Physics-informed Blind Reconstruction of Dense Fields from Sparse Measurements using Neural Networks with a Differentiable Simulator
This addresses a fundamental challenge in sampling and signal processing for applications like fluid mechanics, offering a novel approach that avoids reliance on unavailable data.
The paper tackled the problem of reconstructing dense physical fields from sparse measurements without requiring prior spatial statistics or dense field examples, achieving superior results over existing statistical and neural network methods on three standard fluid mechanics problems.
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.