Discover scientific equations from data using LLM-guided evolutionary search (LLM-SR). Multi-island algorithm with softmax-based cluster sampling, island reset, and LLM-proposed equation mutations. Use for symbolic regression and equation discovery.

Symbolic Equation Discovery Discover interpretable scientific equations from data using LLM guided evolutionary search. Input $0 — Dataset description, variable names, and physical context References LLM SR patterns (prompts, evolution, sampling): ~/.claude/skills/symbolic equation/references/llmsr patterns.md Workflow (from LLM SR) Step 1: Define Problem Specification Create a specification with: 1. Input variables : Physical quantities with types (e.g., x: np.ndarray , v: np.ndarray ) 2. Output variable : Target quantity to predict 3. Evaluation function : Fitness metric (typically negative MSE with parameter optimization) 4. Physical context : Domain knowledge to guide equation discovery Step 2: Initialize Multi Island Buffer Create N islands (default: 10) for population diversity Each island maintains independent clusters of equations Clusters group equations by performance signature Step 3: Evolutionary Search Loop Repeat until convergence or max samples: 1. Select island : Random island selection 2. Build prompt : Sample top equations from clusters (softmax weighted by score) 3. LLM proposes : Generate new equation as improved version 4. Evaluate : Execute on test data, compute fitness score 5. Register : Add to island's cluster if valid Step 4: Prompt Construction Present previous equations as versioned sequence: Step 5: Island Reset (Diversity Maintenance) Periodically (default: every 4 hours): 1. Sort islands by best score 2. Reset bottom 50% of islands 3. Seed each reset island with best equation from a surviving island 4. Restart cluster sampling temperature Step 6: Extract Best Equations After search completes: 1. Collect best equation from each island 2. Rank by fitness score 3. Simplify if possible (algebraic simplification) 4. Report with physical interpretation Cluster Sampling Temperature scheduled softmax over cluster scores: Higher temperature → more exploration Lower temperature → more exploitation of best clusters Within clusters: shorter programs are preferred (Occam's razor) Rules Equations must use only standard mathematical operations Parameter optimization via scipy BFGS or Adam Fitness = negative MSE (higher is better) Timeout protection for equation evaluation No recursive equations allowed Physical interpretability is preferred over pure fit Related Skills Upstream: [data analysis](../data analysis/), [math reasoning](../math reasoning/) Downstream: [paper writing section](../paper writing section/) See also: [algorithm design](../algorithm design/)

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