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Agent skill

Define Equations

by PINA-org in PINA-org/PINA

Define PDEs, ODEs, boundary conditions, and custom equations for PINA physics-driven problems.

MITAuto-check passedAI & LLM Engineering

Install Define Equations

skills CLI
$ npx skills add PINA-org/PINA --skill define-equations -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install PINA-org/PINA define-equations --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ git clone --depth 1 https://github.com/PINA-org/PINA.git skills-src && mkdir -p .claude/skills && cp -r skills-src/.opencode/skills/define-equations .claude/skills/define-equations && rm -rf skills-src

Use ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.

Claude Code skills documentation · loads skills from .claude/skills/

Facts

Skill name
define-equations
GitHub stars
798
Token cost
~1.2k tokens
SKILL.md length
399 words
Files
2
Skills in repo
10
Repo updated
First seen
Licence
MIT

At a glance

Define PDEs, ODEs, boundary conditions, and custom equations for PINA physics-driven problems.

  • Works in 5 steps: Check the equation zoo → Unknown equation → Define boundary conditions → …
  • Tasks that involve Deep learning
  • SKILL.md covers Step 1 — Check the equation zoo, Step 2 — Unknown equation, Step 3 — Define boundary… and Step 4 — Custom equation…, plus 2 more sections
  • Instructions only: no scripts, shell commands, URLs or credentials in SKILL.md

What it does

Define Equations is an agent skill from PINA-org/PINA. Define PDEs, ODEs, boundary conditions, and custom equations for PINA physics-driven problems. Covers the equation zoo, custom equation functions, and inverse problem equation signatures.

Its SKILL.md is about 1.2k tokens, which your agent loads only when the skill is triggered. The skill folder holds 1 other file (for example `famous_odes_pdes.json`). Compatibility notes: opencode, codex, claude

It sits in AI & LLM Engineering, covering Deep learning. The repository describes itself as: Physics-Informed Neural networks for Advanced modeling. The licence is MIT.

When your agent uses it

  • Tasks that involve Deep learning

Example prompts

  • “/define-equations”

Requirements

  • Python 3
  • Compatibility (from SKILL.md): opencode, codex, claude

Workflow steps

5 steps, taken from the step headings in SKILL.md.

  1. Check the equation zoo
  2. Unknown equation
  3. Define boundary conditions
  4. Custom equation functions
  5. Build conditions

What it can do on your machine

Read from SKILL.md and the folder at commit 0cd8afb. It shows what the files ask for, not the result of running them.

  • Tool permissions

    Pre-approves nothing: there is no allowed-tools line, so your agent's usual permission prompts apply.

    From allowed-tools in the SKILL.md frontmatter.

  • Runs code

    No scripts in the folder and no shell commands in SKILL.md (its code samples are python).

    From the folder's file list and the shell code blocks in SKILL.md.

  • Network

    No URLs in SKILL.md.

    From URLs in SKILL.md, links to its own repository left out.

  • Credentials

    Names no API keys, tokens, secrets or passwords.

    From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

  • Compatibility

    opencode, codex, claude

    From compatibility in the SKILL.md frontmatter.

Context cost

Define Equations loads about 1.2k tokens when it runs. Until then it costs about 51 tokens; SKILL.md has 399 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~51
When it runs · the whole SKILL.md, loaded when a task matches
~1.2k

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Auto-check passed

The automated check found no risky patterns in SKILL.md.

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.

SKILL.md

The full file from PINA-org/PINA at commit 0cd8afb, republished under its MIT licence (© PINA-org). 399 words, ~1,158 tokens.

Download SKILL.mdSave it as .claude/skills/define-equations/SKILL.md (or your agent's skills folder). This skill also uses 1 other file; get the full folder from GitHub.
name
define-equations
description
Define PDEs, ODEs, boundary conditions, and custom equations for PINA physics-driven problems. Covers the equation zoo, custom equation functions, and inverse problem equation signatures.
compatibility
opencode, codex, claude
license
MIT
metadata.audience
users
metadata.workflow
problem-creation

Define Equations for a PINA Problem

[!IMPORTANT] Read RULES.md before using this skill — it applies to all skills. This is a sub-skill of create-problem. Load the entry-point skill first.

Use this skill when the problem is physics-driven and you need to define the governing equations and boundary conditions.

Step 1 — Check the equation zoo

What physical equations apply?

First check if the equation is available in the built-in zoo:

Zoo classEquation
FixedValue(value)u - v = 0 (Dirichlet BC)
FixedGradient(value)∂u/∂n - v = 0 (Neumann BC)
FixedFlux(value)div(u) - v = 0 (flux BC)
FixedLaplacian(value)Δu - v = 0 (Laplacian BC)
PoissonEquation(forcing_f)Δu = f
BurgersEquation(nu)u_t + u u_x = ν u_xx
AdvectionEquation(beta)u_t + β·∇u = 0
AllenCahnEquation(ε, α)u_t = ε u_xx + α (u - u³)
DiffusionReactionEquation(λ)u_t = λ Δu + f
HelmholtzEquation(k)Δu + k² u = f
AcousticWaveEquation(c)u_tt = c² Δu

If the equation matches one of these, use it directly.

Step 2 — Unknown equation

If the equation is not in the zoo:

  1. Check if the equation is present in .opencode/skills/define-equations/famous_odes_pdes.json, if not present search the web for the equation form, common PINN implementation, and known boundary/initial conditions.
  2. Present the found formulation to the user and ask:

    I found this equation: <formulation>. Should I use this or would you like to provide your own?

  3. If the user provides their own, use that instead.
Show full SKILL.md (183 more words)Show less

Step 3 — Define boundary conditions

What boundary conditions apply? (Dirichlet, Neumann, Robin, periodic, etc.)

A well-posed PDE problem needs both the PDE and its boundary/initial conditions. Common types:

  • Dirichlet: FixedValue(value) — imposes u = value on the boundary
  • Neumann: FixedGradient(value) — imposes ∂u/∂n = value
  • Flux: FixedFlux(value) — imposes div(u) = value
  • Laplacian: FixedLaplacian(value) — imposes Δu = value

For zoo boundary conditions, use components and d parameters when the problem has multiple output variables:

python
FixedGradient(0.0, components=["theta"], d=["t"])

Step 4 — Custom equation functions

Import the required utilities:

python
from pina.operator import grad
from pina.equation import Equation
Standard PDE (2 arguments)
python
def my_pde(input_, output_):
    u_x = grad(output_, input_, components=["u"], d=["x"])
    u = output_.extract(["u"])
    return u_x - u
Inverse problem (3 arguments)

When the problem is also an InverseProblem, the equation function receives a third argument params_ (a dict of unknown parameters):

python
def my_pde_inverse(input_, output_, params_):
    f = torch.exp(-2 * (input_["x"] - params_["mu1"])**2)
    return laplacian(output_, input_, components=["u"], d=["x"]) - f

Step 5 — Build conditions

Wrap equations in Condition objects. Return to the condition-setup or create-problem skill for this step.

python
from pina import Condition

conditions = {
    "interior": Condition(domain="D", equation=Equation(my_pde)),
    "dirichlet_bc": Condition(domain="boundary", equation=FixedValue(0.0)),
    "neumann_bc": Condition(domain="boundary", equation=FixedGradient(0.0)),
    "ic": Condition(domain="t0", equation=Equation(initial_cond)),
}

Checklist

  • Equation identified (zoo class or custom Equation)
  • If equation was unknown: searched the web, presented the found formulation to the user, and confirmed before using
  • Both the PDE and boundary/initial conditions are defined
  • Custom equations use correct function signature: (input_, output_) for standard, (input_, output_, params_) for inverse
  • Operator calls use LabelTensor with correct components and d parameter names

© PINA-org, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file

Files

SKILL.md and 1 other file in .opencode/skills/define-equations of PINA-org/PINA.

  • SKILL.md
  • famous_odes_pdes.json

Open the folder on GitHubat commit 0cd8afb

Compare with similar skills

Define Equations next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.

Define Equations compared with similar skills
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CLIP Image-Text MatchingOrchestra-Research/AI-Research-SKILLs13k7 repos~1.7kAutomated safety check: PassMIT
Add Function Bodyonnx/onnx22k—~1.1kAutomated safety check: PassApache-2.0

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Categories

Questions about Define Equations

What does Define Equations do?

Define PDEs, ODEs, boundary conditions, and custom equations for PINA physics-driven problems. Define Equations is an agent skill from PINA-org/PINA. Define PDEs, ODEs, boundary conditions, and custom equations for PINA physics-driven problems.

When should I use Define Equations?

Define Equations fits situations like: tasks that involve Deep learning.

How do I install Define Equations in Claude Code?

Run `npx skills add PINA-org/PINA --skill define-equations -a claude-code`. Or copy the skill folder (.opencode/skills/define-equations in PINA-org/PINA) into .claude/skills/define-equations in your project. Claude Code loads it when a task matches its description.

How do I install Define Equations in Codex?

Run `npx skills add PINA-org/PINA --skill define-equations -a codex`. Or copy the skill folder (.opencode/skills/define-equations in PINA-org/PINA) into .agents/skills/define-equations in your project. Codex loads it when a task matches its description.

Can I use Define Equations in Cursor, Gemini CLI or GitHub Copilot?

Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add PINA-org/PINA --skill define-equations -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/define-equations, .gemini/skills/define-equations, .github/skills/define-equations and .opencode/skills/define-equations in your project.

What does Define Equations need to run?

SKILL.md names no scripts, command-line tools or credentials: Define Equations is instructions for the agent only. Our summary lists: Python 3. Compatibility (from SKILL.md): opencode, codex, claude.

Does Define Equations access the network?

SKILL.md contains no URLs. Any network use would come from the scripts or tools the agent runs. This is read from the text; nothing was executed.

Is Define Equations safe to install?

Our automated static check of SKILL.md found no risky patterns, such as piping downloads into a shell, reading credential files or hidden Unicode. It is not a guarantee. Review the folder before installing.

What licence does Define Equations use?

Define Equations is published under the MIT licence (declared in SKILL.md). It allows redistribution, so the full SKILL.md is shown on this page.

How many tokens does Define Equations use?

About 1.2k tokens (SKILL.md is roughly 4.6k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.

What are the alternatives to Define Equations?

Skills that share tags, products or a category with Define Equations: Add Uint Support (pytorch/pytorch, 104k stars), Segment Anything Model Guide (Orchestra-Research/AI-Research-SKILLs, 13k stars), Add Op (onnx/onnx, 22k stars) and CLIP Image-Text Matching (Orchestra-Research/AI-Research-SKILLs, 13k stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Define Equations?

PINA-org (a GitHub organization) maintains it in PINA-org/PINA, which has 798 GitHub stars. The repository holds 10 skills in this directory. The repository was last updated on October 6, 2026.

Source: PINA-org/PINA on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.