Exploring Physical Latent Spaces for High-Resolution Flow Restoration

TL;DR

This paper introduces a novel approach that uses physical latent spaces derived from PDE simulations to enhance high-resolution flow restoration, enabling neural networks to learn more accurate and flexible fluid flow representations.

Contribution

It presents a new method of integrating physics-based latent spaces with neural networks, allowing for improved flow restoration and the discovery of alternative dynamics.

Findings

Enhanced flow restoration accuracy across turbulence scenarios

Neural networks can modify physical states to better satisfy learning objectives

Significant improvements in modeling complex fluid flows

Abstract

We explore training deep neural network models in conjunction with physics simulations via partial differential equations (PDEs), using the simulated degrees of freedom as latent space for a neural network. In contrast to previous work, this paper treats the degrees of freedom of the simulated space purely as tools to be used by the neural network. We demonstrate this concept for learning reduced representations, as it is extremely challenging to faithfully preserve correct solutions over long time-spans with traditional reduced representations, particularly for solutions with large amounts of small scale features. This work focuses on the use of such physical, reduced latent space for the restoration of fine simulations, by training models that can modify the content of the reduced physical states as much as needed to best satisfy the learning objective. This autonomy allows the neural networks to discover alternate dynamics that significantly improve the performance in the given tasks. We demonstrate this concept for various fluid flows ranging from different turbulence scenarios to rising smoke plumes.