Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks

Tomographic background oriented Schlieren (Tomo-BOS) imaging measures density or temperature fields in three dimensions 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...

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Published in:	Journal of fluid mechanics Vol. 915
Main Authors:	Cai, Shengze, Wang, Zhicheng, Fuest, Frederik, Jeon, Young Jin, Gray, Callum, Karniadakis, George Em
Format:	Journal Article
Language:	English
Published:	Cambridge, UK Cambridge University Press 25.03.2021
Subjects:	Algorithms Coffee computational methods convection Data Datasets Deep learning Dimensions Experiments Fluid dynamics Fluid flow Fluid mechanics Heat transfer Hydrodynamics Imaging Imaging techniques Inference JFM Papers machine learning MATHEMATICS AND COMPUTING Neural networks Partial differential equations Physics Pressure Temperature distribution Temperature fields Velocity Velocity distribution Visualization computational methods convection machine learning
ISSN:	0022-1120, 1469-7645
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Abstract	Tomographic background oriented Schlieren (Tomo-BOS) imaging measures density or temperature fields in three dimensions 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 three-dimensional (3-D) velocity and pressure fields from snapshots of 3-D temperature fields obtained by Tomo-BOS imaging. The 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 two-dimensional 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 centre 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.
AbstractList	Tomographic background oriented Schlieren (Tomo-BOS) imaging measures density or temperature fields in three dimensions 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 three-dimensional (3-D) velocity and pressure fields from snapshots of 3-D temperature fields obtained by Tomo-BOS imaging. The 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 two-dimensional 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 centre 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. Furthermore, the results in this paper indicate that the proposed deep learning technique can become a promising direction in experimental fluid mechanics. Tomographic background oriented Schlieren (Tomo-BOS) imaging measures density or temperature fields in three dimensions 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 three-dimensional (3-D) velocity and pressure fields from snapshots of 3-D temperature fields obtained by Tomo-BOS imaging. The 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 two-dimensional 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 centre 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.
ArticleNumber	A102
Author	Wang, Zhicheng Fuest, Frederik Karniadakis, George Em Cai, Shengze Jeon, Young Jin Gray, Callum
Author_xml	– sequence: 1 givenname: Shengze orcidid: 0000-0003-0122-6864 surname: Cai fullname: Cai, Shengze organization: 1Division of Applied Mathematics, Brown University, Providence, RI 02912, USA – sequence: 2 givenname: Zhicheng orcidid: 0000-0002-5856-6459 surname: Wang fullname: Wang, Zhicheng organization: 1Division of Applied Mathematics, Brown University, Providence, RI 02912, USA – sequence: 3 givenname: Frederik surname: Fuest fullname: Fuest, Frederik organization: 2LaVision GmbH, Anna-Vandenhoeck-Ring 19, D-37081 Goettingen, Germany – sequence: 4 givenname: Young Jin surname: Jeon fullname: Jeon, Young Jin organization: 2LaVision GmbH, Anna-Vandenhoeck-Ring 19, D-37081 Goettingen, Germany – sequence: 5 givenname: Callum surname: Gray fullname: Gray, Callum organization: 3LaVision Inc., 211 W. Michigan Ave., Ypsilanti, MI 48197, USA – sequence: 6 givenname: George Em surname: Karniadakis fullname: Karniadakis, George Em email: george_karniadakis@brown.edu organization: 1Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
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Publisher	Cambridge University Press
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Snippet	Tomographic background oriented Schlieren (Tomo-BOS) imaging measures density or temperature fields in three dimensions using multiple camera BOS projections,...
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SubjectTerms	Algorithms Coffee computational methods convection Data Datasets Deep learning Dimensions Experiments Fluid dynamics Fluid flow Fluid mechanics Heat transfer Hydrodynamics Imaging Imaging techniques Inference JFM Papers machine learning MATHEMATICS AND COMPUTING Neural networks Partial differential equations Physics Pressure Temperature distribution Temperature fields Velocity Velocity distribution Visualization
Title	Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks
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