A PINN methodology for temperature field reconstruction in the PIV measurement plane: Case of Rayleigh-Bénard convection

Abstract

We present a method to infer temperature fields from stereo particle image velocimetry (PIV) data in turbulent Rayleigh-Bénard convection (RBC) using physics-informed neural networks (PINNs). The physical setup is a cubic RBC cell with Rayleigh number and Prandtl number . With data available only in a vertical plane, the residuals of the governing partial differential equations are minimized at a set of collocation points in an enclosing 3D domain of finite thickness along the direction perpendicular to the plane. Dynamic collocation point sampling strategies are used to overcome the lack of 3D labeled information and to optimize the overall PINN convergence. In particular, in the out-of-plane direction, the collocation points are distributed according to a normal distribution, in order to emphasize the region where data is provided. Along the vertical direction, we leverage direct numerical simulation (DNS) meshing information and sample points from an optimized kernel-density estimation. This sampling approach balances labeled information by pointing greater attention to critical regions, particularly in areas with high temperature gradients within the thermal boundary layers. Using DNS planar three-component velocity data, we successfully validate the accurate reconstruction of the temperature fields in the PIV plane. We evaluate the robustness of our method with respect to characteristics of the labeled data used for training: the data time span, the sampling frequency, some noisy data, and omission of boundary data, aiming to better accommodate the challenges associated with experimental data. Developing PINNs on controlled simulation data is a crucial step towards their effective training and deployment on experimental data. The key is to systematically introduce noise, gaps, and uncertainties in simulated data to mimic real-world conditions and ensure robust generalization.