What is math-model-selector?

A guidance tool that routes a problem to the most suitable mathematical framework using a decision-tree approach.

When should I trigger it?

When you have a problem but aren’t sure which mathematical domain applies; use trigger phrases like 'what math should I use' or 'how do I model this'.

A Framework Recommendation, a concrete Starting Point with key equations, suggested Tools, and Related Skills to pull in.

math-model-selector

npx machina-cli add skill parcadei/Continuous-Claude-v3/math-model-selector --openclaw

Files (1)

SKILL.md

3.3 KB

Math Model Selector

When to Use

Trigger on phrases like:

"what math should I use"
"which mathematical framework"
"how do I model this"
"what kind of problem is this"
"formalize this problem"

Use when user has a problem but doesn't know which mathematical domain applies.

Process

Guide user through decision tree using Polya-style questions:

1. Identify the quantity

Ask: "What quantity or phenomenon are you trying to understand?"

Physics problem -> conservation laws, differential equations
Economics -> equilibrium, optimization
Data patterns -> statistics, regression

2. Characterize change

Ask: "What changes, and how does it change?"

Discrete steps -> difference equations, recurrences
Continuous rate -> ODEs
Rate of rate matters -> 2nd order ODEs
Spatial variation -> PDEs

3. Check for uncertainty

Ask: "Is there randomness or uncertainty involved?"

Deterministic -> standard analysis
Epistemic uncertainty -> Bayesian methods
Random process -> probability theory, stochastic processes

4. Optimization check

Ask: "Are you optimizing something?"

Convex objective -> linear/quadratic programming
Non-convex -> gradient descent, evolutionary methods
Discrete choices -> combinatorics, integer programming

5. Answer precision

Ask: "What level of answer do you need?"

Rough estimate -> dimensional analysis
Qualitative behavior -> phase portraits, stability
Numerical answer -> simulation
Exact closed form -> analytical methods

Key Questions to Ask

What changes? (discrete vs continuous)
What causes the change? (rate dependencies)
What's random? (uncertainty type)
What's being optimized? (objective function)
How precise? (qualitative vs quantitative)

Output Format

Framework Recommendation:
- Primary: [framework name]
- Why: [one-sentence justification]

Starting Point:
- Key equations: [relevant formulas]
- Initial approach: [first step]

Tools to Use:
- [specific script or computation tool]

Related Skills:
- [domain skill to activate next]

Example Interaction

User: I want to model how a rumor spreads through a population

Claude: Let me help you find the right framework.

Q1: What quantity are we tracking?
> Number of people who heard the rumor over time.

Q2: What causes it to change?
> Spread rate depends on who knows and who doesn't.

Q3: Is there randomness?
> Assume deterministic (average behavior) for now.

Q4: Optimizing anything?
> No, just understanding dynamics.

Q5: What precision?
> Qualitative behavior, maybe predict peak rate.

Framework Recommendation:
- Primary: First-order ODE (logistic growth)
- Why: Rate depends on current state nonlinearly

Starting Point:
- dN/dt = r * N * (1 - N/K)
- N = heard count, K = population, r = spread rate

Tools:
- sympy_compute.py solve (equilibrium)
- Phase line for qualitative behavior

Related Skills:
- math/math-intuition-builder (understand the model)
- odes-pdes/first-order-odes (solve it)

Co-activates

After framework selection, suggest:

math-intuition-builder - to understand the framework
Relevant domain skill - for actual computation
math-mode - for symbolic verification

Source

git clone https://github.com/parcadei/Continuous-Claude-v3/blob/main/.claude/skills/math/math-model-selector/SKILL.mdView on GitHub

Overview

It helps you pick the right mathematical framework when the domain is unclear. By guiding you through a Polya-style decision tree—covering quantity, change, uncertainty, optimization, and precision—it surfaces a primary framework and a practical starting point for modeling.

How This Skill Works

It asks a sequence of targeted questions to classify the problem and then outputs a Framework Recommendation, a Starting Point with key equations, and suggested Tools. It also lists Related Skills to activate next. The process emphasizes identifying the quantity, characterizing change, checking uncertainty, evaluating optimization, and deciding the required precision.

When to Use It

What math should I use?
Which mathematical framework should apply to this problem?
How do I model this?
What kind of problem is this?
Formalize this problem

Quick Start

Step 1: Answer the five decision questions to identify quantity, change, uncertainty, optimization, and precision.
Step 2: Review the Framework Recommendation and extract the Starting Point (key equations and first steps).
Step 3: Use the specified Tools and Related Skills to implement and verify the model.

Best Practices

Follow the five-step decision tree: identify quantity, characterize change, check uncertainty, optimization, and precision.
Ask focused clarifying questions to determine the dominant dynamics before choosing a framework.
Match the framework to the problem's nature: deterministic vs stochastic, continuous vs discrete, optimization vs description.
Provide a concrete Starting Point with key equations and an initial approach.
Use the recommended tools and Related Skills to validate and implement the model.

Example Use Cases

Modeling rumor spread with a first-order ODE (logistic growth) to illustrate framework choice.
Physics problem: conservation laws leading to differential equations (ODEs/PDEs).
Economics problem: equilibrium analysis or optimization to justify chosen framework.
Data-driven problem: selecting regression/statistics for pattern fitting.
Uncertain processes: applying probability theory or stochastic processes to model randomness.

Frequently Asked Questions

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