Integrable Deep Learning

We explain the motivation for proposing the concept and framework of integrable deep learning(IDL),and focuse on a series of advances we have made in IDL algorithms.1.Two-stage PINN methods based on conservation laws,and PINN methods based on the Miura transformation;2.Lax pair-informed neural networks(LPNNs)and DT-LPNN combined with the Darboux transformation;3.Novel convolutional neural network architectures for integrable systems,including pseudo grid-based physics-informed convolutional-recur-rent network(PG-PhyCRNet)and polynomial extractor for rogue wave patterns(PE-RWP).