Mamba-Assisted Non-Markovian Closure for Reduced-Order Modeling
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Computer Science > Machine Learning
Title:Mamba-Assisted Non-Markovian Closure for Reduced-Order Modeling
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.
| Comments: | Code will be released upon acceptance |
| Subjects: | Machine Learning (cs.LG); Numerical Analysis (math.NA); Machine Learning (stat.ML) |
| Report number: | PNNL-SA-223691 |
| Cite as: | arXiv:2606.05371 [cs.LG] |
| (or arXiv:2606.05371v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.05371
arXiv-issued DOI via DataCite (pending registration)
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