Higher Dimension

Research on higher dimensions focuses on developing methods to effectively model, analyze, and utilize data and systems existing in spaces beyond our familiar three-dimensional world. Current efforts concentrate on adapting existing algorithms, such as neural networks (including Physics-Informed Neural Networks and Extreme Learning Machines) and dimensional analysis techniques, to handle the computational challenges posed by high-dimensional data, particularly in areas like signal processing, partial differential equation solving, and machine learning. These advancements are crucial for improving accuracy and efficiency in various fields, including computer experiments, multivariate time series classification, and natural language processing, where high-dimensional representations are increasingly common. The ultimate goal is to develop robust and scalable tools for extracting meaningful insights from complex, high-dimensional datasets.