Transfer Operator

Transfer operators are mathematical tools used to describe the evolution of probability distributions in dynamical systems, finding applications across diverse fields from fluid dynamics to machine learning. Current research focuses on improving the accuracy and efficiency of estimating these operators from data, often employing techniques like kernel density estimation, optimal transport, and neural network architectures such as DeepONets, to address challenges in transfer learning and long-term forecasting. These advancements enable more accurate modeling of complex systems and efficient solutions to problems in various scientific and engineering domains, including material science, robotics, and the analysis of complex networks.