DON-LSTM: Multi-Resolution Learning with DeepONets and Long Short-Term Memory Neural Networks
Abstract
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.
Cite
@article{arxiv.2310.02491,
title = {DON-LSTM: Multi-Resolution Learning with DeepONets and Long Short-Term Memory Neural Networks},
author = {Katarzyna Michałowska and Somdatta Goswami and George Em Karniadakis and Signe Riemer-Sørensen},
journal= {arXiv preprint arXiv:2310.02491},
year = {2023}
}
Comments
18 pages, 3 figures