DeepONet Framework

Deep Operator Networks (DeepONets) are a novel type of neural network designed to efficiently approximate complex mathematical operators, particularly those governing solutions to partial differential equations (PDEs). Current research focuses on enhancing DeepONet architectures, such as incorporating multi-task learning and Bayesian methods, to improve accuracy, handle uncertainty, and reduce training costs. These advancements are enabling more robust and efficient solutions for a wide range of scientific and engineering problems, including fluid dynamics, heat transfer, and power grid simulations, by providing accurate and uncertainty-quantified surrogate models. The ability to learn and generalize from relatively small datasets makes DeepONets a powerful tool for tackling computationally expensive simulations.