In this section
@article{Sreekumar:2026:10.1098/rspa.2025.1004,
author = {Sreekumar, A and Komis, G and Barman, SK and Astolfi, A and Chronopoulos, D},
doi = {10.1098/rspa.2025.1004},
journal = {Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences},
title = {From snapshots to manifolds: a practical roadmap for interpolatory reduced-order modelling},
url = {http://dx.doi.org/10.1098/rspa.2025.1004},
volume = {482},
year = {2026}
}
TY - JOUR
AB - Abstract – Interpolatory reduced-order models (ROMs) rapidly approximate high-dimensional systems by constructing and blending low-order systems at selected interpolation points. This avoids repeated projection of full-order operators and yields orders-of-magnitude speed-ups, making these methods well-suited for real-time prediction, optimization and control. Existing surveys examine individual techniques in isolation and employ advanced differential-geometric or system-theoretic formalisms, limiting accessibility to the broader engineering and computational communities. In contrast, this review proposes a novel taxonomy categorizing all interpolation-based ROM families without cataloguing every variant. For each family, the core mathematical ideas are conveyed through pseudocode and originally integrated into a unified six-stage workflow, accompanied by explicit (Formula presented) cost analyses. We then highlight key methodological extensions required for complex, real-world applications focusing on computational mechanics. A combined quantitative and qualitative assessment against six canonical benchmarks and traditional projection–based ROMs provides performance insights. The result is a practical roadmap enabling engineers and scientists to select, adapt and deploy interpolation-based ROMs with clarity and assurance.
AU - Sreekumar,A
AU - Komis,G
AU - Barman,SK
AU - Astolfi,A
AU - Chronopoulos,D
DO - 10.1098/rspa.2025.1004
PY - 2026///
SN - 1364-5021
TI - From snapshots to manifolds: a practical roadmap for interpolatory reduced-order modelling
T2 - Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences
UR - http://dx.doi.org/10.1098/rspa.2025.1004
VL - 482
ER -