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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.<\/jats:p>","DOI":"10.1007\/s10444-024-10109-8","type":"journal-article","created":{"date-parts":[[2024,3,12]],"date-time":"2024-03-12T20:03:23Z","timestamp":1710273803000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Structured interpolation for multivariate transfer functions of quadratic-bilinear systems"],"prefix":"10.1007","volume":"50","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3362-4103","authenticated-orcid":false,"given":"Peter","family":"Benner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4564-5999","authenticated-orcid":false,"given":"Serkan","family":"Gugercin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1667-4862","authenticated-orcid":false,"given":"Steffen W. 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