Reduced-order modeling of high-dimensional dynamical systems is often hindered by the non-Markovian closure term that represents the effect of unresolved variables on the resolved dynamics. Inspired by the Mori--Zwanzig formalism, in which the closure takes the form of a memory functional of the resolved trajectory, we recast closure modeling as a sequence modeling problem and propose the Mamba-Assisted Closure (MAC) framework: a Mamba-based sequence model, trained to predict the closure from the resolved trajectory, is coupled with the reduced-order governing equations through a numerical integrator to advance the resolved variables in time. A key feature of the framework is its exploitation of the dual representation of state-space models -- the model is trained in a sequence-to-sequence fashion via the convolutional form, and deployed for step-by-step autoregressive rollout via the recurrent form, yielding both efficient long-trajectory training and constant per-step inference cost. On the viscous Burgers' equation and the chaotic two-scale Lorenz '96 system, the MAC model substantially outperforms the Markovian reduced-order model, the GRU-based sequence model, and the Wilks method in predictive accuracy and long-time rollout stability.

翻译：高维动力系统的降阶建模常受困于非马尔可夫闭合项，即未分辨变量对已分辨动力学的影响。受Mori-Zwanzig形式启发（该形式中闭合项表现为已分辨轨迹的记忆泛函），我们将闭合建模重新定义为序列建模问题，提出Mamba辅助闭合（MAC）框架：一种基于Mamba的序列模型，通过训练从已分辨轨迹中预测闭合项，并通过数值积分器与降阶控制方程耦合，实现已分辨变量的时间推进。该框架的核心特征在于利用状态空间模型的双重表征——模型通过卷积形式以序列到序列的方式训练，并通过循环形式进行逐步自回归部署，从而实现高效的长轨迹训练与恒定的每步推理成本。在粘性Burgers方程和混沌双尺度Lorenz '96系统上，MAC模型在预测精度和长时间滚动稳定性方面显著优于马尔可夫降阶模型、GRU基序列模型以及Wilks方法。