DCNO: Improving Operator Learning through Multi-Stream Dynamic Connections

Transformer-based neural operators offer strong representational capacity for solving partial differential equations (PDEs). However, preserving early latent physical information while allowing representations to evolve remains a challenge as operator depth increases. To address this problem, we propose the Dynamic Connection Neural Operator (DCNO), which assigns information persistence and representation evolution to distinct but interacting latent streams. Specifically, DCNO maintains a slowly evolving operator-memory stream alongside more freely evolving working streams, with each operator layer dynamically reading from all streams. This design keeps early latent information accessible while allowing working representations to evolve through progressive transformations. Extensive experiments across diverse PDE benchmarks demonstrate that DCNO consistently improves predictive performance, while depth-focused analyses further reveal more effective utilization of increased operator depth.