Multivariate Function

Multivariate functions, mapping multiple inputs to a single output, are central to numerous scientific and engineering problems, with research focusing on efficient approximation and optimization techniques. Current efforts explore novel architectures like physics-informed neural networks leveraging tensor decompositions to overcome the curse of dimensionality, and alternative neuron activation functions within Kolmogorov-Arnold networks to improve performance and stability. These advancements are crucial for enhancing the accuracy and efficiency of machine learning models and enabling the analysis of complex high-dimensional systems in diverse fields, including partial differential equation solving and image processing.