Basis Function

Basis functions are fundamental building blocks for approximating complex functions in various scientific and engineering domains, aiming to represent data efficiently and accurately. Current research focuses on developing adaptive and computationally efficient basis function selection methods, exploring novel architectures like Kolmogorov-Arnold networks and incorporating them into models such as Gaussian processes and Physics-Informed Neural Networks. These advancements improve the accuracy and scalability of function approximation across diverse applications, including solving partial differential equations, time series forecasting, and system identification, leading to more efficient and interpretable models.