Multi-scale reconstruction of turbulent rotating flows with proper orthogonal decomposition and generative adversarial networks

Abstract

Data reconstruction of rotating turbulent snapshots is investigated utilizing data-driven tools. This problem is crucial for numerous geophysical applications and fundamental aspects, given the concurrent effects of direct and inverse energy cascades. Additionally, benchmarking of various reconstruction techniques is essential to assess the trade-off between quantitative supremacy, implementation complexity and explicability. In this study, we use linear and nonlinear tools based on the proper orthogonal decomposition (POD) and generative adversarial network (GAN) for reconstructing rotating turbulence snapshots with spatial damages (inpainting). We focus on accurately reproducing both statistical properties and instantaneous velocity fields. Different gap sizes and gap geometries are investigated in order to assess the importance of coherency and multi-scale properties of the missing information. Surprisingly enough, concerning point-wise reconstruction, the nonlinear GAN does not outperform one of the linear POD techniques. On the other hand, the supremacy of the GAN approach is shown when the statistical multi-scale properties are compared. Similarly, extreme events in the gap region are better predicted when using GAN. The balance between point-wise error and statistical properties is controlled by the adversarial ratio, which determines the relative importance of the generator and the discriminator in the GAN training.

Multi-Scale Reconstruction of Turbulent Rotating Flows with Generative Diffusion Models

“…Under strong rotation, the flow tends to become quasi-2D, characterized by the formation of large-scale coherent vortical structures parallel to the rotation axis [47]. We adopt the same experimental framework as our previous work [23], and explore possible improvements from DMs. We set up a mock field-measurement, anticipating being able to obtain data from a gappy 2D slice of the original 3D volume of rotating turbulence, orthogonal to the axis of rotation.…”

“…POD-based methods are fundamentally linear, yielding reconstructions with smooth flow properties, associated with few leading POD modes. In the context of turbulent flows, this implies that POD-like methods primarily emphasize large-scale structures [22,23]. In recent years, machine learning has led to an increasing number of successful applications in reconstruction tasks for simple and idealized fluid mechanics problems (see [24] for a brief review).…”

“…In recent years, machine learning has led to an increasing number of successful applications in reconstruction tasks for simple and idealized fluid mechanics problems (see [24] for a brief review). We refer to super-resolution applications (i.e., finding high-resolution flow fields from low-resolution data) [25][26][27], inpainting (i.e., reconstructing flow fields having spatial damages) [23,28], and inferring volumetric flows from surface or two-dimensional (2D)-section measurements [29][30][31]. However, much remains to be clarified concerning benchmarks and challenges, and this is even more important for realistic turbulent set-up and at increasing flow complexity, e.g., for increasing Reynolds numbers.…”

“…To move from proof-of-concept to quantitative benchmarks, in a previous work [23], we systematically compared POD-based methods with generative adversarial networks (GANs) [32] using both point-wise and statistical reconstruction objectives for fully developed rotating turbulent flows, accounting for different gap sizes and geometries. GANs belong to the large family of generative models, i.e., machine learning algorithms that produce data according to a probability distribution optimized to resemble that of the data used in the training.…”

“…Contrary to expectations, despite their non-linearity, GANs only matched the best linear POD techniques in point-wise reconstruction. However, GANs showed superior performance in capturing the statistical multi-scale non-Gaussian fluctuation characteristics of three-dimensional (3D) turbulent flow [23].…”