Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling

Wenzel, Tizian; Haasdonk, Bernard; Kleikamp, Hendrik; Ohlberger, Mario; Schindler, Felix

Research article in edited proceedings (conference) | Peer reviewed

Abstract

In the framework of reduced basis methods, we recently introduced a new certified hierarchical and adaptive surrogate model, which can be used for efficient approximation of input-output maps that are governed by parametrized partial differential equations. This adaptive approach combines a full order model, a reduced order model and a machine-learning model. In this contribution, we extend the approach by leveraging novel kernel models for the machine learning part, especially structured deep kernel networks as well as two layered kernel models. We demonstrate the usability of those enhanced kernel models for the RB-ML-ROM surrogate modeling chain and highlight their benefits in numerical experiments.

Details about the publication

Editors: Lirkov, I.; Margenov, S.

Book title: Large-Scale Scientific Computations

Page range: 117-125

Publisher: Springer Nature

Place of publication: Cham

Title of series: Lecture Notes in Computer Science

Volume of series: 13952

Status: Published

Release year: 2024

Language in which the publication is written: English

Conference: Large-Scale Scientific Computations. LSSC 2023, Sozopol, Bulgaria

ISBN: 978-3-031-56207-5

DOI: 10.1007/978-3-031-56208-2_11

Keywords: Deep Kernel Methods; Certified RB-ML-ROM Modeling; Machine Learning; Reduced Order Models; Error Estimation

Authors from the University of Münster

Kleikamp, Hendrik	Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Ohlberger, Mario	Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger) Center for Nonlinear Science Center for Multiscale Theory and Computation (CMTC)
Schindler, Felix Tobias	Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)

Projects the publication originates from

ML-MORE: Machine learning and model order reduction to predict the efficiency of catalytic filters. Subproject 1: Model Order Reduction (ML-MORE)

Duration: 01/04/2020 - 31/12/2023

Funded by: Federal Ministry of Research, Technology and Space

Type of project: Participation in federally funded joint project

Promotionen, aus denen die Publikation resultiert

Parametrized optimal control and transport-dominated problems: Reduced basis methods, nonlinear reduction strategies and data driven surrogates
Candidate: Kleikamp, Hendrik | Supervisors: Ohlberger, Mario | Reviewers: Ohlberger, Mario; Breiten, Tobias
Period of time: 01/01/2021 - 19/12/2024
Doctoral examination procedure finished at: Doctoral examination procedure at University of Münster