Multivariate predictions of local reduced‐order‐model errors and dimensions |
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| Authors: | Azam Moosavi Răzvan Ştefănescu Adrian Sandu |
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| Affiliation: | 1. Computational Science Laboratory, Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA;2. Global Validation Model Department, Spire Global, Boulder, CO, USA |
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| Abstract: | This paper introduces multivariate input‐output models to predict the errors and bases dimensions of local parametric Proper Orthogonal Decomposition reduced‐order models. We refer to these mappings as the multivariate predictions of local reduced‐order model characteristics (MP‐LROM) models. We use Gaussian processes and artificial neural networks to construct approximations of these multivariate mappings. Numerical results with a viscous Burgers model illustrate the performance and potential of the machine learning‐based regression MP‐LROM models to approximate the characteristics of parametric local reduced‐order models. The predicted reduced‐order models errors are compared against the multifidelity correction and reduced‐order model error surrogates methods predictions, whereas the predicted reduced‐order dimensions are tested against the standard method based on the spectrum of snapshots matrix. Since the MP‐LROM models incorporate more features and elements to construct the probabilistic mappings, they achieve more accurate results. However, for high‐dimensional parametric spaces, the MP‐LROM models might suffer from the curse of dimensionality. Scalability challenges of MP‐LROM models and the feasible ways of addressing them are also discussed in this study. |
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| Keywords: | local reduced‐order models proper orthogonal decomposition regression machine learning techniques |
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