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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations.

Maziar Raissi1,2, Alireza Yazdani3, George Em Karniadakis1

  • 1Division of Applied Mathematics, Brown University, Providence, RI 02906, USA. maziar.raissi@colorado.edu george_karniadakis@brown.edu.

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Hidden fluid mechanics (HFM) uses physics-informed deep learning to extract fluid velocity and pressure from images, even with noise. This novel framework solves complex fluid dynamics problems where direct measurement is difficult.

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Area of Science:

  • Fluid dynamics
  • Computational physics
  • Biomedical engineering

Background:

  • Flow visualization has historically aided the study of fluid motion in physical and biological systems.
  • The Navier-Stokes equations theoretically describe fluid flow, but extracting quantitative data like velocity and pressure from visual observations remains challenging.
  • Direct measurement of fluid dynamics can be difficult or impossible in many scenarios.

Purpose of the Study:

  • To develop a novel physics-informed deep-learning framework, Hidden Fluid Mechanics (HFM), to overcome limitations in extracting quantitative fluid dynamics data from observations.
  • To create a versatile framework that encodes the Navier-Stokes equations, enabling analysis across diverse geometries and conditions.
  • To demonstrate the practical application of HFM in extracting otherwise inaccessible quantitative information from physical and biomedical systems.

Main Methods:

  • Developed Hidden Fluid Mechanics (HFM), a physics-informed deep-learning framework.
  • Integrated the Navier-Stokes equations directly into the neural network architecture.
  • Designed HFM to be agnostic to specific geometries, initial, and boundary conditions for broad applicability.

Main Results:

  • Successfully demonstrated HFM for various physical and biomedical flow problems.
  • Enabled the extraction of quantitative velocity and pressure fields from flow visualization data.
  • Showcased HFM's robustness to low-resolution imagery and significant noise in observational data.

Conclusions:

  • HFM provides a powerful, data-driven approach to quantitatively analyze fluid motion.
  • The framework's ability to handle noisy and low-resolution data opens new possibilities for fluid dynamics research and applications.
  • HFM offers a significant advancement in fluid mechanics, particularly for scenarios where direct measurement is impractical.