README.md

metadata

title: Differ Hug
emoji: 📊
colorFrom: gray
colorTo: green
sdk: gradio
sdk_version: 5.31.0
python_version: '3.11'
app_file: app.py
pinned: false

Differ Hug: ODE Research Platform

An interactive platform for exploring and analyzing ordinary differential equations (ODEs), focused on gene regulatory systems and numerical diagnostics.

Features

ode System

• Gene Regulatory ODE System: Cooperative sigmoidal activation model
• Numerical Integration: High-precision DOP853 solver with RK45 fallback
• Initial Conditions: Circular/sector-based ensembles with controllable center and radius

Diagnostics & Metrics

• FTLE: Finite-Time Lyapunov Exponent with R² reliability metric
• Hurst Exponent: Rescaled range (R/S) analysis for time series
• Curvature Statistics: Mean, median, std, p10, p90 of curvature radius
• Path Length: Total arclength of trajectories
• Local Z-score: Nearest-neighbor analysis of curvature metrics
• Anomaly Score: Combined robust z-scores for outlying trajectories

Visualization

• Phase Portrait: Trajectories in phase space with annotations
• Time Series: x(t) and y(t) evolution over time
• Shadowing Analysis: Perturbation growth visualization
• Metrics Table: Full diagnostic output with highlighting

Requirements

gradio>=4.44.1
numpy>=1.24.0
scipy>=1.10.0
matplotlib>=3.7.0
pandas (optional for extended functionality)

Usage

Run the application locally:

python app.py

The app will be available at http://localhost:7860

ODE System

The gene regulatory system:

$$\{\begin{array}{l}{\displaystyle \frac{dx}{dt}=\frac{K{x}^{1\mathrm{/}\alpha }}{b^{1\mathrm{/}\alpha }+x^{1\mathrm{/}\alpha }}-{\gamma }_{1}x,}\\ {\displaystyle \frac{dy}{dt}=\frac{K{y}^{1\mathrm{/}\alpha }}{b^{1\mathrm{/}\alpha }+y^{1\mathrm{/}\alpha }}-{\gamma }_{2}y\mathrm{.}}\end{array}\backslash begin\{cases\}\; \backslash displaystyle\; \backslash frac\{dx\}\{dt\}\; =\; \backslash frac\{K\backslash ,x^\{1/\backslash alpha\}\}\{b^\{1/\backslash alpha\}\; +\; x^\{1/\backslash alpha\}\}\; -\; \backslash gamma\_1\backslash ,x,\backslash \backslash [10pt]\; \backslash displaystyle\; \backslash frac\{dy\}\{dt\}\; =\; \backslash frac\{K\backslash ,y^\{1/\backslash alpha\}\}\{b^\{1/\backslash alpha\}\; +\; y^\{1/\backslash alpha\}\}\; -\; \backslash gamma\_2\backslash ,y.\; \backslash end\{cases\}$$

Parameters

• alpha: Controls sigmoid steepness (1/alpha = Hill coefficient)
• K: Maximum activation rate
• b: Half-activation constant
• gamma1, gamma2: Decay rates

Project Structure

differ-hug/
├── app.py                 # Gradio UI entry point
├── differ_hug/            # Core computation package
│   ├── __init__.py
│   ├── compute.py         # Numerical computation functions
│   ├── plotting.py        # Visualization functions
│   ├── params.py          # Parameter serialization
│   └── docs.py            # Documentation helpers
└── differential_equations_streamlit_src/  # Original Streamlit code (archived)

Migration Notes

This is a Gradio port of the original Streamlit implementation. Key changes:

• Replaced streamlit with gradio
• Separated computation logic from UI
• Preserved all numerical diagnostics
• Made torch-based neural network solvers optional

Citation

If you use this tool in your research, please cite:

@software{differ_hug,
  author = {Krizhanovsky, Andrey},
  title = {Differ Hug: ODE Research Platform},
  url = {https://huggingface.co/spaces/componavt/differ-hug},
  year = {2026}
}