DON-LSTM: Multi-Resolution Learning with DeepONets and Long Short-Term Memory Neural Networks

• URL: http://arxiv.org/abs/2310.02491v1
• Date: Tue, 3 Oct 2023 23:43:16 GMT
• Title: DON-LSTM: Multi-Resolution Learning with DeepONets and Long Short-Term Memory Neural Networks
• Authors: Katarzyna Micha{\l}owska and Somdatta Goswami and George Em Karniadakis and Signe Riemer-S{\o}rensen
• Abstract summary: Deep operator networks (DeepONets, DONs) offer a distinct advantage over traditional neural networks in their ability to be trained on multi-resolution data. We propose a novel architecture, named DON-LSTM, which extends the DeepONet with a long short-term memory network (LSTM) We show that the proposed multi-resolution DON-LSTM achieves significantly lower generalization error and requires fewer high-resolution samples compared to its vanilla counterparts.
• Score: 1.8434042562191815
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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