Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks
TLDR
In this article, the authors proposed a new method based on physics-informed neural networks (PINNs) to infer the full continuous three-dimensional (3D) velocity and pressure fields from snapshots of 3-D temperature fields obtained by Tomo-BOS imaging.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.read more
Citations
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Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations
TL;DR: In this paper, the authors proposed a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled advection dispersion and Darcy flow equations with space-dependent hydraulic conductivity.
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Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations
TL;DR: In this article, the authors proposed a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled advection dispersion and Darcy flow equations with space-dependent hydraulic conductivity.
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When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
TL;DR: In this article, a prior generalization bound via the complexity of the target functions in the PDE problem, and a posterior generalization constraint via the posterior matrix norms of the networks after optimization were provided for general multi-layer PINNs and extended PINNs.
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Physics-informed neural networks (PINNs) for fluid mechanics: A review.
TL;DR: In this article, a physics-informed neural network (PINN) is proposed for inverse flow problems, which integrates seamlessly data and mathematical models, and demonstrates the effectiveness of PINNs for inverse problems related to three-dimensional wake flows, supersonic flows and biomedical flows.
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PDE-constrained Models with Neural Network Terms: Optimization and Global Convergence.
TL;DR: In this article, the optimization of a class of linear elliptic partial differential equation (PDE) models with neural network terms was studied, and the neural network parameters were optimized using gradient descent, where the gradient was evaluated using an adjoint PDE.
References
More filters
Journal ArticleDOI
Deep learning
TL;DR: Deep learning is making major advances in solving problems that have resisted the best attempts of the artificial intelligence community for many years, and will have many more successes in the near future because it requires very little engineering by hand and can easily take advantage of increases in the amount of available computation and data.
Posted Content
Adam: A Method for Stochastic Optimization
Diederik P. Kingma,Jimmy Ba +1 more
TL;DR: In this article, the adaptive estimates of lower-order moments are used for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimate of lowerorder moments.
Journal ArticleDOI
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
TL;DR: In this article, the authors introduce physics-informed neural networks, which are trained to solve supervised learning tasks while respecting any given laws of physics described by general nonlinear partial differential equations.
Book
Particle Image Velocimetry: A Practical Guide
TL;DR: In this paper, the authors present a practical guide for the planning, performance and understanding of experiments employing the PIV technique, which is primarily intended for engineers, scientists and students, who already have some basic knowledge of fluid mechanics and nonintrusive optical measurement techniques.
Journal ArticleDOI
Solving high-dimensional partial differential equations using deep learning
TL;DR: A deep learning-based approach that can handle general high-dimensional parabolic PDEs using backward stochastic differential equations and the gradient of the unknown solution is approximated by neural networks, very much in the spirit of deep reinforcement learning with the gradient acting as the policy function.