Similarity Learning with neural networks

Understanding and predicting the behavior of complex physical systems is a cornerstone of scientific and engineering endeavors. In fluid mechanics, for instance, accurately simulating real operational conditions is essential for the design and optimization of pipelines, aerospace components, and various industrial processes. However, full-scale simulations of such systems are often prohibitively expensive and time-consuming due to the intricate dynamics and vast parameter spaces involved. This poses a significant challenge for researchers and engineers who seek to explore and optimize these systems efficiently. One promising approach to mitigate these challenges is the identification of scaling similarities and symmetry groups within physical systems. By uncovering the correct scaling relations, we can develop smaller, more manageable models that accurately capture the essential behavior of real-world scenarios. These scaled models not only reduce computational costs but also accelerate the design and testing processes by allowing for efficient exploration of the parameter space. Moreover, understanding these scaling laws deepens our insight into the fundamental principles governing these systems, enabling us to generalize findings from simplified models to full-scale applications with greater confidence. In recent years, the application of machine learning in fluid mechanics has been on the rise, offering innovative tools to address complex problems that are difficult to solve analytically.