Mamba-Assisted Non-Markovian Closure for Reduced-Order Modeling

2026-06-03

AI Summary

This work addresses the challenge of accurately representing non-Markovian closure terms arising from unresolved variables in reduced-order modeling of high-dimensional dynamical systems. The authors propose the Mamba-based MAC (Mamba-Aided Closure) framework, which reformulates closure modeling as a sequence prediction task and couples the closure term with the reduced-order equations through a numerical integrator to evolve the resolved variables. The method innovatively leverages the dual convolutional and recurrent representations inherent in state-space models: during training, it exploits convolution for efficient learning of long-range trajectory dependencies, while at inference time it switches to a recurrent mode to enable autoregressive roll-out predictions with constant computational cost. Evaluated on the viscous Burgers equation and the chaotic multiscale Lorenz '96 system, MAC significantly outperforms Markovian closures, GRU-based approaches, and the Wilks stochastic parameterization, demonstrating superior prediction accuracy and long-term stability.

Abstract

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.

Problem

• non-Markovian closure
• reduced-order modeling
• Mori–Zwanzig formalism
• memory effects
• high-dimensional dynamical systems

Innovation

• Mamba
• non-Markovian closure
• reduced-order modeling
• state-space model
• sequence modeling