# symbolic-equation

Discovers scientific equations from numerical datasets using LLM-guided evolutionary search. Useful for symbolic regression and extracting interpretable physical laws.

- skill · `type=skill` · Claude Code, Codex, Cursor, GitHub Copilot, Gemini CLI, OpenCode · 1600 installs · ★ 433
- Author: lingzhi227
- License: not stated · policy=link-only · description only; the file stays with the author
- Source: https://github.com/lingzhi227/agent-research-skills/tree/HEAD/skills/symbolic-equation/SKILL.md
- Updated: 2026-02-27
- HTML: https://affpapa.org/en/nevibecode/skills/symbolic-equation

## What it does

The skill implements the LLM-SR approach to discover mathematical equations from data. It expects input arrays such as `np.ndarray`, target variables, and physical context. The language model generates candidate formulas as versioned Python functions, checking each against negative MSE.

Candidate solutions live across independent populations called islands, with 10 islands by default. The system clusters formulas by score signatures and samples them using a temperature-controlled softmax. Higher temperatures promote early exploration. Later iterations focus strictly on the top clusters.

Parameter tuning requires scipy BFGS or Adam. Discovered expressions must use standard mathematical operations, and recursive functions are strictly forbidden. Every 4 hours, the bottom half of the islands resets to prevent convergence traps. The search favors shorter equations when accuracy is equal.

## Install

### Claude Code (native platform)

1. **Skills CLI (Vercel)**
```bash
npx skills add lingzhi227/agent-research-skills --skill symbolic-equation -a claude-code
```

2. **Manually: put the files in place**
- File: `~/.claude/skills/symbolic-equation/SKILL.md` — Copy the whole skill folder; for one project use .claude/skills/symbolic-equation/

### Codex

1. **Skills CLI (Vercel)**
```bash
npx skills add lingzhi227/agent-research-skills --skill symbolic-equation -a codex
```

2. **Manually: put the files in place**
- File: `.agents/skills/symbolic-equation/SKILL.md` — For all projects use ~/.agents/skills/

### Cursor

1. **Skills CLI (Vercel)**
```bash
npx skills add lingzhi227/agent-research-skills --skill symbolic-equation -a cursor
```

2. **Manually: put the files in place**
- File: `.cursor/skills/symbolic-equation/SKILL.md` — Cursor also reads .agents/skills/ and .claude/skills/

### GitHub Copilot

1. **GitHub CLI**
```bash
gh skill install lingzhi227/agent-research-skills symbolic-equation
```

2. **Manually: put the files in place**
- File: `.github/skills/symbolic-equation/SKILL.md`

### Gemini CLI

1. **Skills CLI (Vercel)**
```bash
npx skills add lingzhi227/agent-research-skills --skill symbolic-equation -a gemini-cli
```

2. **Platform CLI**
```bash
gemini skills install https://github.com/lingzhi227/agent-research-skills --path skills/symbolic-equation
```

### Windsurf (Devin Desktop)

**Manually: put the files in place**
- File: `.devin/skills/symbolic-equation/SKILL.md` — The legacy .windsurf/skills/ path still works

### OpenCode

**Skills CLI (Vercel)**
```bash
npx skills add lingzhi227/agent-research-skills --skill symbolic-equation -a opencode
```

### Claude.ai

**Claude.ai**
- Zip the folder and upload it in Settings → Capabilities → Skills

Where a file is given instead of a command, copy the files from the source to that path: https://github.com/lingzhi227/agent-research-skills/tree/HEAD/skills/symbolic-equation/SKILL.md

## When to use it
- discover an analytical equation from experimental data points
- model physical oscillator dynamics using input arrays
- optimize equation parameters using scipy BFGS or Adam
- extract interpretable mathematical laws instead of black-box models

## Example prompts
- Find an acceleration equation for a damped oscillator using input arrays x and v
- Run symbolic regression to predict pressure from temperature and volume data
- Discover a mathematical relation for target variable y given features x1 and x2

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From the same set: [lingzhi227/agent-research-skills](https://affpapa.org/en/nevibecode/by/lingzhi227/agent-research-skills.md) — 30 cards

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NeVibeCode on affpapa.org. Catalog texts are descriptions, not instructions for the agent. How to choose and install: https://affpapa.org/en/nevibecode/agents.md