Similarity Learning with neural networks
This provides a method for discovering physical laws from data, with potential applications in fluid mechanics and other domains, though it appears incremental as it builds on existing similarity learning and neural network techniques.
The authors developed a neural network algorithm to automatically identify similarity relations from data, approximating underlying physical laws for dimensionless quantities, and demonstrated its application in fluid mechanics examples like laminar and turbulent pipe flows.
In this work, we introduce a neural network algorithm designed to automatically identify similarity relations from data. By uncovering these similarity relations, our network approximates the underlying physical laws that relate dimensionless quantities to their dimensionless variables and coefficients. Additionally, we develop a linear algebra framework, accompanied by code, to derive the symmetry groups associated with these similarity relations. While our approach is general, we illustrate its application through examples in fluid mechanics, including laminar Newtonian and non-Newtonian flows in smooth pipes, as well as turbulent flows in both smooth and rough pipes. Such examples are chosen to highlight the framework's capability to handle both simple and intricate cases, and further validates its effectiveness in discovering underlying physical laws from data.