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.

Quality

90%

Does it follow best practices?

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Securityby

Passed

No findings from the security scan

Quality

Content

80%

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

A token-efficient, highly actionable reference packed with executable patterns and prescriptive tables. Its main gaps are the absence of an explicit sequenced workflow with validation checkpoints and a lack of progressive disclosure via separate reference files.

Suggestions

Add a short numbered end-to-end training workflow with explicit validation checkpoints (e.g. train → check val nRMSE → verify both nRMSE formulas beat baseline → report) to lift workflow_clarity.

Move the longer, self-contained code blocks (loss implementations, the dual nRMSE metric) into reference files under references/ and link to them from SKILL.md to introduce genuine one-level-deep progressive disclosure.

Make the validation/feedback loop explicit in the nRMSE section — state the pass condition and what to do if a baseline is not beaten.

Dimension	Reasoning	Score
Conciseness	The body is dense and assumes competence — code, tight commentary, and tables — without explaining concepts Claude already knows (no 'what is a PDE' or library introductions), so most tokens earn their place.	3 / 3
Actionability	It provides copy-paste-ready, executable code with concrete shapes, weights, and noise levels (e.g. NOISE_STD values, h1_loss, frequency_loss) plus a recommended-combinations table, matching the fully-executable anchor.	3 / 3
Workflow Clarity	Sections are logically ordered (principle → data → noise → loss → normalization → metric → split → pitfalls) but there is no explicit step sequence with validation checkpoints; validation is only implicit ('verify you beat baselines under both'), so it sits at the level-2 anchor rather than 3.	2 / 3
Progressive Disclosure	The document is well-sectioned but monolithic — all content is inline in SKILL.md with no bundle files or one-level-deep references, and at ~190 lines it exceeds the under-50-line exception, so the level-2 anchor (good structure, content that could be split is inline) fits better than 3.	2 / 3
	Total	10 / 12 Passed

Description

100%

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 precise, third-person description that names concrete capabilities and provides an explicit usage trigger with natural domain terminology. It cleanly satisfies the what/when pair and is highly distinct.

Dimension	Reasoning	Score
Specificity	The description lists multiple concrete capabilities — 'rollout training, noise injection for stability, multi-component loss functions (H1, frequency-sensitive, boundary-aware), per-channel normalization... PDEBench nRMSE metric' — matching the anchor for enumerating several specific actions.	3 / 3
Completeness	It answers both what ('Training patterns... Covers rollout training, noise injection...') and when via an explicit 'Use when...' clause, satisfying the top anchor and avoiding the missing-trigger cap at 2.	3 / 3
Trigger Term Quality	It surfaces the natural domain vocabulary a practitioner would actually say — 'FNO, DeepONet, CNO', 'neural operator', 'PDE solutions' — plus the explicit 'Use when training any neural operator that predicts time-dependent PDE solutions' trigger.	3 / 3
Distinctiveness Conflict Risk	The niche — autoregressive neural PDE solvers with named operator families — is narrow and clearly distinct, with triggers unlikely to fire for unrelated skills.	3 / 3
	Total	12 / 12 Passed

Validation

93%

Warnings & errors only

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

Criteria	Description	Result
frontmatter_unknown_keys	Unknown frontmatter key(s) found; consider removing or moving to metadata	Warning

	Total	15 / 16 Passed

Repository: synthetic-sciences/openscience
Path: backend/cli/skills/physics/autoregressive-neural-pde-solver/SKILL.md
Commit: 52845c3

Reviewed: about 9 hours ago

Table of Contents

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