Experiments, field observations, and large-scale numerical simulations have traditionally been the primary sources of data for the discipline of fluid mechanics. In point of fact, over the course of the last few decades, big data have become a reality in the field of fluid mechanics research (Pollard et al. 2016). This is primarily attributable to the development of high-performance computing architectures as well as advancements in experimental measurement capabilities. The past half-century has seen the development of a wide variety of methods for processing this kind of data, ranging from cutting-edge algorithms for data processing and compression to databases devoted to fluid dynamics (Perlman et al. 2007,Wu & Moin 2008). On the other hand, the interpretation of data pertaining to fluid mechanics has traditionally depended heavily on a combination of statistical analysis, domain expertise, and heuristic algorithms. The proliferation of data in today’s world is pervasive across all areas of scientific study. Deriving insights and information that can be put into action from data has become not just a new method of doing scientific research but also a business opportunity. Our generation is living through an unprecedented confluence of factors, including (a) vast and increasing volumes of data; (b) advancements in computational hardware and reduced costs for computation, data storage, and transfer; (c) highly advanced algorithms; (d) an increase in the availability of open source software and benchmark problems; and (e) substantial and ongoing investment by industry on data-driven problem solving.
In turn, these developments have fostered fresh interest and success in the discipline of machine learning (ML), which is used to extract information from this data. Machine learning is now making significant progress in the field of fluid mechanics. These learning algorithms can be placed into one of three categories: supervised, semisupervised, or unsupervised learning , depending on the amount of knowledge the learning machine has access to on the data being processed (LM). ML offers a modelling framework that is both flexible and modular, and it can be adapted to address a wide variety of challenges in the field of fluid mechanics. Some examples of these challenges include reduced-order modelling, experimental data processing, shape optimization, turbulence closure modelling, and control. It is possible to draw parallels between the development of numerical methods in the 1940s and 1950s to solve the equations of fluid dynamics and the current movement in the focus of scientific investigation away from fundamental principles and toward data-driven approaches. The field of fluid mechanics stands to gain from the use of learning algorithms, while at the same time posing problems that might propel the development of these algorithms to the point where they complement human knowledge and engineering intuition.
The history of the intersection between machine learning and fluid dynamics is lengthy and might perhaps be unexpected. In the early 1940s, Kolmogorov, one of the founding fathers of statistical learning theory, believed turbulence to be one of the theory’s most important application fields (Kolmogorov 1941). In the 1950s and 1960s, there were two main innovations that contributed to the advancement of machine learning. On the one hand, we can differentiate between cybernetics (Wiener 1965) and expert systems that are designed to imitate the thinking process of the human brain, and on the other hand, we can differentiate between machines like the perceptron (Rosenblatt 1958) that aim to automate processes like classification and regression. The use of perceptrons as a classification method generated a great deal of enthusiasm. However, this excitement was extinguished when it was discovered that their capabilities had serious restrictions (Minsky and Papert 1969): Single-layer perceptrons were only capable of learning linearly separable functions, and they were incapable of learning the XOR function. It was established fact that multilayer perceptrons were capable of learning the XOR function; nevertheless, it is possible that their development was constrained by the computational resources available at the time (a recurring theme in ML research). Soon after, people’s interest in artificial intelligence (AI) in general also began to wane, which contributed to the decline in interest in perceptrons.
The problems that arise in fluid dynamics are distinct from those that must be solved in other applications of machine learning, such as image identification and advertising. In order to properly study fluid flows, it is frequently necessary to exactly quantify the physical mechanisms that are operating below them. In addition, fluid flows often display complicated, multiscale phenomena, the comprehension and management of which are still in a significant state of flux. Unsteady flow fields call for machine learning algorithms that are able to handle nonlinearities and numerous spatiotemporal scales, both of which are perhaps absent from the most common ML techniques. In addition, many popular applications of ML, such as playing the game Go, depend on low-cost system assessments and an extensive categorization of the process that has to be taught. This is something that must be done. This is not the case when dealing with fluids, however, as tests involving fluids may be difficult to replicate or automate, and simulations involving fluids may need large-scale supercomputers that run for lengthy periods of time. Machine learning has also become essential in the field of robotics, where algorithms like reinforcement learning (RL) are utilised on a regular basis in autonomous driving and flight. Even though many types of robots work in fluids, it would appear that the complexities of fluid dynamics are not a primary consideration in the design of these robots at this time. Solutions that mimic the forms and processes found in nature are frequently the standard, evoking memories of the early days of aviation (for more information, see the sidebar entitled “Learning Fluid Mechanics: From Living Organisms to Machines). When robotic devices’ energy consumption and dependability in complicated flow conditions become a problem, we believe that a deeper knowledge and exploitation of fluid mechanics will become crucial in the design of those devices.
In the context of flow control, actively or passively modifying flow dynamics for the purpose of achieving an engineering aim can change the character of the system. This renders it hard to make predictions based on data collected from uncontrolled systems. Flow data may be abundant in certain dimensions, such as the spatial resolution, but they may be limited in others. For instance, it may be too expensive to carry out parametric research. In addition, flow data might be quite diverse, which means that selecting the kind of LM requires extra caution and attention. Additionally, the majority of fluid systems are not in a stable state, and even for flows that are stationary, it may be prohibitively costly to achieve conclusions that are statistically convergent. Birds, bats, insects, fish, whales, and a variety of other aquatic and aerial life-forms are capable of remarkable feats of fluid manipulation. They do this by optimising and controlling their shape and motion in order to harness unsteady fluid forces for the purpose of agile propulsion, efficient migration, and other exquisite manoeuvres. The remarkable optimization and control of fluid flow that can be seen in biological systems is a source of inspiration for people of all ages and cultures. How do these creatures become able to control the flow environment in which they live? To this day, we are only aware of a single species that is capable of controlling fluids through an understanding of the Navier–Stokes equations. Since the beginning of recorded history, humans have been developing and building new tools to harness the power of fluids, including but not limited to dams, irrigation systems, mills, and sailing vessels.
In the beginning, success was gained via the use of intuitive design; but, in the last hundred years, quantitative analysis and physics-based design have made it possible to attain unprecedented levels of performance. Indeed, the application of physics to the engineering of fluid systems is one of the pinnacles of human accomplishment. However, there are significant difficulties associated with equation-based analysis of fluids. These difficulties, which include high dimensionality and nonlinearity, make it impossible to arrive at closed-form solutions and limit the amount of effort that can be put into real-time optimization and control. We are rediscovering how to draw insights from past experiences just as the new millennium is getting underway, and this time we are armed with increasingly potent tools in the fields of machine learning and data-driven optimization.