Temperature and pressure reconstruction in turbulent Rayleigh-B\'enard convection by Lagrangian velocities using PINN

TL;DR

This paper presents a physics-informed neural network approach to reconstruct temperature and pressure fields in turbulent Rayleigh-Bénard convection using Lagrangian velocity data, validated on both DNS and experimental PTV data, demonstrating high accuracy and practical applicability.

Contribution

The study introduces a PINN-based method capable of reconstructing temperature and pressure fields from Lagrangian velocities in turbulent convection, applicable to both simulated and experimental data.

Findings

Achieved 90% correlation with ground truth in DNS data.

Successfully reconstructed realistic temperature and pressure fields from experimental data.

Demonstrated applicability of PINNs in complex turbulent flow conditions.

Abstract

Velocity, pressure, and temperature are the key variables for understanding thermal convection, and measuring them all is a complex task. In this paper, we demonstrate a method to reconstruct temperature and pressure fields based on given Lagrangian velocity data. A physics-informed neural network (PINN) based on a multilayer perceptron architecture and a periodic sine activation function is used to reconstruct both the temperature and the pressure for two cases of turbulent Rayleigh-B\'enard convection (Pr = 6.9, Ra = $10^9$). The first dataset is generated with DNS and it includes Lagrangian velocity data of 150000 tracer particles. The second contains a PTV experiment with the same system parameters in a water-filled cubic cell, and we observed about 50000 active particle tracks per time step with the open-source framework proPTV. A realistic temperature and pressure field could be reconstructed in both cases, which underlines the importance of PINNs also in the context of experimental data. In the case of the DNS, the reconstructed temperature and pressure fields show a 90\% correlation over all particles when directly validated against the ground truth. Thus, the proposed method, in combination with particle tracking velocimetry, is able to provide velocity, temperature, and pressure fields in convective flows even in the hard turbulence regime. The PINN used in this paper is compatible with proPTV and is part of an open source project. It is available on request at https://github.com/DLR-AS-BOA.