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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
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Updated: May 25, 2025

Image-based Lagrangian Particle Tracking in Bed-load Experiments
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Physics-informed deep learning for stochastic particle dynamics estimation.

Yongyu Zhang1, Junlun Zhu1, Hao Xie2

  • 1Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China.

Proceedings of the National Academy of Sciences of the United States of America
|February 27, 2025
PubMed
Summary
This summary is machine-generated.

We developed a new AI method, the stochastic particle-informed neural network (SPINN), to precisely analyze particle movement. SPINN improves understanding of complex diffusion dynamics in various materials.

Keywords:
anomalous diffusionmachine learningsingle-particle trackingstochastic differential equation

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Area of Science:

  • Physics
  • Biophysics
  • Materials Science

Background:

  • Single-particle tracking offers high precision for studying complex systems.
  • Particle dynamics at micro/nanoscales are inherently stochastic, complicating analysis.
  • Current methods often assume pseudo-steady states, limiting accuracy.

Purpose of the Study:

  • To introduce a novel deep learning framework, the stochastic particle-informed neural network (SPINN).
  • To model and infer particle diffusion dynamics by integrating stochastic differential equations.
  • To enhance the temporal resolution of stochastic dynamics for improved analysis.

Main Methods:

  • Developed SPINN, a physics-informed deep learning framework.
  • Integrated stochastic differential equations for modeling diffusion.
  • Autonomously explored parameter spaces and distinguished deterministic/stochastic components.

Main Results:

  • Validated SPINN on anomalous diffusion datasets, reducing variability and preserving correlations.
  • Accurately characterized different stochastic diffusion processes.
  • Revealed enhanced microrheological properties during hydrogel gelation.
  • Uncovered interfacial dynamics during liquid-liquid phase separation.

Conclusions:

  • SPINN improves the estimation and prediction of complex diffusion behaviors.
  • The framework offers insights into underlying physical mechanisms at mesoscopic scales.
  • Enhanced temporal resolution facilitates detailed analysis of stochastic dynamics.