  We propose the Artificial Intelligence Velocimetry-Thermometry (AIVT) method
to infer hidden temperature fields from experimental turbulent velocity data.
This physics-informed machine learning method enables us to infer continuous
temperature fields using only sparse velocity data, hence eliminating the need
for direct temperature measurements. Specifically, AIVT is based on
physics-informed Kolmogorov-Arnold Networks (not neural networks) and is
trained by optimizing a combined loss function that minimizes the residuals of
the velocity data, boundary conditions, and the governing equations. We apply
AIVT to a unique set of experimental volumetric and simultaneous temperature
and velocity data of Rayleigh-B\'enard convection (RBC) that we acquired by
combining Particle Image Thermometry and Lagrangian Particle Tracking. This
allows us to compare AIVT predictions and measurements directly. We demonstrate
that we can reconstruct and infer continuous and instantaneous velocity and
temperature fields from sparse experimental data at a fidelity comparable to
direct numerical simulations (DNS) of turbulence. This, in turn, enables us to
compute important quantities for quantifying turbulence, such as fluctuations,
viscous and thermal dissipation, and QR distribution. This paradigm shift in
processing experimental data using AIVT to infer turbulent fields at DNS-level
fidelity is a promising avenue in breaking the current deadlock of quantitative
understanding of turbulence at high Reynolds numbers, where DNS is
computationally infeasible.
