Editorial: Data-driven modeling and optimization in fluid dynamics: From physics-based to machine learning approaches

Data-driven modeling has made a dramatic impact in computational science and engineering and, in particular, in computational fluid dynamics (CFD). One of the earliest uses of data in CFD is the proper orthogonal decomposition (POD), which was introduced by Lumley and his collaborators more than half a century ago. POD is based on a simple yet powerful idea: In the classical Galerkin framework (used in standard numerical methods, e.g., finite element or spectral methods), replace the general purpose basis functions with data-driven basis functions. This very simple idea has made a profound impact in CFD, reducing the computational cost of standard numerical methods by orders of magnitude and enabling challenging numerical simulations in shape optimization, flow control, and uncertainty quantification. Since Lumley’s pioneering work, the field of data-driven modeling has witnessed a tremendous development. Probably the most exciting research area in this field is the use of machine learning. Over the last decade, the focus in data-driven modeling has shifted from physics-based strategies to machine learning approaches, in which instead of merely changing different components of classical methods (e.g., changing the basis in POD), one completely overhauls the entire framework (e.g., instead of using a Galerkin framework, one leverages machine learning algorithms to determine all the model operators). At this point, one natural question is which strategy should be used in CFD? Should one use physics-based or machine learning models? We believe that, as is often the case when discussing numerical methods, the truth is somewhere in the middle. That is, we believe that data-driven models that combine the physical and mathematical insight with machine learning strategies can revolutionize CFD and break new barriers in shape optimization, flow control, and uncertainty quantification. This Research Topic, which OPEN ACCESS