咖啡杯上的水流：通过物理信息神经网络从面向断层背景的纹影视频推断3D速度和压力场
Flow over an espresso cup: Inferring 3D velocity and pressure fields from tomographic background oriented schlieren videos via physics-informed neural networks
摘要：
断层背景定向纹影（Tomo-BOS）成像使用多个相机BOS投影测量3D中的密度或温度场，并且对于复杂流体动力学问题的瞬时流动可视化特别有用。我们提出了一种新的方法，基于物理信息的神经网络（PINNs）来推断完整的连续三维速度和压力场的快照的三维温度场获得的Tomo-BOS成像。PINN无缝地集成了所观察到的流体流动的基础物理和可视化数据，从而能够使用有限的实验数据来推断潜在的量。在这个隐藏的流体力学范例，我们训练的神经网络，通过最小化的损失函数组成的数据失配项和与耦合的Navier-Stokes方程和传热方程的残差项。我们首先量化所提出的方法的准确性的基础上的2D合成数据集浮力驱动的流，并随后将其应用到的Tomo-BOS数据集，在那里我们能够推断的瞬时速度和压力场的咖啡杯的基础上提供的温度场的Tomo-BOS成像。此外，我们进行了一个独立的PIV实验，以验证PINN推断的非定常速度场的中心平面。为了解释所观察到的流动物理，我们还进行了系统的PINN模拟在不同的雷诺数和理查森数和量化的速度和压力场的变化。本文的研究结果表明，所提出的深度学习技术可以成为实验流体力学的一个有前途的方向。
英文摘要：
Tomographic background oriented schlieren (Tomo-BOS) imaging measures density or temperature fields in 3D using multiple camera BOS projections, and is particularly useful for instantaneous flow visualizations of complex fluid dynamics problems. We propose a new method based on physics-informed neural networks (PINNs) to infer the full continuous 3D velocity and pressure fields from snapshots of 3D temperature fields obtained by Tomo-BOS imaging. PINNs seamlessly integrate the underlying physics of the observed fluid flow and the visualization data, hence enabling the inference of latent quantities using limited experimental data. In this hidden fluid mechanics paradigm, we train the neural network by minimizing a loss function composed of a data mismatch term and residual terms associated with the coupled Navier-Stokes and heat transfer equations. We first quantify the accuracy of the proposed method based on a 2D synthetic data set for buoyancy-driven flow, and subsequently apply it to the Tomo-BOS data set, where we are able to infer the instantaneous velocity and pressure fields of the flow over an espresso cup based only on the temperature field provided by the Tomo-BOS imaging. Moreover, we conduct an independent PIV experiment to validate the PINN inference for the unsteady velocity field at a center plane. To explain the observed flow physics, we also perform systematic PINN simulations at different Reynolds and Richardson numbers and quantify the variations in velocity and pressure fields. The results in this paper indicate that the proposed deep learning technique can become a promising direction in experimental fluid mechanics.
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