Benner, PeterGugercin, SerkanWerner, Steffen W. R.2025-12-122025-12-122024-04-011019-7168https://hdl.handle.net/10919/139917High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting large-scale nonlinear systems. The high dimensionality of the dynamics causes computational bottlenecks, especially when these large-scale systems need to be simulated for a variety of situations such as different forcing terms. This motivates model reduction where the goal is to replace the full-order dynamics with accurate reduced-order surrogates. Interpolation-based model reduction has been proven to be an effective tool for the construction of cheap-to-evaluate surrogate models that preserve the internal structure in the case of weak nonlinearities. In this paper, we consider the construction of multivariate interpolants in frequency domain for structured quadratic-bilinear systems. We propose definitions for structured variants of the symmetric subsystem and generalized transfer functions of quadratic-bilinear systems and provide conditions for structure-preserving interpolation by projection. The theoretical results are illustrated using two numerical examples including the simulation of molecular dynamics in crystal structures.application/pdfenCreative Commons Attribution 4.0 InternationalModel order reductionQuadratic-bilinear systemsStructure-preserving approximationMultivariate interpolationArticle - Refereedhttps://doi.org/10.1007/s10444-024-10109-85021572-9044