Investigation of Nonlinear Relations Among Flow Profiles Using Artificial Neural Networks

This study investigated the ability of artificial neural networks (ANNs) to resolve the nonlinear dynamics inherent in the behavior of complex fluid flows, which often exhibit multifaceted characteristics that challenge traditional analytical or numerical methods. By employing flow profile pairs that are generated through high-fidelity numerical simulations, encompassing both the one-dimensional benchmark problems and the more intricate three-dimensional boundary layer transition problem, this research convincingly demonstrates that neural networks possess a remarkable capacity to effectively capture the discontinuities and the subtle wave characteristics that occur at small scales within complex fluid flows, thereby showcasing their robustness in handling intricate fluid dynamics phenomena. Furthermore, even in the context of challenging three-dimensional problems, this study reveals that the average velocity profiles can be predicted with a high degree of accuracy, utilizing a limited number of input profiles during the training phase, which underscores the efficiency and efficacy of the model in understanding complex systems. The findings of this study significantly underscore the immense potential that artificial neural networks, along with deep learning methodologies, hold in advancing our comprehension of the fundamental physics that govern complex fluid dynamics systems, while concurrently demonstrating their applicability across a variety of flow scenarios and their capacity to yield insightful revelations regarding the nonlinear relationships that exist among diverse flow parameters, thus paving the way for future research in this critical area of study.