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

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.