AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold networks.

Journal: Science advances
Published Date: May 7, 2025

Abstract

We propose the artificial intelligence velocimetry-thermometry (AIVT) method to reconstruct a continuous and differentiable representation of the temperature and velocity in turbulent convection from measured three-dimensional (3D) velocity data. AIVT is based on physics-informed Kolmogorov-Arnold networks and trained by optimizing a loss function that minimizes residuals of the velocity data, boundary conditions, and governing equations. We apply AIVT to a set of simultaneously measured 3D temperature and velocity data of Rayleigh-Bénard convection, obtained by combining particle image thermometry and Lagrangian particle tracking. This enables us to directly compare machine learning results to true volumetric, simultaneous temperature and velocity measurements. We demonstrate that AIVT can reconstruct and infer continuous, instantaneous velocity and temperature fields and their gradients from sparse experimental data at a high resolution, providing an additional approach for understanding thermal turbulence.

Authors

  • Juan Diego Toscano
    Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.
  • Theo Käufer
    Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, Ilmenau, Germany.
  • Zhibo Wang
    School of Engineering, Brown University, Providence, RI 02912, USA.
  • Martin Maxey
    Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.
  • Christian Cierpka
    Institute of Thermodynamics and Fluid Mechanics, Technische Universität Ilmenau, Ilmenau, Germany.
  • George Em Karniadakis
    Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.

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