Achieving accurate and robust global situational awareness of a complex time-evolving field from a limited number of sensors has been a long-standing challenge. This reconstruction problem is especially difficult when sensors are sparsely positioned in a seemingly random or unorganized manner, which is often encountered in a range of scientific and engineering problems. Moreover, these sensors could be in motion and could become online or offline over time. The key leverage in addressing this scientific issue is the wealth of data accumulated from the sensors. As a solution to this problem, we propose a data-driven spatial field recovery technique founded on a structured grid-based deep-learning approach for arbitrary positioned sensors of any numbers. It should be noted that naive use of machine learning becomes prohibitively expensive for global field reconstruction and is furthermore not adaptable to an arbitrary number of sensors. In this work, we consider the use of Voronoi tessellation to obtain a structured-grid representation from sensor locations, enabling the computationally tractable use of convolutional neural networks. One of the central features of our method is its compatibility with deep learning-based super-resolution reconstruction techniques for structured sensor data that are established for image processing. The proposed reconstruction technique is demonstrated for unsteady wake flow, geophysical data and three-dimensional turbulence. The current framework is able to handle an arbitrary number of moving sensors and thereby overcomes a major limitation with existing reconstruction methods. Our technique opens a new pathway toward the practical use of neural networks for real-time global field estimation.

通过有限数量的传感器实现对复杂时间演化领域的准确和稳健的全球态势感知一直是一项长期挑战。当传感器以看似随机或无组织的方式稀疏放置时，这种重建问题尤其困难，这在一系列科学和工程问题中经常遇到。此外，这些传感器可能处于运动状态，并且随着时间的推移可能会在线或离线。解决这个科学问题的关键杠杆是传感器积累的大量数据。作为该问题的解决方案，我们提出了一种数据驱动的空间场恢复技术，该技术基于结构化的基于网格的深度学习方法，适用于任意数量的任意定位传感器。应该注意的是，机器学习的幼稚使用对于全局场重建来说变得非常昂贵，而且还不能适应任意数量的传感器。在这项工作中，我们考虑使用 Voronoi 细分从传感器位置获得结构化网格表示，从而使卷积神经网络在计算上易于使用。我们方法的核心特征之一是它与基于深度学习的超分辨率重建技术的兼容性，这些技术是为图像处理而建立的结构化传感器数据。所提出的重建技术针对不稳定尾流、地球物理数据和三维湍流进行了演示。当前框架能够处理任意数量的移动传感器，从而克服了现有重建方法的主要限制。我们的技术为实际使用神经网络进行实时全局场估计开辟了一条新途径。