High Dimensional Problem

High-dimensional problems, characterized by a large number of variables or parameters, pose significant challenges across diverse scientific fields. Current research focuses on developing efficient algorithms and model architectures, such as neural operators, Alternating and Iteratively-Reweighted Least Squares (AIRLS), and various Bayesian optimization enhancements, to overcome computational limitations and improve accuracy in high-dimensional settings. These advancements are crucial for tackling complex problems in areas like reliability analysis, economic modeling, and machine learning, enabling more accurate and efficient solutions where traditional methods fall short. The development of dimension-insensitive metrics and robust methods for handling noise and outliers further enhances the reliability and interpretability of results.