论文标题
转移学习增强了deponet，以长期预测进化方程
Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations
论文作者
论文摘要
Deep Operator Network（DeepOnet）在各种学习任务中表现出了巨大的成功，包括偏微分方程的学习解决方案操作员。特别是，它提供了一种有效的方法来预测有限时间范围内的演化方程。然而，在长期的预测中，香草陶器遭受了稳定退化的问题。本文提出了一个{\ em转移学习}辅助deponet，以增强稳定性。我们的想法是使用转移学习来依次更新Deponets，因为在不同时间范围内学到的繁殖者的替代物。不断发展的deponets可以更好地跟踪进化方程的各种复杂性，而只需要通过对一小部分操作员网络进行有效培训来更新。通过系统的实验，我们表明，所提出的方法不仅提高了DeepOnet的长期准确性，同时保持相似的计算成本，而且还大大减少了训练集的样本量。
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.
