Merge pull request #74 from 20saaa02/active-matter-feature

An example of EPDE application to a problem, involving active matter.

Author: Maslyaev

.DS_Store

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+# Data-Driven Symbolic Equation Discovery of Multi-Robot Dynamics
+
+This repository presents a physics-informed machine learning pipeline for the analysis of multi-robot trajectory data and the discovery of interpretable mathematical models describing their dynamics.
+
+The workflow combines:
+* Trajectory preprocessing
+* Hyperparameter optimization with **Optuna**
+* Symbolic regression via **EPDE**.
+
+## Project Goal
+
+The goal of this work is to develop a hyperparameter optimization with **Optuna** for identifying accurate, compact, and interpretable systems of ordinary differential equations (ODEs) governing the motion of robots based on experimental trajectory data.
+
+---
+##  Data Description
+
+* **Pickle file** contains raw experimental data extracted from video tracking.
+* For each robot and timestep:
+  * robot ID,
+  * 2D coordinates `(x, y)`.
+* Supported robot shapes:
+  * circle
+  * oval
+
+---
+## Components
+
+`DataProcessor`
+* Extracts coordinates
+* Normalizes trajectories (MinMax scaling)
+
+`discovery_science.ipynb`
+* Splits trajectories into segments
+* Runs EPDE for symbolic regression
+* Uses Optuna for hyperparameter tuning
+* Outputs differential equations
+
+---
+## Hyperparameter optimization
+
+For each trajectory segment of `n_parts` independently:
+
+* **Optuna** optimizes EPDE parameters:
+
+  * polynomial window,
+  * smoothing sigma,
+  * boundary,
+  * population size.
+
+* **Optuna** optimizes TEDEOUS parameters:
+
+  * the number and frequency of Fourier transform embeddings,
+  * the number of layers
+  
+* Objective balances:
+
+  * equation residuals,
+  * model complexity,
+  * reconstruction stability.
+---
+
+## Repository Structure
+
+```
+.
+├── discovery_science_mezo.ipynb
+├── data_process.py
+├── {circle|oval}/
+│   ├── data/
+│       └── {circle_data_00_330_[30_bots_PWM_10_15cw_15ccw_D_41cm].MP4.pickle | oval_data_[30_bots_PWM_1_exp_1].pickle}
+│   ├── levels_robots_ids.json
+│   ├── EPDE_output_micro/
+│       ├── robot_{id}/
+│           └── {n}_parts/
+│               └── {with|without}_force/
+│                   ├── part_{nk}_system_best_params.json
+│                   ├── part_{nk}_system_history_plot.html
+│                   ├── part_{nk}_system_importances_plots.html
+│                   ├── system_{nk}.csv
+│                   └── part_{nk}_obj_func_and_equations.txt
+│   └── EPDE_output_meso
+│       ├── robot_{ids}
+│           └── ...
+└── README.md
+```
+---
+
+## Dependencies
+
+Core libraries:
+* numpy, pandas, scipy
+
+Machine Learning
+* scikit-learn
+
+Optimization & Discovery
+* epde
+* optuna
+
+Utility
+* dill (pickle)
+* pathlib
+* json
+
+---
+## Research Outcomes
+* Developed a unified pipeline for data-driven discovery of dynamical systems
+
+---
+
+## Limitations and Assumptions
+
+* Robot ID < 100
+* Only `oval` and `circle` supported
+* derivatives up to second order
+* EPDE sensitive to noise and hyperparameters
+
+---
+
+For more information, see the repository https://github.com/20saaa02/Active_Matter
+
+
+
+
+
+

examples/.DS_Store

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+{
+    "best_params": {
+        "poly_window": 11,
+        "population_size": 14,
+        "sigma": 5,
+        "boundary": 7
+    },
+    "score": 155.68504506502222
+}