Super Resolution for Turbulent Flows in 2D: Stabilized Physics Informed Neural Networks

TL;DR

This paper introduces a physics-informed neural network with embedded observer mechanisms for super-resolution of turbulent flows, capable of estimating unknown forces and reconstructing high-resolution flow data from low-resolution noisy inputs.

Contribution

The novel neural network design integrates a Luenberger-type observer and force estimation to enhance super-resolution of turbulent flows with unknown destabilizing forces.

Findings

Successfully recovers unknown forcing from data.

Accurately predicts high-resolution turbulent flows from low-resolution noisy observations.

Demonstrates robustness and stability in turbulent flow reconstruction.

Abstract

We propose a new design of a neural network for solving a zero shot super resolution problem for turbulent flows. We embed Luenberger-type observer into the network's architecture to inform the network of the physics of the process, and to provide error correction and stabilization mechanisms. In addition, to compensate for decrease of observer's performance due to the presence of unknown destabilizing forcing, the network is designed to estimate the contribution of the unknown forcing implicitly from the data over the course of training. By running a set of numerical experiments, we demonstrate that the proposed network does recover unknown forcing from data and is capable of predicting turbulent flows in high resolution from low resolution noisy observations.