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

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 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 new and unique 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, for the first time and unlike previous studies,
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 a new approach for understanding thermal
turbulence.