The only weaknesses are the absence of an explicit ordered workflow with error-recovery loops and a monolithic single-file layout that could offload reference detail to keep the body leaner.

Suggestions

Add a short numbered workflow section (data layout → split → training loop with noise → loss selection → val-based checkpointing → one-shot test evaluation) so the topical sections read as an explicit pipeline with feedback loops (e.g., 'if rollout diverges after ~10 steps, re-check noise σ and layout', expanding the pitfalls row into a retry step).

Move the full loss-function implementations and the two nRMSE variants into a references/ file (e.g., references/losses.md, references/metrics.md), keeping one-line summaries and usage weights in SKILL.md, to bring the body closer to a lean overview with one-level-deep references.

Fix the small code smell of two consecutive NOISE_STD assignments (1e-3 then 5e-3) by making the value a single configurable constant or a commented choice, so the snippet is unambiguous when copied verbatim.

DimensionReasoningScore

Conciseness

The body is lean and code-forward: every section delivers a pattern as executable Python plus a one-line rationale ("This prevents the model from relying on artificially clean inputs"), and it assumes Claude's competence by never explaining what FNO, PDEs, or teacher forcing are. The only near-redundancy is the short noise-level bullet list echoing the code comments, which is minor and matches the level-5 anchor; level 4 would require trimmable over-explanation, which is not present.

5 / 5

Actionability

Guidance is copy-paste ready throughout: a complete rollout training loop with tensor shapes ("inp = torch.cat([inp[:, :, 1:, :], pred], dim=-2)"), working h1_loss / frequency_loss / boundary-weighting implementations, both PDEBench-style nRMSE functions, a concrete 8000/1000/1000 split, and a pitfalls table with symptom→fix pairs. This matches the level-5 anchor (fully executable, covering common cases) rather than level 4's 'minor gaps'.

5 / 5

Workflow Clarity

Sections follow a coherent training-pipeline order (data layout → rollout training → noise → losses → normalization → metric → split → pitfalls) with real checkpoints: validation split for "Checkpoint selection", test "evaluated ONCE", and "Always compute BOTH and verify you beat baselines under both". It falls short of level 5 because there is no explicit step-by-step sequence with feedback/recovery loops (e.g., what to do when rollout diverges beyond the one-line pitfalls table), but it is clearly above level 3, where checkpoints would be merely implicit.

4 / 5

Progressive Disclosure

The skill is a single self-contained file with well-organized, clearly headed sections and no nested or chained references — nothing is buried and navigation is easy. It scores 4 rather than 5 because at ~190 lines some reference-grade detail (full loss-function variants, nRMSE discussion) is inlined in SKILL.md where a one-level-deep references/ file would keep the overview leaner; it is well above level 3, since the structure is good and no content is misplaced or hidden.

4 / 5

Total

18

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20

Passed

Description

100%Weight 40%Scale 1-5

Based on the skill's description, can an agent find and select it at the right time? Clear, specific descriptions lead to better discovery.

An exemplary description: specific, dense, and correctly voiced, with an explicit 'Use when...' trigger clause and comprehensive domain vocabulary. Both what the skill does and when to reach for it are answered concretely without any padding.

DimensionReasoningScore

Specificity

The description enumerates multiple concrete capabilities — "rollout training, noise injection for stability, multi-component loss functions (H1, frequency-sensitive, boundary-aware), per-channel normalization... and the PDEBench nRMSE metric" — with no vague filler. Coverage within the stated domain is comprehensive, matching the level-5 anchor rather than the 'several specific actions; minor gaps' of level 4.

5 / 5

Completeness

It explicitly answers both questions: what it does ("Training patterns... Covers rollout training, noise injection, multi-component loss functions...") and when to use it ("Use when training any neural operator that predicts time-dependent PDE solutions"). This matches the level-5 good_overall_example structure exactly; level 4 would leave the 'when' less explicit.

5 / 5

Trigger Term Quality

Natural terms a practitioner would actually say are comprehensively covered with synonyms: "training", "autoregressive", "neural PDE solvers", "FNO", "DeepONet", "CNO", "neural operator", "rollout", "PDEBench", "nRMSE", "time-dependent PDE solutions". These are the domain's real vocabulary (not jargon-avoidant or generic); level 4 would require noticeably missing variations, and none are apparent for this domain.

5 / 5

Distinctiveness Conflict Risk

The niche is tightly scoped to autoregressive neural-operator training with distinct, domain-specific triggers (FNO/DeepONet/CNO, rollout, PDEBench), creating minimal overlap risk with generic ML training or physics-informed skills. Level 4's 'minor overlap risk with closely related skills' does not apply — the trigger set is unambiguous.

5 / 5

Total

20

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20

Passed

Validation

93%

Checks the skill against the spec for correct structure and formatting. All validation checks must pass before discovery and implementation can be scored.

Validation — 15 / 16 Passed

Validation for skill structure

CriteriaDescriptionResult

frontmatter_unknown_keys

Unknown frontmatter key(s) found; consider removing or moving to metadata

Warning

Total

15

/

16

Passed

Repository
synthetic-sciences/openscience
Reviewed

Table of Contents

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