Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations - Xu, Wuzhe; Lu, Yulong; Wang, Li (Proceedings of the AAAI Conference on Artificial Intelligence, 2023)
Deep operator network (DeepONet) has demonstrated greatsuccess in various learning tasks, including learning solutionoperators of partial differential equations. In particular, it provides an efficient approach to predicting the evolution equationsin a finite time horizon. Nevertheless, the vanilla DeepONetsuffers from the issue of stability degradation in the long-time prediction. This paper proposes a transfer-learning aidedDeepONet to enhance the stability. Our idea is to use transferlearning to sequentially update the DeepONets as the surro-gates for propagators learned in different time frames. Theevolving DeepONets can better track the varying complexitiesof the evolution equations, while only need to be updated byefficient training of a tiny fraction of the operator networks.Through systematic experiments, we show that the proposedmethod not only improves the long-time accuracy of Deep-ONet while maintaining similar computational cost but alsosubstantially reduces the sample size of the training set.