Special issue on machine learning and data-driven methods in fluid dynamics

Abstract

Machine learning (i.e., modern data-driven optimization and applied regression) is a rapidly growing field of research that is having a profound impact across many fields of science and engineering. In the past decade, machine learning has become a critical complement to existing experimental, computational, and theoretical aspects of fluid dynamics. In this short article, we are excited to introduce this special issue highlighting a number of promising avenues of ongoing research to integrate machine learning and data-driven techniques in the field of fluid dynamics. We will also attempt to provide a broader perspective, outlining recent successes, opportunities, and open challenges, while balancing optimism and skepticism. In the field of fluid dynamics, there is an interesting parallel between the rise of machine learning in recent years and the rise of computational science decades earlier. Neither approach fundamentally changes the scientific questions being asked nor the higher-level objectives. Rather, both approaches provide sophisticated tools for analysis based on emerging technologies, enabling the community to address scientific questions at a greater scale and a broader scope than was previously possible. In the early years of computational fluid dynamics, there were voices of both extreme skepticism and open-ended optimism that these new approaches would supplant existing techniques. In reality, computational techniques have provided another valuable perspective for scientific inquiry, complementing more traditional approaches. It is therefore reasonable to believe that machine learning and data-intensive analysis will have a similar impact, complementing other well-established techniques to expand our collective capabilities. Machine learning offers a wealth of techniques to discover patterns in high-dimensional data [5,6], extending traditional modal expansions that have been a cornerstone of fluid dynamics for decades [26,27]. Despite this great potential, it is important to recognize that these algorithms must be used properly, and that a single tool alone will not be equipped to address every task. The same factors that make data-driven and machine learning methods so appealing-namely, that they are relatively easy to use and do not require expert knowledge-can also serve as a potential downfall. Much as users of CFD software are cautioned against blind application of these numerical tools without proper knowledge, training, and verification/validation, we must adopt a similar philosophy for the use of data-driven and machine learning tools. Communicated by Tim Colonius.

Retracing hypoxia in Eckernförde Bight (Baltic Sea)

“…In our model frameworks we distinguish between two types of ventilation: for one, vertical mixing driven by isotropic turbulence and composed of a parameterization of constant background mixing complemented by a surface mixed layer model that mimics the effect of convection, shear instability, and wind-induced turbulence (more specifically we use the KPP scheme of Large et al, 1994). Vertical mix- H. Dietze and U. Löptien: Retracing hypoxia in Eckernförde Bight ing is difficult to constrain in models because direct observations of turbulence are rare and additional complexity arises from numerical subtleties in models (e.g., Burchard et al, 2008). That said, we use the fidelity of simulated temperatures as a proxy for the realism of mixing rates: our simulations LoMix and MedMix featuring a vertical diffusivity of 5 × 10 −5 and 10 −4 m 2 s −1 both fit the observations inside the bight reasonably well.…”

Machine-learning-based spatio-temporal super resolution reconstruction of turbulent flows

“…In recent years, machine learning methods have been utilized to tackle various problems in fluid dynamics (Brenner, Eldredge & Freund 2019; Brunton, Hemanti & Taira 2020 a ; Fukami, Fukagata & Taira 2020 a ; Brunton, Noack & Koumoutsakos 2020 b ). Applications of machine learning for turbulence modelling have been particularly active in fluid dynamics (Kutz 2017; Duraisamy, Iaccarino & Xiao 2019).…”

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

“…2021). Since a few studies have also recently recognized the challenges of the current form of CNN-AE for turbulence (Brunton, Hemati & Taira 2020; Fukami et al. 2020 c ; Glaws, King & Sprague 2020; Nakamura et al.…”