Operator learning has undergone rapid development in recent years and gradually emerged as a transformative machine-learning paradigm. In this talk, I will provide an overview of the operator-learning framework and its applications to address modern computational challenges, with a focus on quantum many-body dynamics. Using a recent study by our group, I will demonstrate how established machine-learning frameworks, such as recurrent neural networks (RNNs) which is traditionally used for time-series modeling, can be effectively adapted to learn operators. These learned operators enable the development of efficient solvers for simulating the nonequilibrium dynamics of quantum many-body systems. Finally, I will explain the potential of the operator-learning paradigm to address other key challenges in this area, particularly given the fact that quantum many-body dynamics are often high-dimensional but not necessarily chaotic.
