This repository contains the code for the manuscript:
Data-driven discovery of stochastic dynamical equations of collective motion. Nabeel, A., Jadhav, V., Sire, C., Theraulaz, G., Escobedo, R., Iyer, S. K., & Guttal, V. (2023). DOI: 10.1088/1478-3975/ace22d
The code is divided into two parts:
- The directory
/spp_modelcontains MATLAB code to simulate the agent-based models. - The directory
/sde_discoverycontains code to discover mesoscale SDEs from the simulated trajectories.
Generate data of positions and velocities to calculate group polarisation for given group size and parameters.
Use Matlab code /spp_model/sim_data.m to generate all the required data to calculate group polarisation. Positions, velocities of agents are stored in .mat file named n_pw.mat.
Variables are commented within the code. To reproduce the results, it is advised to run for at least T = 3500 and the number of realisations (no_it) = 15. Interaction rates, number of interacting neighbours (k_alg) and all the parameters can be changed in sim_data.m.
To simulate stochastic pairwise interaction set k_alg = 1 in sim_data.m. Similarly set k_alg = 2 and k_alg = n for ternary and Vicsek like averaging model respectively.
After running the simulation, use the data in n_pw.mat to calculate the order parameter, i.e., group polarisation. To do so, run the Matlab code /figures/grp_pol.m. This file stores all the required data in the n_pw.csv file in the format [mx, my, m].
To see the collective motion of agents, run the code /spp_model/simulations.m. Make sure to load n_pw.mat. Variables are defined within the code and can be changed accordingly.
The notebook /sde_discovery/sde-discovery.ipynb contains code to analyze the order-parameter time series and discover mesoscale stochastic differential equations. The code uses the CSV file generated from the MATLAB code above. An example CSV file, corresponding to the ternary local interaction model is provided.