Title: Temperature and pressure reconstruction in turbulent Rayleigh-Bénard convection by Lagrangian velocities using PINN Show Chinese title

Title: 使用PINN通过拉格朗日速度重建湍流瑞利-贝纳德对流中的温度和压力

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. Show Chinese abstract

Abstract: 速度、压力和温度是理解热对流的关键变量，同时测量它们是一项复杂任务。 本文展示了一种基于给定拉格朗日速度数据重建温度和压力场的方法。 使用一种基于多层感知器架构和周期性正弦激活函数的物理信息神经网络（PINN），针对湍流瑞利-本纳德对流（Pr = 6.9，Ra = $10^9$）的两个案例，重建了温度和压力。 第一组数据由直接数值模拟（DNS）生成，其中包括 150000 个示踪粒子的拉格朗日速度数据。 第二组包含水填充立方腔中的粒子图像测速（PTV）实验，系统参数相同，在每个时间步长内通过开源框架 proPTV 观察到约 50000 条活跃粒子轨迹。 在这两种情况下都可以重建出真实的温度和压力场，这强调了 PINNs 在实验数据背景下的重要性。 对于 DNS 情况，当直接与真实值验证时，重建的温度和压力场在所有粒子上显示出 90% 的相关性。 因此，所提出的方法结合粒子跟踪测速仪可以在对流流动中，甚至在强湍流区域提供速度、温度和压力场。 本文使用的 PINN 兼容 proPTV，并且是开源项目的一部分。 可以通过 https://github.com/DLR-AS-BOA 请求获取。