Reducing data resolution for better super-resolution: Reconstructing turbulent flows from noisy observation

Fuente: arXiv
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Auteurs principaux: Yeo, Kyongmin, Zimoń, Małgorzata J., Zayats, Mykhaylo, Zhuk, Sergiy
Format: Preprint
Publié: 2024
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author Yeo, Kyongmin
Zimoń, Małgorzata J.
Zayats, Mykhaylo
Zhuk, Sergiy
author_facet Yeo, Kyongmin
Zimoń, Małgorzata J.
Zayats, Mykhaylo
Zhuk, Sergiy
contents A super-resolution (SR) method for the reconstruction of Navier-Stokes (NS) flows from noisy observations is presented. In the SR method, first the observation data is averaged over a coarse grid to reduce the noise at the expense of losing resolution and, then, a dynamic observer is employed to reconstruct the flow field by reversing back the lost information. We provide a theoretical analysis, which indicates a chaos synchronization of the SR observer with the reference NS flow. It is shown that, even with noisy observations, the SR observer converges toward the reference NS flow exponentially fast, and the deviation of the observer from the reference system is bounded. Counter-intuitively, our theoretical analysis shows that the deviation can be reduced by increasing the lengthscale of the spatial average, i.e., making the resolution coarser. The theoretical analysis is confirmed by numerical experiments of two-dimensional NS flows. The numerical experiments suggest that there is a critical lengthscale for the spatial average, below which making the resolution coarser improves the reconstruction.
format Preprint
id arxiv_https___arxiv_org_abs_2411_05240
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Reducing data resolution for better super-resolution: Reconstructing turbulent flows from noisy observation
Yeo, Kyongmin
Zimoń, Małgorzata J.
Zayats, Mykhaylo
Zhuk, Sergiy
Fluid Dynamics
Dynamical Systems
A super-resolution (SR) method for the reconstruction of Navier-Stokes (NS) flows from noisy observations is presented. In the SR method, first the observation data is averaged over a coarse grid to reduce the noise at the expense of losing resolution and, then, a dynamic observer is employed to reconstruct the flow field by reversing back the lost information. We provide a theoretical analysis, which indicates a chaos synchronization of the SR observer with the reference NS flow. It is shown that, even with noisy observations, the SR observer converges toward the reference NS flow exponentially fast, and the deviation of the observer from the reference system is bounded. Counter-intuitively, our theoretical analysis shows that the deviation can be reduced by increasing the lengthscale of the spatial average, i.e., making the resolution coarser. The theoretical analysis is confirmed by numerical experiments of two-dimensional NS flows. The numerical experiments suggest that there is a critical lengthscale for the spatial average, below which making the resolution coarser improves the reconstruction.
title Reducing data resolution for better super-resolution: Reconstructing turbulent flows from noisy observation
topic Fluid Dynamics
Dynamical Systems
url https://arxiv.org/abs/2411.05240