symbolic-equation

Q: How do I install symbolic-equation?

Run npx skills add https://github.com/lingzhi227/agent-research-skills --skill symbolic-equation in your project. The skills CLI detects the agents you use and copies the skill into the right folder. For Claude Code you can also place the skill folder at ~/.claude/skills/symbolic-equation/ (personal) or .claude/skills/symbolic-equation/ (project).

by lingzhi227AI & Agents

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.

Installs: 1.6K
Last 24h: —
Trending rank: —
Security: Not audited

Install

Works with every agent the skills CLI supports.

npx skills add https://github.com/lingzhi227/agent-research-skills --skill symbolic-equation

01
Install
Run the command in your project. The CLI asks which agents to install for.
02
Describe the task
Ask your agent for something this skill covers. It loads symbolic-equation automatically when relevant.
03
Review the result
The agent follows the SKILL.md steps, scripts and references bundled with the skill.

SKILL.md

The instructions your agent reads when the skill is triggered.

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

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:

Select island: Random island selection
Build prompt: Sample top equations from clusters (softmax-weighted by score)
LLM proposes: Generate new equation as improved version
Evaluate: Execute on test data, compute fitness score
Register: Add to island's cluster if valid

Step 4: Prompt Construction

Present previous equations as versioned sequence:

def equation_v0(x, v, params):
    """Initial version."""
    return params[0] * x

def equation_v1(x, v, params):
    """Improved version of equation_v0."""
    return params[0] * x + params[1] * v

def equation_v2(x, v, params):
    """Improved version of equation_v1."""
    # LLM completes this

Step 5: Island Reset (Diversity Maintenance)

Periodically (default: every 4 hours):

Sort islands by best score
Reset bottom 50% of islands
Seed each reset island with best equation from a surviving island
Restart cluster sampling temperature

Step 6: Extract Best Equations

After search completes:

Collect best equation from each island
Rank by fitness score
Simplify if possible (algebraic simplification)
Report with physical interpretation

Cluster Sampling

Temperature-scheduled softmax over cluster scores:

temperature = T_init * (1 - (num_programs % period) / period)
probabilities = softmax(cluster_scores / temperature)

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, math-reasoning
Downstream: paper-writing-section
See also: algorithm-design

FAQ

What does the symbolic-equation skill do?

How do I install symbolic-equation?

Run npx skills add https://github.com/lingzhi227/agent-research-skills --skill symbolic-equation in your project. The skills CLI detects the agents you use and copies the skill into the right folder. For Claude Code you can also place the skill folder at ~/.claude/skills/symbolic-equation/ (personal) or .claude/skills/symbolic-equation/ (project).

Which AI agents can use symbolic-equation?

Any agent that supports the open Agent Skills format (a folder with a SKILL.md file), including Claude Code, Codex, Cursor, GitHub Copilot, Gemini CLI, Windsurf, Cline, OpenCode and more.

Is symbolic-equation safe to install?

No partner security audit is available yet. Skills can run commands and scripts, so read the SKILL.md and any bundled files before installing.

Who maintains symbolic-equation?

It is published by lingzhi227 in lingzhi227/agent-research-skills. It has 1,563 recorded installs.