有限传感器条件下流体流动重构的浅层神经网络方法
Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
摘要：
在许多应用中，从有限的测量和有限的数据重建流体流场或一些其他高维状态是重要的。在这项工作中，我们提出了一种基于浅层神经网络的学习方法，这样的流体流动重建。我们的方法学习传感器测量和高维流体流场之间的端到端映射，而无需对原始数据进行任何繁重的预处理。假设没有先验知识，估计方法纯粹是数据驱动的。我们证明了在流体力学和海洋学的三个例子的性能，表明这种现代数据驱动的方法优于传统的模式近似技术，通常用于流重建。所提出的方法不仅表现出优越的性能特性，它也可以产生与该领域的传统方法相当的性能水平，使用显着更少的传感器。因此，数学架构是理想的新兴全球监测技术，测量数据往往是有限的。
英文摘要：
In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such fluid flow reconstruction. Our approach learns an end-to-end mapping between the sensor measurements and the high-dimensional fluid flow field, without any heavy preprocessing on the raw data. No prior knowledge is assumed to be available, and the estimation method is purely data-driven. We demonstrate the performance on three examples in fluid mechanics and oceanography, showing that this modern data-driven approach outperforms traditional modal approximation techniques which are commonly used for flow reconstruction. Not only does the proposed method show superior performance characteristics, it can also produce a comparable level of performance with traditional methods in the area, using significantly fewer sensors. Thus, the mathematical architecture is ideal for emerging global monitoring technologies where measurement data are often limited.
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