Physics-Based Deep Learning for Flow Problems

It is the tradition for the fluid community to study fluid dynamics problems via numerical simulations such as finite-element, finite-difference and finite-volume methods. These approaches use various mesh techniques to discretize a complicated geometry and eventually convert governing equations int...

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Autores principales:	Yubiao Sun, Qiankun Sun, Kan Qin
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	deep learning physics-informed neural networks partial differential equation automatic differentiation surrogate model Technology T
Acceso en línea:	https://doaj.org/article/3e2ce04ef0e14e50bf12d9c3e86bbc0d
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id	oai:doaj.org-article:3e2ce04ef0e14e50bf12d9c3e86bbc0d
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spelling	oai:doaj.org-article:3e2ce04ef0e14e50bf12d9c3e86bbc0d2021-11-25T17:28:33ZPhysics-Based Deep Learning for Flow Problems10.3390/en142277601996-1073https://doaj.org/article/3e2ce04ef0e14e50bf12d9c3e86bbc0d2021-11-01T00:00:00Zhttps://www.mdpi.com/1996-1073/14/22/7760https://doaj.org/toc/1996-1073It is the tradition for the fluid community to study fluid dynamics problems via numerical simulations such as finite-element, finite-difference and finite-volume methods. These approaches use various mesh techniques to discretize a complicated geometry and eventually convert governing equations into finite-dimensional algebraic systems. To date, many attempts have been made by exploiting machine learning to solve flow problems. However, conventional data-driven machine learning algorithms require heavy inputs of large labeled data, which is computationally expensive for complex and multi-physics problems. In this paper, we proposed a data-free, physics-driven deep learning approach to solve various low-speed flow problems and demonstrated its robustness in generating reliable solutions. Instead of feeding neural networks large labeled data, we exploited the known physical laws and incorporated this physics into a neural network to relax the strict requirement of big data and improve prediction accuracy. The employed physics-informed neural networks (PINNs) provide a feasible and cheap alternative to approximate the solution of differential equations with specified initial and boundary conditions. Approximate solutions of physical equations can be obtained via the minimization of the customized objective function, which consists of residuals satisfying differential operators, the initial/boundary conditions as well as the mean-squared errors between predictions and target values. This new approach is data efficient and can greatly lower the computational cost for large and complex geometries. The capacity and generality of the proposed method have been assessed by solving various flow and transport problems, including the flow past cylinder, linear Poisson, heat conduction and the Taylor–Green vortex problem.Yubiao SunQiankun SunKan QinMDPI AGarticledeep learningphysics-informed neural networkspartial differential equationautomatic differentiationsurrogate modelTechnologyTENEnergies, Vol 14, Iss 7760, p 7760 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	deep learning physics-informed neural networks partial differential equation automatic differentiation surrogate model Technology T
spellingShingle	deep learning physics-informed neural networks partial differential equation automatic differentiation surrogate model Technology T Yubiao Sun Qiankun Sun Kan Qin Physics-Based Deep Learning for Flow Problems
description	It is the tradition for the fluid community to study fluid dynamics problems via numerical simulations such as finite-element, finite-difference and finite-volume methods. These approaches use various mesh techniques to discretize a complicated geometry and eventually convert governing equations into finite-dimensional algebraic systems. To date, many attempts have been made by exploiting machine learning to solve flow problems. However, conventional data-driven machine learning algorithms require heavy inputs of large labeled data, which is computationally expensive for complex and multi-physics problems. In this paper, we proposed a data-free, physics-driven deep learning approach to solve various low-speed flow problems and demonstrated its robustness in generating reliable solutions. Instead of feeding neural networks large labeled data, we exploited the known physical laws and incorporated this physics into a neural network to relax the strict requirement of big data and improve prediction accuracy. The employed physics-informed neural networks (PINNs) provide a feasible and cheap alternative to approximate the solution of differential equations with specified initial and boundary conditions. Approximate solutions of physical equations can be obtained via the minimization of the customized objective function, which consists of residuals satisfying differential operators, the initial/boundary conditions as well as the mean-squared errors between predictions and target values. This new approach is data efficient and can greatly lower the computational cost for large and complex geometries. The capacity and generality of the proposed method have been assessed by solving various flow and transport problems, including the flow past cylinder, linear Poisson, heat conduction and the Taylor–Green vortex problem.
format	article
author	Yubiao Sun Qiankun Sun Kan Qin
author_facet	Yubiao Sun Qiankun Sun Kan Qin
author_sort	Yubiao Sun
title	Physics-Based Deep Learning for Flow Problems
title_short	Physics-Based Deep Learning for Flow Problems
title_full	Physics-Based Deep Learning for Flow Problems
title_fullStr	Physics-Based Deep Learning for Flow Problems
title_full_unstemmed	Physics-Based Deep Learning for Flow Problems
title_sort	physics-based deep learning for flow problems
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/3e2ce04ef0e14e50bf12d9c3e86bbc0d
work_keys_str_mv	AT yubiaosun physicsbaseddeeplearningforflowproblems AT qiankunsun physicsbaseddeeplearningforflowproblems AT kanqin physicsbaseddeeplearningforflowproblems
_version_	1718412278974382080

Physics-Based Deep Learning for Flow Problems

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