It is what it means
https://e64eabc8-2c1e-42e0-84f6-1e3d58636060-00-33mgc75tepvde.janeway.replit.dev:5000/
A cross-domain discovery engine that searches for mathematical structures shared between different systems.
Instead of starting from a fixed model or equation, the engine compares systems from many fields (biology, economics, physics, computer science, etc.) and attempts to transfer mechanisms from one domain to another.
The goal is to discover useful mathematical structures that may apply to problems they were not originally designed for.
Philosophy
Mathematics is not tied to a specific subject.
Many equations that were originally created for one field later turned out to describe completely different systems.
Examples:
- Heat diffusion → information spreading in networks
- Game theory → evolutionary biology
- Fluid dynamics → traffic flow
- Logistic growth → neural activation, population growth, learning saturation
The Inspiration Engine searches for these shared structures automatically.
How the Engine Works
The engine follows this pipeline:
subject ↓ extract possible mechanisms ↓ search systems containing those mechanisms ↓ combine mechanisms ↓ generate mathematical structure ↓ test if the structure is meaningful
This approach focuses on mechanism transfer, not just equation generation.
The engine tries to answer a question like:
"What mathematical rules from other systems might apply to this problem?"
Example
Input subject:
self improving discovery engine
Possible mechanisms extracted:
adaptation optimization feedback
The engine searches its system database for systems containing these mechanisms and may produce a dynamical model such as:
dx/dt = a x (1 - x)
This equation represents growth with limiting feedback, a structure that appears across many domains.
Features
- Cross-domain system database
- Mechanism extraction from subjects
- Mechanism-based system search
- Automatic equation generation
- Equilibria detection
- Symmetry detection
- Invariant detection
- Discovery mode for exploring new models without a specific subject
Discovery Mode
Discovery Mode ignores the subject and searches for interesting mathematical structures by combining mechanisms across systems.
This allows the engine to explore new potential models that may apply across multiple domains.
Project Structure
app.py inspiration_engine.py system_database.py mechanism_graph.py templates/ data/
Key components:
inspiration_engine.py Core discovery engine.
system_database.py Collection of systems and mechanisms.
mechanism_graph.py Relationships and weights between mechanisms.
app.py Web interface for interacting with the engine.
What This Project Is (and Isn't)
This project is not a general AI system.
It is an experimental tool for exploring:
- mechanism transfer
- cross-domain mathematical modeling
- structural similarities between systems
It is closer to a mathematical discovery tool than a traditional machine learning system.
Possible Applications
- algorithm design
- modeling complex systems
- cross-domain research exploration
- idea generation for mathematical models
- discovering structures shared across scientific fields
Future Ideas
Possible directions for the project:
- expanding the system database
- improving mechanism extraction
- discovering new algorithm update rules from generated equations
- learning new systems from research papers
Author
Created by Stephen
License
Open for experimentation and exploration.