Polynomial Basis

Polynomial basis functions are fundamental tools for approximating complex functions, with current research focusing on optimizing their application within various machine learning models, particularly graph neural networks (GNNs) and physics-informed neural networks (PINNs). A key trend involves developing adaptive and learnable polynomial bases that can overcome limitations of fixed, predefined bases, improving performance on tasks like graph classification and solving partial differential equations. These advancements offer significant potential for enhancing the accuracy and efficiency of numerous computational methods across diverse scientific and engineering disciplines.