Smooth Function

Smooth function approximation focuses on efficiently and accurately representing smooth functions using various computational methods, primarily aiming to overcome the challenges posed by high dimensionality and limited data. Current research emphasizes the use of neural networks, particularly shallow networks and those incorporating multiplicative operations, alongside derivative-free optimization techniques that rely solely on function comparisons. These advancements are crucial for diverse applications, including control systems, machine learning optimization, and scientific computing, where efficient and reliable function approximation is essential for model building and prediction.