Operator Learning

Operator learning focuses on developing machine learning models that approximate mappings between infinite-dimensional function spaces, primarily to efficiently solve complex partial differential equations (PDEs) and model dynamical systems. Current research emphasizes developing novel architectures like DeepONets, Fourier Neural Operators, and Graph Neural Operators, along with exploring the use of Gaussian Processes and incorporating physical constraints for improved accuracy and generalization. This field is significant because it offers the potential for faster, more accurate, and more scalable solutions to complex scientific and engineering problems compared to traditional numerical methods, particularly in scenarios with limited data or high dimensionality.