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Updated: Aug 10, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Learning hydrodynamic equations for active matter from particle simulations and experiments.

Rohit Supekar^1,2, Boya Song², Alasdair Hastewell²

¹Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139.

Proceedings of the National Academy of Sciences of the United States of America

|February 10, 2023

Summary

This study introduces a new framework to discover hydrodynamic equations for active matter from microscopic data. It enables parallel measurement of hydrodynamic parameters directly from simulations and experiments.

Keywords:

active matter coarse-graining hydrodynamic equations sparse regression

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Last Updated: Aug 10, 2025

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Area of Science:

Physics
Complex Systems
Active Matter Physics

Background:

High-resolution imaging and particle simulations advance active matter studies.
Data-driven algorithms can learn continuum models (partial differential equations - PDEs) from simulation data.
Learning macroscopic hydrodynamic equations directly from active matter experiments or simulations is challenging, especially for complex systems.

Purpose of the Study:

To develop a framework for discovering partial differential equation (PDE) models from microscopic data of active matter systems.
To incorporate physical symmetries into the model discovery process.
To enable direct inference of hydrodynamic equations from experimental and simulation data.

Main Methods:

Utilizing spectral basis representations and sparse regression algorithms.
Applying the framework to microscopic simulation and experimental data.
Incorporating relevant physical symmetries into the discovery of partial differential equations (PDEs).

Main Results:

The framework successfully discovers hydrodynamic equations for active matter systems.
Learned equations reproduce observed self-organized collective dynamics from simulations and experiments.
Enables parallel measurement of numerous hydrodynamic parameters directly from video data.

Conclusions:

The developed framework offers a powerful approach to inferring macroscopic hydrodynamic equations for active matter.
It overcomes limitations of traditional methods for complex, heterogeneous, or nondilute systems.
Facilitates direct quantitative analysis of collective behaviors from microscopic observations.