论文标题

一项有关重建壁式流动温度场的卷积神经网络的研究

A Study on Convolution Neural Network for Reconstructing the Temperature Field of Wall-Bounded Flows

论文作者

Leite, Victor Coppo, Merzari, Elia, Ponciroli, Roberto, Ibarra, Lander

论文摘要

在本研究中,探索了新的卷积神经网络(CNN)模型的功能,其最重要的目标是根据在流体域的边界上采取的有限测量点重建壁结合流的温度场。为此,我们采用了一种利用CNN功能提供的算法,并提供有关物理问题管理方程的其他信息。近年来,在使用CNN进行重建和表征感兴趣的物理变量的空间分布方面取得了巨大进展。原则上,CNN可以用相对减少的参数代表任何连续的数学函数。但是,根据物理问题施加的复杂性,该技术变得不可行。本研究采用了具有数据效力函数近似值的物理知情的神经元网络技术。作为概念证明,CNN经过训练,以根据位于域边界的有限数量的传感器来检索加热通道的温度。在这种情况下,训练数据是考虑到稳态下各种流量条件的温度场解决方案,例如改变雷诺和prandtl数字。此外,考虑了MSR的更复杂几何形状的示范案例。 对CNN性能的评估是由平均L2进行的,最大LINF欧几里得规范源于实际解决方案和CNN的预测之间的差异。最后,进行灵敏度分析,以便考虑到不可避免的噪声的潜在实际应用方案,对CNN的鲁棒性进行了测试。为此,原始的测试输入被覆盖,随机数的正态分布靶向靶向测量点中不同水平的噪声。

In the present study, the capabilities of a new Convolutional Neural Network (CNN) model are explored with the paramount objective of reconstructing the temperature field of wall-bounded flows based on a limited set of measurement points taken at the boundaries of the fluid domain. For that, we employ an algorithm that leverages the CNN capabilities provided with additional information about the governing equations of the physical problem. Great progress has been made in recent years towards reconstructing and characterizing the spatial distribution of physical variables of interest using CNNs. In principle, CNNs can represent any continuous mathematical function with a relatively reduced number of parameters. However, depending on the complexity imposed by the physical problem, this technique becomes unfeasible. The present study employs a Physics Informed Neuron Network technique featuring a data-efficient function approximator. As a proof of concept, the CNN is trained to retrieve the temperature of a heated channel based on a limited number of sensors placed at the boundaries of the domain. In this context, the training data are the temperature fields solutions considering various flows conditions at steady state, e.g varying the Reynolds and the Prandtl numbers. Additionally, a demonstration case considering the more complex geometry of a MSR is also provided. Assessment on the performance of the CNN is done by the mean L2 and the maximum Linf Euclidean norms stemmed from the difference between the actual solutions and the predictions made by the CNN. Finally, a sensitivity analysis is carried out such that the robustness of the CNN is tested considering a potential real application scenario where noise is inevitable. For that, the original test inputs are overlaid with a normal distribution of random numbers targeting to mimic different levels of noise in the measurement points.

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