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Creators/Authors contains: "Geelen, Rudy"

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  1. ; ; (, Computer Methods in Applied Mechanics and Engineering)
    Free, publicly-accessible full text available February 1, 2026
  2. ; ; ; (, Chaos: An Interdisciplinary Journal of Nonlinear Science)
    We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation. 
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  3. ; ; (, 62nd IEEE Conference on Decision and Control (CDC))
    We present a novel framework for learning cost-efficient latent representations in problems with highdimensional state spaces through nonlinear dimension reduction. By enriching linear state approximations with low-order polynomial terms we account for key nonlinear interactions existing in the data thereby reducing the problem’s intrinsic dimensionality. Two methods are introduced for learning the representation of such low-dimensional, polynomial manifolds for embedding the data. The manifold parametrization coefficients can be obtained by regression via either a proper orthogonal decomposition or an alternating minimization based approach. Our numerical results focus on the one-dimensional Korteweg-de Vries equation where accounting for nonlinear correlations in the data was found to lower the representation error by up to two orders of magnitude compared to linear dimension reduction techniques. 
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  4. ; ; (, Computer Methods in Applied Mechanics and Engineering)
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