Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications. State-of-the-art methods either use spatial statistics or rely on examples of dense fields in the training phase, which often are not available, and thus rely on synthetic data. Here, we present a reconstruction method that generates dense fields from sparse measurements, without assuming availability of the spatial statistics, nor of examples of the dense fields. This is made possible through the introduction of an automatically differentiable numerical simulator into the training phase of the method. The method is shown to have superior results over statistical and neural network based methods on a set of three standard problems from fluid mechanics.

翻译：从稀疏测量生成密集物理场是采样、信号处理及众多其他应用中的一个基础性问题。现有最先进方法要么利用空间统计信息，要么在训练阶段依赖密集场示例——这些数据通常难以获取，因而往往依赖于合成数据。本文提出一种重建方法，能够在既不假设空间统计信息可得、也不依赖密集场示例的情况下，从稀疏测量生成密集场。这一目标的实现得益于在方法训练阶段引入了自动可微分数值模拟器。在流体力学领域的三个标准问题上，该方法被证明优于基于统计方法与神经网络的方法。