Deep operator networks (DeepONets, DONs) offer a distinct advantage over
traditional neural networks in their ability to be trained on multi-resolution
data. This property becomes especially relevant in real-world scenarios where
high-resolution measurements are difficult to obtain, while low-resolution data
is more readily available. Nevertheless, DeepONets alone often struggle to
capture and maintain dependencies over long sequences compared to other
state-of-the-art algorithms. We propose a novel architecture, named DON-LSTM,
which extends the DeepONet with a long short-term memory network (LSTM).
Combining these two architectures, we equip the network with explicit
mechanisms to leverage multi-resolution data, as well as capture temporal
dependencies in long sequences. We test our method on long-time-evolution
modeling of multiple non-linear systems and show that the proposed
multi-resolution DON-LSTM achieves significantly lower generalization error and
requires fewer high-resolution samples compared to its vanilla counterparts.

通过在深度操作网络中增加长期短期记忆网络，我们提出了一种名为 DON-LSTM 的新型架构，使网络具备了利用多分辨率数据和捕捉长序列中的时间依赖性的能力。在多个非线性系统的长时间演化建模任务中，我们测试了我们的方法，并展示了提出的多分辨率 DON-LSTM 相对于其原始对照模型，在泛化误差显著减小且需要更少高分辨率样本的优势。