{"ID":3084643,"CreatedAt":"2026-06-05T06:46:15.197025399Z","UpdatedAt":"2026-06-06T19:15:30.205453645Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.05371","arxiv_id":"2606.05371","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.","short_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...","url_abs":"https://arxiv.org/abs/2606.05371","url_pdf":"https://arxiv.org/pdf/2606.05371v1","authors":"[\"Zhi-Feng Wei\",\"Saad Qadeer\",\"Panos Stinis\"]","published":"2026-06-03T19:18:50Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.NA\",\"stat.ML\"]","methods":"[]","has_code":false}