DOI: 10.5061/dryad.jm63xsjnj
title: AIVT: Inference of turbulent thermal convection from measured 3D velocity data by physics-informed Kolmogorov-Arnold Networks

description: 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.
description: # AIVT: Inference of turbulent thermal convection from measured 3D
 velocity data by physics-informed Kolmogorov-Arnold Networks Dataset DOI:
 [10.5061/dryad.jm63xsjnj](10.5061/dryad.jm63xsjnj) ## Description of the
 data and file structure **"AIVT: Inference of turbulent thermal
 convection from measured 3D velocity data by physics-informed
 Kolmogorov-Arnold Networks"** You can find our code
 at [https://zenodo.org/records/15028727](https://zenodo.org/records/15028727). ### Files and variables #### File: Data\_txyzuvwT.mat **Description:** .mat file The provided .mat file contains two numpy arrays accessible via keys 'txyz' and 'uvwT.' These arrays correspond to the temporal and spatial coordinates (inputs) and the experimental velocity and temperature fields (outputs). ##### Variables * Input variables 'txyz': * t: time * x,y,z: Spatial coordinates * Output variables 'uvwT': * u,v,w: velocity components in x,y, and z directions respectively * T: temperature ##### Units The data is provided in non-dimensional form, meaning that all physical quantities were rescaled using characteristic reference values to eliminate units. This approach simplifies the equations and allows the results to be more generally applicable. In our case: * Time was rescaled using a characteristic timescale derived from the height of the domain, gravitational acceleration, thermal expansion coefficient, and temperature difference. * Spatial coordinates were rescaled by the characteristic height, so all positions are expressed as fractions of this reference length. * Temperature was rescaled by subtracting a reference (cold) temperature and dividing by the overall temperature difference, resulting in dimensionless values ranging from 0 to 1. * Velocity was rescaled using a characteristic speed based on buoyancy effects, which depends on the height, gravitational acceleration, thermal expansion, and temperature difference. Since the governing equations were solved directly in non-dimensional form from the beginning, no physical units are required to replicate the results provided in the paper. ## Code/software This matfile can be opened with the open software scipy in python accessible via: `import scipy` Then the specific variables can be reached as: `Loaded_data=scipy.io.loadmat(./Data_txyzuvwT.mat)` `X_star_f= Loaded_data['txyz']` -&gt; Numpy array where each column corresponds to the  t,x,y,z temporal and spatial components. `u_star_f = Loaded_data['uvwT']` -&gt; Numpy array where each column corresponds to the u,v,w,T experimental fields. ## Access information Other publicly accessible locations of the data: * None Data was derived from the following sources: * Paper