DRVN (deep random vortex network): A new physics-informed machine learning method for simulating and inferring incompressible fluid flows

doi:10.1063/5.0110342

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	DRVN (deep random vortex network): A new physics-informed machine learning method for simulating and inferring incompressible fluid flows
	Zhang, Rui 1; Hu, Peiyan 1; Meng, Qi 2,4; Wang, Yue 2; Zhu, Rongchan 3; Chen, Bingguang 1; Ma, Zhi-Ming 1; Liu, Tie-Yan 2
	2022-10-01
发表期刊	PHYSICS OF FLUIDS
ISSN	1070-6631
卷号	34 期号:10 页码:21
摘要	We present the deep random vortex network (DRVN), a novel physics-informed framework for simulating and inferring the fluid dynamics governed by the incompressible Navier-Stokes equations. Unlike the existing physics-informed neural network (PINN), which embeds physical and geometry information through the residual of equations and boundary data, DRVN automatically embeds this information into neural networks through neural random vortex dynamics equivalent to the Navier-Stokes equation. Specifically, the neural random vortex dynamics motivates a Monte Carlo-based loss function for training neural networks, which avoids the calculation of derivatives through auto-differentiation. Therefore, DRVN can efficiently solve Navier-Stokes equations with non-differentiable initial conditions and fractional operators. Furthermore, DRVN naturally embeds the boundary conditions into the kernel function of the neural random vortex dynamics and, thus, does not need additional data to obtain boundary information. We conduct experiments on forward and inverse problems with incompressible Navier-Stokes equations. The proposed method achieves accurate results when simulating and when inferring Navier-Stokes equations. For situations that include singular initial conditions and agnostic boundary data, DRVN significantly outperforms the existing PINN method. Furthermore, compared with the conventional adjoint method when solving inverse problems, DRVN achieves a 2 orders of magnitude improvement for the training time with significantly precise estimates. Published under an exclusive license by AIP Publishing.
DOI	10.1063/5.0110342
收录类别	SCI
语种	英语
资助项目	Microsoft Research AI4Science
WOS研究方向	Mechanics ; Physics
WOS类目	Mechanics ; Physics, Fluids & Plasmas
WOS记录号	WOS:000876715800007
出版者	AIP Publishing
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60723
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Rui; Hu, Peiyan
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 2.Microsoft Res AI4Sci, Beijing, Peoples R China 3.Bielefeld Univ Math, Bielefeld, Germany 4.Univ Chinese Acad Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Rui,Hu, Peiyan,Meng, Qi,et al. DRVN (deep random vortex network): A new physics-informed machine learning method for simulating and inferring incompressible fluid flows[J]. PHYSICS OF FLUIDS,2022,34(10):21.
APA	Zhang, Rui.,Hu, Peiyan.,Meng, Qi.,Wang, Yue.,Zhu, Rongchan.,...&Liu, Tie-Yan.(2022).DRVN (deep random vortex network): A new physics-informed machine learning method for simulating and inferring incompressible fluid flows.PHYSICS OF FLUIDS,34(10),21.
MLA	Zhang, Rui,et al."DRVN (deep random vortex network): A new physics-informed machine learning method for simulating and inferring incompressible fluid flows".PHYSICS OF FLUIDS 34.10(2022):21.