From snapshots to manifolds: a practical roadmap for interpolatory reduced-order modelling
Year: 2026
Type: article
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 O(⋅) 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.
Institutions: KU Leuven, King Abdullah University of Science and Technology
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Awards: Deep Learning-based delamination assessment of complex composite structures from UGW responses under varying environment, Automated online monitoring of smart composite structures, Developing Multifunctionally Optimal composite Structures for construction and transportation applications with an emphasis on environmental sustainability
OpenAlex ID: W7162435211