用于三维瑞利-贝纳德对流同化任务的周期性激活物理信息神经网络

IF 2.5 3区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computers & Fluids Pub Date : 2024-08-30 DOI:10.1016/j.compfluid.2024.106419
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引用次数: 0

摘要

我们将物理信息神经网络应用于立方体单元中的三维瑞利-贝纳德对流(瑞利数为 Ra=106,普朗特数为 Pr=0.7),从给定的温度场同化速度矢量场,反之亦然。利用直接数值模拟提供的相应地面实况数据,我们可以评估多层感知器五个隐藏层中每个层所使用的不同激活函数(正弦、双曲正切和指数线性单元)和不同神经元数量(32、64、128、256)的性能。主要结果是,在分析指标、与地面实况的相关性和平均平均误差方面,使用周期性激活函数(正弦)通常有利于提高同化性能。正弦激活物理信息神经网络的结果质量更高,这也体现在推断速度场或温度场的概率密度函数和功率谱上。在两个同化方向上,基于速度的温度场同化似乎更具挑战性,因为它对神经元数量的限制更明显,低于这个数量就无法实现可行的同化结果。
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Periodically activated physics-informed neural networks for assimilation tasks for three-dimensional Rayleigh–Bénard convection

We apply physics-informed neural networks to three-dimensional Rayleigh–Bénard convection in a cubic cell with a Rayleigh number of Ra=106 and a Prandtl number of Pr=0.7 to assimilate the velocity vector field from given temperature fields and vice versa. With the respective ground truth data provided by a direct numerical simulation, we are able to evaluate the performance of the different activation functions applied (sine, hyperbolic tangent and exponential linear unit) and different numbers of neurons (32, 64, 128, 256) for each of the five hidden layers of the multi-layer perceptron. The main result is that the use of a periodic activation function (sine) typically benefits the assimilation performance in terms of the analyzed metrics, correlation with the ground truth and mean average error. The higher quality of results from sine-activated physics-informed neural networks is also manifested in the probability density function and power spectra of the inferred velocity or temperature fields. Regarding the two assimilation directions, the assimilation of temperature fields based on velocities appears to be more challenging in the sense that it exhibits a sharper limit on the number of neurons below which viable assimilation results cannot be achieved.

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来源期刊
Computers & Fluids
Computers & Fluids 物理-计算机:跨学科应用
CiteScore
5.30
自引率
7.10%
发文量
242
审稿时长
10.8 months
期刊介绍: Computers & Fluids is multidisciplinary. The term ''fluid'' is interpreted in the broadest sense. Hydro- and aerodynamics, high-speed and physical gas dynamics, turbulence and flow stability, multiphase flow, rheology, tribology and fluid-structure interaction are all of interest, provided that computer technique plays a significant role in the associated studies or design methodology.
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