  Achieving accurate and robust global situational awareness of a complex
time-evolving field from a limited number of sensors has been a longstanding
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 can be in motion and can 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 the na\"ive use of machine learning becomes prohibitively
expensive for global field reconstruction and is furthermore not adaptable to
an arbitrary number of sensors. In the present 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 the present 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. The
presented technique opens a new pathway towards the practical use of neural
networks for real-time global field estimation.
