Identification of Effective Dimensionless Groups in Fluid Mechanics Using Machine Learning: A Buckingham Pi Theorem-Based Approach

Dimensional analysis is one of the fundamental tools in fluid mechanics, employed to simplify complex problems and extract key parameters governing flow behavior. However, the Buckingham Pi theorem, while effective in determining these groups and their ratios, faces limitations in selecting the most influential ones. In this paper, we introduce a machine learning-based approach where all initial dimensionless groups are first extracted using a programming module, followed by the application of machine learning algorithms to identify and prioritize the key groups. The results indicate that this method not only automates the selection of dimensionless parameters but also enables the discovery of more complex relationships and improves the accuracy of flow modeling.

کلیدواژه ها:

Buckingham Pi ، Fluids ، Machine Learning ، Correlation Matrix