Summary

This PR adds a new example, examples/Active_Matter, demonstrating the application of EPDE to symbolic discovery of multi-robot dynamics from experimental trajectory data.

Added

• Active_Matter example workflow;
• trajectory preprocessing utilities;
• Optuna-based hyperparameter optimization for EPDE runs;
• example notebooks for equation discovery;
• sample datasets for circular and oval robots;
• identification results and generated outputs.

Motivation

Selection of EPDE hyperparameters often requires multiple manual experiments and significantly affects the quality of the discovered equations.

This example introduces an automated hyperparameter optimization workflow based on Optuna. The optimization procedure searches for parameter configurations that improve equation quality while reducing the amount of manual tuning required from the user.

Benefits

• reduced manual effort during model discovery;
• faster identification workflow through automated parameter search;
• improved robustness across different trajectory segments;
• more accurate and compact discovered equations;
• demonstration of EPDE on real experimental multi-robot datasets.

Purpose

The example illustrates how EPDE can be applied to real-world trajectory data to identify interpretable systems of differential equations describing collective robot dynamics.

Notes

The example is intended as a research and demonstration workflow and does not modify the core EPDE functionality.