Proper Orthogonal Decomposition

Proper Orthogonal Decomposition (POD) is a dimensionality reduction technique used to simplify complex systems, primarily focusing on efficiently approximating solutions to partial differential equations (PDEs) and representing high-dimensional data. Current research emphasizes integrating POD with various machine learning architectures, such as deep neural networks (DeepONets), convolutional autoencoders, and recurrent neural networks (LSTMs), to create more accurate and computationally efficient reduced-order models (ROMs). These hybrid POD-machine learning approaches are proving valuable in diverse fields, including fluid dynamics, aerospace engineering, and electrical machine design, by enabling faster simulations, real-time predictions, and improved data analysis for complex systems.