Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations
This work addresses a stability issue in operator networks for PDEs, offering an incremental improvement for computational science applications.
The paper tackles the stability degradation of DeepONet in long-time predictions of evolution equations by proposing a transfer-learning aided approach that sequentially updates DeepONets across time frames, resulting in improved accuracy and reduced training sample size while maintaining computational cost.
Deep operator network (DeepONet) has demonstrated great success in various learning tasks, including learning solution operators of partial differential equations. In particular, it provides an efficient approach to predict the evolution equations in a finite time horizon. Nevertheless, the vanilla DeepONet suffers from the issue of stability degradation in the long-time prediction. This paper proposes a {\em transfer-learning} aided DeepONet to enhance the stability. Our idea is to use transfer learning to sequentially update the DeepONets as the surrogates for propagators learned in different time frames. The evolving DeepONets can better track the varying complexities of the evolution equations, while only need to be updated by efficient training of a tiny fraction of the operator networks. Through systematic experiments, we show that the proposed method not only improves the long-time accuracy of DeepONet while maintaining similar computational cost but also substantially reduces the sample size of the training set.