shock-capturing-neural-operators

Architectures and techniques for neural operators on discontinuous PDE solutions (shocks, contact discontinuities, steep gradients). Covers local-global spectral design (ShockFNO), reflection padding for non-periodic BCs, resolution scaling for shock width, and frequency-band error diagnostics. Use for low-viscosity Burgers, compressible Euler, Riemann problems, or any PDE where standard FNO produces Gibbs oscillations.

Quality

80%

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Quality

Content

68%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 technically solid, well-structured reference with executable code and useful selection tables. Its main weakness is the absence of an explicit diagnostic-to-architecture feedback workflow, which keeps workflow clarity mid-range.

Suggestions

Add an explicit workflow that sequences the frequency-band error diagnostic as a validation checkpoint: diagnose error bands, then map high-band failure to a stronger architecture (e.g., graduate from Enhanced FNO to ShockFNO).

Replace the `...` placeholder in `ShockTubeFNO1d` with a minimal concrete FNO block instantiation or a clear note that standard FNO layers plug in here, so the example is fully executable.

Move the 'Future Directions' literature table into a separate reference file to keep the core SKILL.md lean and improve progressive disclosure.

Dimension	Reasoning	Score
Conciseness	The body is dense and data-rich with minimal padding, though the framing of the Gibbs phenomenon as 'a mathematical limitation, not a training problem' slightly over-explains a concept Claude already knows.	4 / 5
Actionability	Mostly executable guidance: complete `FNOBlock` and `frequency_band_errors` code blocks are copy-paste ready, but `ShockTubeFNO1d` uses `...` placeholders for the standard FNO layers, leaving a minor gap.	4 / 5
Workflow Clarity	Selection tables and a diagnostic tool provide implicit guidance (match problem to architecture, then check frequency-band errors), but there is no explicit sequenced workflow or validation checkpoint loop tying diagnosis back to architecture choice.	3 / 5
Progressive Disclosure	The skill is well-organized into clearly headed sections with easy navigation and no bundle files to traverse, though at ~130 lines the tangential 'Future Directions' literature table could be externalized.	4 / 5
	Total	15 / 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 a clear niche, lists concrete techniques, and provides an explicit 'Use for' trigger. The only gap is a few additional natural synonyms that practitioners might use.

Suggestions

Add a couple of common synonyms to the trigger clause (e.g., 'hyperbolic conservation laws', 'shock-tube problems') to broaden natural-term coverage.

Consider mentioning 'wavelet' or 'spectral methods' as alternate phrasings users may invoke when seeking shock-capturing approaches.

Dimension	Reasoning	Score
Specificity	The description enumerates multiple concrete capabilities — 'local-global spectral design (ShockFNO), reflection padding for non-periodic BCs, resolution scaling for shock width, and frequency-band error diagnostics' — giving comprehensive, specific coverage rather than vague abstractions.	5 / 5
Completeness	It explicitly answers both 'what' ('Architectures and techniques for neural operators on discontinuous PDE solutions') and 'when' via the concrete 'Use for low-viscosity Burgers, compressible Euler, Riemann problems, or any PDE where standard FNO produces Gibbs oscillations' trigger clause.	5 / 5
Trigger Term Quality	Natural practitioner terms are well covered ('low-viscosity Burgers, compressible Euler, Riemann problems', 'Gibbs oscillations', 'shocks, contact discontinuities, steep gradients'), but a few common synonyms like 'hyperbolic conservation laws' or 'shock tube' are absent.	4 / 5
Distinctiveness Conflict Risk	The niche is sharply defined — shock-capturing neural operators tied to Gibbs oscillations and FNO — with triggers unlikely to fire for unrelated skills, giving minimal conflict risk.	5 / 5
	Total	19 / 20 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/shock-capturing-neural-operators/SKILL.md
Commit: 5f2a37b

Reviewed: 4 days ago

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