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

doi:10.1063/5.0110342

	DRVN (deep random vortex network): A new physics-informed machine learning method for simulating and inferring incompressible fluid flows
	Zhang, Rui 2; Hu, Peiyan 2; Meng, Qi 3,4; Wang, Yue 3; Zhu, Rongchan 1; Chen, Bingguang 2; Ma, Zhi-Ming 2; Liu, Tie-Yan 3
刊名	PHYSICS OF FLUIDS
	2022-10-01
卷号	34 期号:10 页码:21
ISSN号	1070-6631
DOI	10.1063/5.0110342
英文摘要	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.
资助项目	Microsoft Research AI4Science
WOS研究方向	Mechanics ; Physics
语种	英语
出版者	AIP Publishing
WOS记录号	WOS:000876715800007
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60722]
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.Bielefeld Univ Math, Bielefeld, Germany 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 3.Microsoft Res AI4Sci, Beijing, Peoples R China 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.