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Reduced Order Models (ROMs) are of considerable importance in many areas ofengineering in which computational time presents difficulties. Establishedapproaches employ projection-based reduction such as Proper OrthogonalDecomposition, however, such methods can become inefficient or fail in the caseof parameteric or strongly nonlinear models. Such limitations are usuallytackled via a library of local reduction bases each of which being valid for agiven parameter vector. The success of such methods, however, is stronglyreliant upon the method used to relate the parameter vectors to the localbases, this is typically achieved using clustering or interpolation methods. Wepropose the replacement of these methods with a Variational Autoencoder (VAE)to be used as a generative model which can infer the local basis correspondingto a given parameter vector in a probabilistic manner. The resultingVAE-boosted parametric ROM \emph{VpROM} still retains the physical insights ofa projection-based method but also allows for better treatment of problemswhere model dependencies or excitation traits cause the dynamic behavior tospan multiple response regimes. Moreover, the probabilistic treatment of theVAE representation allows for uncertainty quantification on the reduction baseswhich may then be propagated to the ROM response. The performance of theproposed approach is validated on an open-source simulation benchmark featuringhysteresis and multi-parametric dependencies, and on a large-scale wind turbinetower characterised by nonlinear material behavior and model uncertainty.

VpROM: A novel Variational AutoEncoder-boosted Reduced Order Model for the treatment of parametric dependencies in nonlinear systems