Ali Mohaghegh | Searcharxiv

arXiv2026

History-aware adaptive reduced-order models via incremental singular value decomposition

Reduced-order models (ROMs) can accelerate high-dimensional dynamical simulations, but their accuracy often deteriorates when online dynamics leave the regime represented by offline training data. We develop a projection-based adaptive ROM framework based on incremental singular value decomposition (iSVD), in which occasional full-order operator evaluations provide correction snapshots for online basis updates. The intrusive ROMs considered here are fully parameterized by the basis, so each update naturally propagates to reduced operators and hyper-reduction machinery. Through its evolving singular structure, iSVD retains an encoded history of the observed dynamics and is history-aware in this sense. We study the method on three nonlinear problems of increasing complexity: the one-dimensional viscous Burgers equation, the Sod shock tube, and a stiff one-dimensional ten-species rotating detonation engine (RDE). The Burgers problem is used to analyze the method and compare iSVD with alternative basis adaptation rules, showing that history-aware updates outperform instantaneous updates and that iSVD gives the strongest overall performance. The Sod and RDE cases demonstrate that these advantages persist in more challenging compressible-flow settings. For the RDE problem, the iSVD adaptive ROM improves upon the current state-of-the-art Direct adaptive ROM baseline in both predictive accuracy and computational efficiency. A cost analysis shows that the dominant online cost comes from interacting with the full-order model to obtain correction snapshots, while the iSVD update itself is negligible. These results identify iSVD as an effective mechanism for online learning of reduced subspaces and suggest a path toward ROMs that remain predictive over horizons several orders of magnitude longer than their initial training window.

cs.LG↗

arXiv2025

Feature-Guided Sampling Strategy for Adaptive Model Order Reduction of Convection-Dominated Problems

Though high-performance computing enables high-fidelity simulations of complex engineering systems, accurately resolving multi-scale physics for real-world problems remains computationally prohibitive, particularly in many-query applications such as optimization and uncertainty quantification. Projection-based model order reduction (MOR) has demonstrated significant potential for reducing computational costs by orders of magnitude through the creation of reduced-order models (ROMs). However, physical problems featuring strong convection, such as hypersonic flows and detonations, pose significant challenges to conventional MOR techniques due to the slow decay of Kolmogorov N-width present in these problems. In the past few years various approaches have been proposed to address this challenge; one of the promising methods is the adaptive MOR. In this work, we introduce a feature-guided adaptive projection-based MOR framework tailored for convection-dominated problems involving flames and shocks. This approach dynamically updates the ROM subspace and incorporates a feature-guided sampling method that strategically selects sampling points to capture prominent convective features, ensuring accurate predictions of crucial dynamics in the target problems. We evaluate the proposed methodology using a suite of challenging convection-dominated test problems, including shocks, flames, and detonations. The results demonstrate the feature-guided adaptive ROM's capability in producing efficient and reliable predictions of the nonlinear convection-dominated physical phenomena in the selected test suite, which are well recognized to be challenging for conventional ROM methods.

physics.flu-dyn↗