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-recurrent network (PG-PhyCRNet) and polynomial extractor for rogue wave patterns (PE-RWP).