Multi-resolution learning with operator- and recurrent neural networks

Operator networks, unlike traditional neural networks can be trained on multi-resolution data. Motivated by the real-world applications where high-resolution data is commonly more difficult to obtain, we leverage this property and present an architecture that combines operator networks with long short-term memory (LSTM) architecture in order to capture long-time behavior of multiple dynamical systems. We show that the proposed models are able to achieve much higher accuracy in high-resolution testing, while the single-resolution counterparts require significantly more high-resolution training samples to achieve competitive results.