A certified and adaptive RB-ML-ROM surrogate approach for parametrized PDEs

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Abstract

In this talk, we present a new surrogate modeling approach to approximate input-output maps occurring in the context of parametrized PDEs. The algorithm is based on a full order model (FOM), reduced order model (ROM) and machine learning (ML) model chain. By applying a posteriori error estimates to the ROM and ML model, we obtain certified results. The model is therefore able to fulfill fixed or adaptively chosen error tolerances for every requested parameter. The reduced order and machine learning models are adapted during the algorithm based on the a posteriori error estimates. In particular, the algorithm provides ML-based results with guaranteed quality statements and error control. Numerical experiments showcase the efficiency of our approach in different scenarios, for instance a parameter optimization problem and uncertainty quantification. In our examples, the reduced basis (RB) method is used as ROM. Further, we employ kernel methods and deep neural networks to generate the ML models, but a wide range of ML algorithms is applicable within the modeling chain.

Speakers from the University of Münster

Kleikamp, Hendrik

Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)