Deep Neural Operator

Deep neural operators (DNOs) are a class of machine learning models designed to efficiently approximate the solution operators of partial differential equations (PDEs), enabling faster and more scalable simulations of complex physical systems. Current research focuses on improving DNO architectures, such as DeepONets and Fourier Neural Operators (FNOs), to handle heterogeneous data, reduce computational costs, and enhance extrapolation capabilities, often incorporating techniques like latent space learning and multifidelity approaches. This field is significant because DNOs offer a powerful alternative to traditional numerical methods for solving PDEs, with applications ranging from additive manufacturing and climate modeling to fluid dynamics and materials science, accelerating scientific discovery and engineering design.