julia-mastery

Imported from imewei/MyClaude (plugins/science-suite/skills/julia-mastery/SKILL.md). Install upstream with npx skills add imewei/MyClaude --skill julia-mastery. Copyright stays with the author.

Loading a routing target. dev-suite:*, research-suite:*, and science-suite:* targets below are slash-only (disable-model-invocation: true) — the Skill tool will not fire them. Load one by reading its file with the Read tool at ${CLAUDE_PLUGIN_ROOT}/skills/<name>/SKILL.md — Claude Code substitutes that variable with this plugin's install directory. A target in a sibling suite is at the same relative path under that suite's own root. Targets from other plugins (superpowers:*, ecc:*, …) are unaffected and invoke normally.

Julia Mastery

Expert guide for writing high-performance, idiomatic Julia code for scientific applications.

Expert Agent

For complex Julia programming, SciML workflows, and performance optimization, delegate to the expert agent:

• julia-pro: Unified specialist for Julia optimization, including Core Julia, SciML (Lux.jl, UDEs), nonlinear dynamics (DynamicalSystems.jl, AUTO-07p -- BifurcationKit.jl blocked on Julia 1.12), Turing.jl, and Package Development.
  • Location: ${CLAUDE_PLUGIN_ROOT}/agents/julia-pro.md
  • Capabilities: Performance tuning, stiff ODE solvers, Bayesian inference, UDEs, bifurcation analysis, equation discovery, and CI/CD setup.

Core Skills

Core Julia Patterns

Multiple dispatch, type stability, and functional programming.

SciML Ecosystem

Unified framework for scientific machine learning and modeling.

Differential Equations

High-performance ODE, PDE, SDE, and DAE solvers.

ModelingToolkit

Symbolic-numeric modeling and acausal system design.

Neural PDE

Physics-informed neural networks (PINNs) in Julia.

Turing Model Design

Bayesian inference and probabilistic programming.

Performance Tuning

Memory optimization, type stability, and benchmarking.

Package Development

Scaffolding, testing, and CI/CD for Julia packages.

Variational Inference Patterns

ADVI and approximate inference with Turing.jl.

Optimization Patterns

Non-linear optimization and parameter estimation with Optimization.jl.

Jump Optimization

Mathematical programming (LP, QP, MIP) with JuMP.jl.

MCMC Diagnostics

Convergence checking and chain analysis.

Julia Testing Patterns

Robust testing strategies with ReTestItems.jl and Aqua.jl.

Package Management

Environment management and Pkg.jl workflows.

Catalyst Reactions

Chemical reaction network modeling.

Visualization Patterns

Data visualization with Makie.jl and Plots.jl.

Web Development

Building scientific web services with Genie.jl/Oxygen.jl.

Modern SciML Stack

Lux.jl, Universal Differential Equations (UDEs), SciMLSensitivity.jl, NeuralPDE.jl v5+.

Nonlinear Dynamics

Bifurcation analysis, chaos, network dynamics, pattern formation, equation discovery.

Interop Patterns

Calling Python and R from Julia.

CI/CD Patterns

GitHub Actions for Julia packages.

Compiler Patterns

PackageCompiler.jl and system images.

Parallel Computing

Multi-threading and distributed computing patterns.

Routing Decision Tree

What is the primary Julia task?
|
+-- Core language: dispatch, type system, metaprogramming, or functional patterns?
|   --> science-suite:core-julia-patterns
|
+-- SciML ecosystem overview or package selection?
|   --> science-suite:sciml-ecosystem
|
+-- ODE / PDE / SDE / DAE solvers?
|   --> science-suite:differential-equations
|
+-- Symbolic-numeric modeling with ModelingToolkit?
|   --> science-suite:modeling-toolkit
|
+-- Physics-informed neural networks (PINNs) in Julia?
|   --> science-suite:neural-pde
|
+-- Bayesian inference or probabilistic programming with Turing.jl?
|   --> science-suite:turing-model-design
|
+-- Memory, type-stability, benchmarking, or allocation profiling?
|   --> science-suite:performance-tuning
|
+-- Package scaffolding, testing, or CI/CD setup?
|   --> science-suite:package-development-workflow
|
+-- Variational inference or ADVI with Turing.jl?
|   --> science-suite:variational-inference-patterns
|
+-- Non-linear optimization or parameter estimation with Optimization.jl?
|   --> science-suite:optimization-patterns
|
+-- Mathematical programming (LP / QP / MIP) with JuMP.jl?
|   --> science-suite:jump-optimization
|
+-- MCMC diagnostics, R-hat, ESS, or chain convergence?
|   --> science-suite:mcmc-diagnostics
|
+-- Writing tests with ReTestItems.jl or Aqua.jl?
|   --> science-suite:julia-testing-patterns
|
+-- Environment management or Pkg.jl workflows?
|   --> science-suite:package-management
|
+-- Chemical reaction network modeling with Catalyst.jl?
|   --> science-suite:catalyst-reactions
|
+-- Data visualization with Makie.jl or Plots.jl?
|   --> science-suite:visualization-patterns
|
+-- Scientific web services with Genie.jl or Oxygen.jl?
|   --> science-suite:web-development-julia
|
+-- Lux.jl neural networks, UDEs, or SciMLSensitivity?
|   --> science-suite:sciml-modern-stack
|
+-- Bifurcation analysis, chaos, network dynamics, or equation discovery?
|   --> science-suite:nonlinear-dynamics
|
+-- Calling Python or R from Julia?
|   --> science-suite:interop-patterns
|
+-- GitHub Actions for Julia packages?
|   --> science-suite:ci-cd-patterns
|
+-- PackageCompiler.jl or system images?
|   --> science-suite:compiler-patterns
|
+-- Multi-threading or distributed computing patterns?
|   --> science-suite:parallel-computing
|
+-- None of the above / concern is ambiguous or spans multiple areas?
    --> Delegate to julia-pro for open-ended triage, or clarify the
        primary concern and re-enter the routing decision tree.

1. Multiple Dispatch & Type System

• Multiple Dispatch: Design functions that specialize based on all argument types.
• Abstract Types: Use abstract types (e.g., AbstractVector) in function signatures for flexibility.
• Concrete Types: Use concrete types in struct fields to ensure type stability and performance.
• Parametric Types: Write generic code that specializes at compile-time for specific types.

2. Performance Optimization

• Type Stability: Use @code_warntype to detect instabilities (red/pink output). Ensure return types are predictable.
• Allocations: Minimize allocations in hot loops by preallocating arrays and using mutating functions (ending in !).
• SIMD & Inbounds: Use @simd and @inbounds (after safety checks) to maximize loop performance.
• StaticArrays: Use StaticArrays.jl for small, fixed-size vectors and matrices to enable stack allocation.

3. The SciML Ecosystem

• Lux.jl: Modern neural networks with explicit parameterization (replaces Flux for SciML). See sciml-modern-stack skill.
• DifferentialEquations.jl: State-of-the-art solvers for ODEs, PDEs, SDEs, and DAEs.
• ModelingToolkit.jl: Symbolic-numeric modeling for simplifying complex systems.
• SciMLSensitivity.jl: Adjoint and forward sensitivity analysis through solvers.
• Optimization.jl: Unified interface for local and global optimization.
• DataDrivenDiffEq.jl: SINDy and equation discovery from data. See equation-discovery skill.
• NeuralPDE.jl: Physics-informed neural networks (PINNs) for solving PDEs.

4. Julia Development Workflow

• Profiling: Use BenchmarkTools.jl for timing and ProfileView.jl for bottleneck identification.
• Metaprogramming: Use macros (@macro) for code generation, but prefer functions when possible. Ensure macros use esc() to avoid hygiene issues.
• Package Management: Use Pkg for managing environments and dependencies.
• Parallelism: Leverage Threads.@threads for shared memory and Distributed for multi-node parallelism.

Checklist

• Verify type stability with @code_warntype on all performance-critical functions
• Confirm struct fields use concrete types (not abstract) for allocation efficiency
• Check that hot loops preallocate output arrays and use mutating functions (ending in !)
• Validate multiple dispatch design: methods specialize on all argument types as intended
• Ensure @simd and @inbounds are applied only after correctness is verified
• Use BenchmarkTools.@btime (not @time) for accurate performance measurements
• Confirm Manifest.toml is committed for reproducible environments
• Check that macros use esc() correctly to avoid hygiene issues
• Validate SciML solver selection matches problem stiffness and accuracy requirements