Grid-Token Neural Operator: Asymmetric Spatiotemporal Coupling for PDE Forecasting

Neural operators offer an efficient surrogate for repeated numerical simulation of partial differential equations (PDEs), but jointly representing spatial detail and temporal dependencies remains challenging. Applying temporal attention at every fine-grid location is costly, whereas compressing the entire evolving state places spatial reconstruction and temporal modeling behind the same bottleneck. To address this trade-off, we propose the Grid-Token Neural Operator (GTNO), which maintains two complementary representations throughout the network: a structured grid for spatial refinement and compact tokens for causal temporal modeling. Each layer couples time-shared local grid updates with token-wise temporal attention through bidirectional interaction. Local grid-to-token routing refreshes the temporal representation, while token-conditioned spectral corrections feed temporal context back to the grid. This asymmetric design concentrates expensive causal sequence modeling on compact tokens while retaining a dedicated spatial pathway. Across five time-dependent PDE benchmarks, GTNO consistently outperforms eight neural operator baselines, demonstrating the effectiveness and efficiency of combining fine spatial evolution with compact temporal modeling.