Mamba-Assisted Non-Markovian Closure for Reduced-Order Modeling
Abstract
Reduced-order modeling of high-dimensional dynamical systems is often hindered by closure effects arising from unresolved variables, which can introduce non-Markovian dependence into the resolved dynamics. Motivated by the history-dependent memory term arising in the Mori--Zwanzig formalism, we recast non-Markovian closure modeling as a sequence modeling problem and propose the Mamba-Assisted Closure (MAC) framework. MAC employs a Mamba-based sequence model to predict the closure from the resolved trajectory and couples the learned closure with the reduced-order governing equations through a numerical integrator to advance the resolved variables in time. During training, the selective scan mechanism in Mamba enables efficient parallel sequence processing with linear scaling in sequence length, while autoregressive inference proceeds through recurrent state updates at essentially constant per-step cost. We evaluate MAC on four benchmark systems with complementary characteristics: the viscous Burgers' equation, the chaotic two-scale Lorenz '96 system, the 3-bus DeMarco--Zheng power-grid system, and the dispersive Korteweg--de Vries equation. Across these benchmarks, MAC consistently improves predictive accuracy and long-time rollout stability relative to the comparison models, demonstrating an effective and computationally scalable approach to non-Markovian closure modeling.
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BibTeX
@misc{wei2026mambaassisted,
title = {{Mamba-Assisted Non-Markovian Closure for Reduced-Order Modeling}},
author = {Zhi-Feng Wei and Saad Qadeer and Panos Stinis},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2606.05371},
eprint = {2606.05371},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.05371},
}
RIS
TY - UNPB
TI - Mamba-Assisted Non-Markovian Closure for Reduced-Order Modeling
AU - Zhi-Feng Wei
AU - Saad Qadeer
AU - Panos Stinis
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2606.05371
UR - https://arxiv.org/abs/2606.05371
AB - Reduced-order modeling of high-dimensional dynamical systems is often hindered by closure effects arising from unresolved variables, which can introduce non-Markovian dependence into the resolved dynamics. Motivated by the history-dependent memory term arising in the Mori--Zwanzig formalism, we recast non-Markovian closure modeling as a sequence modeling problem and propose the Mamba-Assisted Closure (MAC) framework. MAC employs a Mamba-based sequence model to predict the closure from the resolved trajectory and couples the learned closure with the reduced-order governing equations through a numerical integrator to advance the resolved variables in time. During training, the selective scan mechanism in Mamba enables efficient parallel sequence processing with linear scaling in sequence length, while autoregressive inference proceeds through recurrent state updates at essentially constant per-step cost. We evaluate MAC on four benchmark systems with complementary characteristics: the viscous Burgers' equation, the chaotic two-scale Lorenz '96 system, the 3-bus DeMarco--Zheng power-grid system, and the dispersive Korteweg--de Vries equation. Across these benchmarks, MAC consistently improves predictive accuracy and long-time rollout stability relative to the comparison models, demonstrating an effective and computationally scalable approach to non-Markovian closure modeling.
ER -