Extracting Navier-Stokes solutions from noisy data with physics-constrained convolutional neural networks*

Experimental fluid measurements, such as those from PIV and immersed probes, may be corrupted with noise. In this work, we propose a method to extract the solution to the Navier-Stokes equations from noisy and biased data. We introduce the physics-informed convolutional neural network, capable of embedding prior knowledge of the physics in the form of governing equations. This enables us to produce a mapping from the corrupted-observations to the solution of Navier-Stokes equations. Ultimately, this provides the tools required to extract underlying true-solutions to partial differential equations in general.

We showcase this methodology on three physical systems: linear convection-diffusion, non-linear convection-diffusion, and the 2D turbulent Kolmogorov flow. We find that the proposed methodology is capable of removing arbitrary spatially-varying bias, beyond simple stochastic variations in the data, for each system studied. Beyond this, we investigate the robustness of the methodology to multi-modality, magnitude, and form of the corruption - results being agnostic in each case.

This work opens opportunities for the extraction of Navier-Stokes solutions from PIV data and the detection of faulty sensors that introduce biases.