Supplemental Code

Learning hydrodynamic equations for active matter from particle simulations and experiments

PNAS, 2023, Vol. 120, e2206994120

Authors: R. Supekar, B. Song, A. Hastewell, G. P. T. Choi, A. Mietke, J. Dunkel

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The three major steps in the learning framework are:

1. Coarse-graining
2. Spectral projection and smoothing
3. PDE learning

The codes provided need to be run sequentially to execute the above steps. The details are provided below. The starting point is the particle data provided in data/quinke_particle_data_S2.mat, which corresponds to the results presented in Fig. 4 of the manuscript.

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1. Coarse-graining [MATLAB]

• Run coarse_grain_data.m through MATLAB. This takes in the particle data from data/quinke_particle_data_S2.mat and saves the coarse-grained data at data/coarse_grained_field(y,x,t).mat. The generated image data/coarse_grained_frame.png shows the coarse-graining result at a particular frame.

• With Nx=100, Ny=50 (specified inside coarse_grain_data.m), the code should run for ~10 mins.

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2. Spectral representation [Julia]

• If you do not have Julia versions from 1.3 - 1.7, download it from: https://julialang.org/downloads/. Make sure the command julia works from the command line.

• Navigate to the project folder through the command line.

• Saving spectral coefficients of the coarse-grained data:

  • Run julia save_representation.jl. This should run for a few mins.
  • This will save the representations (spectral coefficients) in the files data_representation_cheb_cheb_cheb_*.mat for each field.

• Saving smooth data and time-derivative after imposing cut-offs on the coefficients:

  • Run julia save_smooth_data.jl. This should run for ~ 5 mins.
  • This will save the smooth fields as the file data/_reconstruction_cheb_cheb_cheb_space*_time*.mat.

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3. PDE Learning [Python 3]

We use Python >=3.6.

• Navigate to the project folder through the command line.

• Installing required packages:

Conda[Recommended]:

• If you do not have anaconda, download it from here: https://www.anaconda.com/products/individual. After the installation, make sure the command works from your command line.

• Create a new conda environment from the provided .yml file: run conda env create --name pdel --file=environment.yml

• Activate the environment with conda activate pdel.

OR

PIP:

• If you already have a Python3 installation that you would like to use, do pip3 install -r requirements.txt.

Learning density equation:

• Run python3 learn_density_equation.py. This should run for a few mins.
• After the script runs, the folder data/PDElearn/density_equation/ will have the learning results.
• The file pde_stability.txt lists all the learned PDEs and the files pde_stability_*.txt will have the individual PDEs.

Learning velocity equation:

• Do python3 learn_velocity_equation.py. This should run for a few mins.
• After the script runs, the folder data/PDElearn/velocity_equation/ would have the learning results.
• The file pde_stability.txt lists all the learned PDEs and the files pde_stability_*.txt will have the individual PDEs.