Basis Expansion

Basis expansion techniques aim to represent complex functions or data using a linear combination of simpler basis functions, improving computational efficiency and interpretability. Current research focuses on developing adaptive and dynamic basis expansion methods, employing neural networks (like Fourier Neural Operators) and Gaussian processes, often within online learning frameworks and meta-learning approaches to handle diverse datasets and improve model generalization. These advancements are impacting diverse fields, enabling efficient solutions for problems in signal processing, differential equation solving, and physical modeling, particularly where high dimensionality or complex relationships between variables are involved.