Symbolic Equation

This implements LLM-SR, an evolutionary algorithm where Claude proposes equation mutations instead of random ones. You feed it data with variable names and physical context, and it runs a multi-island search where each island clusters equations by performance, samples top candidates via softmax, and asks the LLM to improve them in versioned prompts. Islands reset periodically to maintain diversity. It's designed for symbolic regression when you want interpretable scientific equations, not just black box fits. The evolutionary loop is clever, using temperature scheduling and Occam's razor within clusters, but you'll need decent computational budget since it evaluates many candidate equations with parameter optimization.

skills.sh installs: 1.6K
GitHub stars: 459
last updated: Aug 21, 2026

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Install

$ npx -y skills add lingzhi227/agent-research-skills --skill symbolic-equation --agent claude-code

Installs into .claude/skills of the current project.

Files

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:

Input variables: Physical quantities with types (e.g., x: np.ndarray, v: np.ndarray)
Output variable: Target quantity to predict
Evaluation function: Fitness metric (typically negative MSE with parameter optimization)
Physical context: Domain knowledge to guide equation discovery

# Example specification
@equation.evolve
def equation(x: np.ndarray, v: np.ndarray, params: np.ndarray) -> np.ndarray:
    """Describe the acceleration of a damped nonlinear oscillator."""
    return params[0] * x