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Speaker

Mengwu Guo

Guest of Cecilia Pagliantini

Title

Bayesian methods of non-intrusive model order reduction

Abstract

Enhanced by machine learning tools, non-intrusive reduced order modeling methods can achieve high efficiency, wide applicability, good feasibility and enlarged industrial relevance. In this talk, two types of Bayesian methods of non-intrusive model order reduction will be discussed for nonlinear problems in simulation science.

The first type trains parametric reduced order models from collected solution data using Gaussian process regression. For further speed-up, multi-fidelity techniques are integrated into the method to take advantage of low-fidelity information and reduce the computational cost of high-fidelity data preparation. Combined with a predefined domain decomposition and global sensitivity analysis, this method has also been applied to the simulations of large-scale engineering structures. In this scheme, the full-order solvers are used offline as a ‘black-box’ for the generation of snapshot data, whereas the online stage is simulation-free and only requires direct outputs from the regression models, which guarantees a reliable and efficient tool for the multi-query, real-time simulations in the digital twining of large engineering assets.

The second type employs operator inference for the non-intrusive reduced order modeling of time-dependent problems. In our work, a probabilistic formulation is presented, in which Bayesian inference is employed to recover the reduced-order operators. Uncertainties in the recovered reduced-order model can be quantified through such a Bayesian scheme, and posterior distributions are thus given for the predictions of future states. When ill-conditioned issues are encountered, recommended penalty coefficients of L_2 regularization can be obtained with the aid of maximum marginal likelihood. Such a reduced order modeling method works as a ‘grey-box’ scheme, which inherits the basic physics but doesn’t require access to the full-order solvers.

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