Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks

TL;DR

This paper introduces AIVT, a physics-informed machine learning method that infers continuous temperature and velocity fields from sparse turbulent velocity data, matching DNS fidelity without direct temperature measurements.

Contribution

The novel AIVT method combines physics-informed Kolmogorov-Arnold Networks with experimental data to reconstruct turbulent fields at high fidelity, bypassing the need for direct temperature measurements.

Findings

AIVT accurately reconstructs temperature and velocity fields from sparse data.

The method achieves fidelity comparable to direct numerical simulations.

AIVT enables quantification of turbulence statistics like dissipation and QR distribution.

Abstract

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.