Fluid mechanics often involves complex systems characterized by a large number of physical parameters, which are usually described by experimental and numerical sparse data (temporal or spatial). The difficulty of obtaining complete spatio-temporal datasets is a common issue with conventional approaches, such as computational fluid dynamics (CFDs) and various experimental methods, particularly when evaluating and modeling turbulent flows. This review paper focuses on the integration of machine learning (ML), specifically physics-informed neural networks (PINNs), as a means to address this challenge. By directly incorporating governing physical equations into neural network training, PINNs present a novel method that allows for the reconstruction of flow from sparse and noisy data. This review examines various applications in fluid mechanics where sparse data is a common problem and evaluates the effectiveness of PINNs in enhancing flow prediction accuracy. An overview of diverse PINNs methods, their applications, and outcomes is discussed, demonstrating their flexibility and effectiveness in addressing challenges related to sparse data and illustrating that the future of fluid mechanics lies in the synergy between data-driven approaches and established physical theories.
Hassan et al. (Thu,) studied this question.