  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.
