Operator Learning Method

Operator learning methods aim to learn mappings between functions, effectively representing complex operators such as those governing partial differential equations (PDEs). Current research focuses on developing efficient architectures like DeepONets, Fourier Neural Operators, and Wavelet Neural Operators, often incorporating techniques like boundary integral equations or finite element methods to improve accuracy and applicability to diverse domains. These advancements enable solving PDEs on complex geometries and learning complex dynamical systems, with applications ranging from material science (homogenization) to biophysics (modeling neuron dynamics). The improved accuracy and efficiency of these methods hold significant promise for accelerating scientific computation and enabling new modeling capabilities across various fields.