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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.

71

Quality

87%

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SecuritybySnyk

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SKILL.md
Quality
Evals
Security

Quality

Content

82%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, highly actionable reference of neural-PDE training patterns with executable code and useful decision/pitfall tables. It is concise and well-structured; the main opportunity is adding an explicit validation/feedback loop around the autoregressive training step and optionally splitting the longer formula blocks into a reference file.

Suggestions

Add an explicit validation checkpoint inside the rollout-training loop (e.g. 'evaluate val nRMSE every N epochs; if it diverges, reduce NOISE_STD / shorten rollout horizon') to close the workflow_clarity gap for a batch/iterative operation.

Consider moving the full nRMSE and multi-component loss implementations into a references/ file, keeping SKILL.md as an overview with the decision table and key snippets, to improve progressive_disclosure given the 187-line body.

Trim a few redundant inline code comments (e.g. '# Always sees perfect input', '# Shift window, append prediction') that restate the surrounding prose, to nudge conciseness toward fully lean.

DimensionReasoningScore

Conciseness

The body is lean and assumes competence (no basic-concept padding); prose like 'The single biggest mistake ...' and the nRMSE WARNING earn their place as domain-specific insight, though a few framing sentences and inline comments could still be trimmed.

4 / 5

Actionability

Provides fully executable, copy-paste-ready functions (h1_loss, frequency_loss, calc_nrmse_pertimestep, calc_nrmse_frobenius, denormalize) plus specific hyperparameter values (NOISE_STD, loss weights) and a problem-type decision table covering the common cases.

5 / 5

Workflow Clarity

The Train/Val/Test split gives a clear sequenced workflow with checkpoints (val for selection, test evaluated ONCE), the nRMSE section requires verifying against both formulas, and the Common Pitfalls table supplies error-recovery guidance; minor validation gaps remain in the rollout-training loop itself.

4 / 5

Progressive Disclosure

Well-organized with clear section headers and no nested references; content is self-contained and cohesive. At ~187 lines it exceeds the 50-line simple-skill threshold, so a couple of the longer reference-style blocks (detailed loss/metric implementations) could optionally be split out, but the current single-level structure is navigable.

4 / 5

Total

17

/

20

Passed

Description

92%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.

A strong, specific description that names concrete capabilities and gives an explicit 'Use when' trigger for a well-defined niche. Trigger-term coverage is good but could add a couple more natural synonyms to be fully comprehensive.

DimensionReasoningScore

Specificity

Lists multiple concrete techniques — 'rollout training, noise injection for stability, multi-component loss functions (H1, frequency-sensitive, boundary-aware), per-channel normalization ... and the PDEBench nRMSE metric' — giving comprehensive, specific coverage rather than vague abstractions.

5 / 5

Completeness

Explicitly answers both what ('Training patterns for ... Covers rollout training, noise injection ...') and when ('Use when training any neural operator that predicts time-dependent PDE solutions.'), with concrete trigger phrasing.

5 / 5

Trigger Term Quality

Includes natural domain terms and synonyms a practitioner would say — 'FNO, DeepONet, CNO', 'neural operator', 'time-dependent PDE solutions' — but a few adjacent natural phrases (e.g. 'operator learning', 'spectral neural operator') are absent, keeping it just below comprehensive.

4 / 5

Distinctiveness Conflict Risk

Occupies a clear niche (autoregressive neural PDE solvers) with distinct, specialized triggers that would not plausibly fire for unrelated skills, so conflict risk is minimal.

5 / 5

Total

19

/

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.

Validation15 / 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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