Super-resolution with dynamics in the loss

TL;DR

This paper introduces a super-resolution method for turbulence that learns to predict high-resolution flow states from coarse data without needing high-resolution training data, using a differentiable flow solver and data assimilation techniques.

Contribution

The authors present a novel super-resolution approach that does not require high-resolution reference data, leveraging a differentiable flow solver and data assimilation for training.

Findings

Achieves similar accuracy to standard super-resolution methods without high-res data.

Outperforms data assimilation in state-estimation on individual trajectories.

Enables accurate flow reconstruction on coarser grids than traditional methods.

Abstract

Super-resolution of turbulence is a term used to describe the prediction of high-resolution snapshots of a flow from coarse-grained observations. This is typically accomplished with a deep neural network and training usually requires a dataset of high-resolution images. An approach is presented here in which robust super resolution can be performed without access to high-resolution reference data, as might be expected in an experiment. The training procedure is similar to data assimilation, wherein the model learns to predict an initial condition that leads to accurate coarse-grained predictions at later times, while only being shown coarse-grained observations. Implementation of the approach requires the use of a fully differentiable flow solver in the training loop to allow for time-marching of predictions. A range of models are trained on data generated from forced, two-dimensional turbulence. The networks have reconstruction errors which are similar to those obtained with `standard' super-resolution approaches using high resolution data. Furthermore, they significantly outperform data-assimilation for state-estimation on individual trajectories, allowing accurate reconstruction on coarser grids than is possible with standard variational approaches.