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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