Spatiotemporal-Aware Mamba Neural Operator for Time-dependent PDE Prediction

Neural operators (NOs) have emerged as efficient surrogates for predicting PDE-governed spatiotemporal dynamical systems. However, accurately modeling both temporal evolution and spatial interactions remains challenging, particularly for turbulent and long-horizon dynamics. We introduce MCANO, an autoregressive Mamba-based neural operator with dedicated temporal and spatial processing. Specifically, the temporal-awareness module employs a lightweight pointwise polynomial-basis lifting and embedding strategy to explicitly characterize temporal evolution patterns at each spatial location, while the spatial-awareness module augments conventional directional scans with a learned offset-based scan to provide an additional feature-conditioned spatial traversal. Building upon MCANO, we further develop MCANOP, a scalable multiphysics pretraining and fine-tuning framework that combines random sub-trajectory sampling, instance-wise normalization, and task-specific adaptation for heterogeneous PDE systems. Across regular-grid, irregular-grid, short-trajectory, and long-trajectory benchmarks, MCANO achieves the best performance on six of nine datasets and ranks second on the remaining three. After task-specific fine-tuning, MCANOP-17M substantially outperforms pretrained models of comparable size across all in-domain and out-of-domain datasets. Our findings highlight the potential of MCANO and MCANOP as parameter-efficient paradigms for accurate PDE prediction, matching or surpassing the performance of significantly larger models.