Physics-informed Blind Reconstruction of Dense Fields from Sparse Measurements using Neural Networks with a Differentiable Simulator

TL;DR

This paper introduces a physics-informed neural network approach with a differentiable simulator to reconstruct dense physical fields from sparse data without relying on statistical models or dense field examples.

Contribution

It presents a novel reconstruction method that integrates a differentiable simulator into neural network training, eliminating the need for prior statistical or example data.

Findings

Outperforms existing statistical and neural methods on fluid mechanics problems.

Does not require prior dense field data or spatial statistics.

Demonstrates superior accuracy in dense field reconstruction.

Abstract

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.