论文标题
二维湍流对流的储层计算模型
Reservoir computing model of two-dimensional turbulent convection
论文作者
论文摘要
储层计算用于建模大规模演变和由此产生的低阶湍流统计数据，该二维湍流雷利 - 雷纳德对流以雷利数字为$ {\ rm ra} = 10^7 $ and prandtl Number $ $ {\ rm pr} = 7 $ interived intertive the intext intertive thecript thecript thecript intive inteact thecript thecript thecript intift theack thecript thection intive nived thection thectio niver intive nived bation，对流流的数值模拟包括一个两步过程。 （1）通过适当的正交分解（POD）快照分析和随后的截断到与最大的总能量振幅相关的第一个150个POD模式的截断来减少原始仿真数据。 （2）储层计算模型的设置和优化，以描述这150度自由度的动态演化，从而描述对流流量的大规模演变。对储层计算模型的预测质量进行了全面测试。该模型的核心是储层，这是一个非常大的稀疏随机网络，该网络由相应的邻接矩阵的光谱半径和一些进一步的超参数构成，以研究预测的质量。我们的工作表明，储层计算模型能够对湍流对流的大规模结构和低阶统计进行建模，这可以为大型循环模型中的中尺度对流过程建模新的途径。
Reservoir computing is applied to model the large-scale evolution and the resulting low-order turbulence statistics of a two-dimensional turbulent Rayleigh-Bénard convection flow at a Rayleigh number ${\rm Ra}=10^7$ and a Prandtl number ${\rm Pr}=7$ in an extended domain with an aspect ratio of 6. Our data-driven approach which is based on a long-term direct numerical simulation of the convection flow comprises a two-step procedure. (1) Reduction of the original simulation data by a Proper Orthogonal Decomposition (POD) snapshot analysis and subsequent truncation to the first 150 POD modes which are associated with the largest total energy amplitudes. (2) Setup and optimization of a reservoir computing model to describe the dynamical evolution of these 150 degrees of freedom and thus the large-scale evolution of the convection flow. The quality of the prediction of the reservoir computing model is comprehensively tested. At the core of the model is the reservoir, a very large sparse random network charcterized by the spectral radius of the corresponding adjacency matrix and a few further hyperparameters which are varied to investigate the quality of the prediction. Our work demonstrates that the reservoir computing model is capable to model the large-scale structure and low-order statistics of turbulent convection which can open new avenues for modeling mesoscale convection processes in larger circulation models.
