| Private Homepage | https://www.uni-muenster.de/AMM/ohlberger/team/felix_schindler.shtml |
| Research Interests | Multiscale analysis of two-phase flow in porous media with complex heterogeneities Model reduction of parametric partial differential equations Numerical analysis of partial differential equations |
| Selected Publications | • Buhr Andreas, Iapichino Laura, Ohlberger Mario, Rave Stephan, Schindler Felix, Smetana Kathrin Localized model reduction for parameterized problems. Model Order Reduction: Volume 2 Snapshot-Based Methods and Algorithms, 2021, pp 245 - 306 online • Rave Stephan, Schindler Felix A locally conservative reduced flux reconstruction for elliptic problems. Special Issue: 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)arXiv Vol. 1903.09082, 2019 online • Ohlberger Mario, Schaefer Michael, Schindler Felix Localized Model Reduction in PDE Constrained Optimization. Shape Optimization, Homogenization and Optimal Control – DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017 International Series of Numerical Mathematics, 2018, pp 143-163 online • Ohlberger M, Rave S, Schindler F True Error Control for the Localized Reduced Basis Method for Parabolic Problems. Model Reduction of Parametrized SystemsMS&A (Modeling, Simulation and Applications) Vol. 2016 (1606.09216), 2017, pp 169-182 online • Leibner T, Milk R, Schindler F Extending DUNE: The dune-xt modules. Archive of Numerical Software Vol. 5 (1), 2017, pp 193-216 online • Ohlberger M, Schindler F Non-Conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE constrained Optimization. Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems: FVCA 8, Lille, France, June 2017, 2017, pp 357-365 online • Milk R, Rave S, Schindler F pyMOR - Generic algorithms and interfaces for model order reduction. SIAM Journal on Scientific Computing Vol. 38 (5), 2016, pp 194-216 online • Ohlberger M, Schindler F Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment. SIAM J. Sci. Comput. Vol. 37 (6), 2015, pp A2865-A2895 online • Albrecht F, Ohlberger M The localized reduced basis multi-scale method with online enrichment. Oberwolfach Reports Vol. 7, 2013, pp 406-409 online • Albrecht F, Haasdonk B, Kaulmann S, Ohlberger M The Localized Reduced Basis Multiscale Method. , 2012, pp 393-403 online |
| Selected Projects | • Localized Reduced Basis Methods for PDE-constrained Parameter Optimization This projects is concerned with model reduction for parameter optimization of nonlinear elliptic partial differential equations (PDEs). The goal is to develop a new paradigm for PDE-constrained optimization based on adaptive online enrichment. The essential idea is to design a localized version of the reduced basis (RB) method which is called Localized Reduced Basis Method (LRBM). online • EXC 2044 - C4: Geometry-based modelling, approximation, and reduction In mathematical modelling and its application to the sciences, the notion of geometry enters in multiple related but different flavours: the geometry of the underlying space (in which e.g. data may be given), the geometry of patterns (as observed in experiments or solutions of corresponding mathematical models), or the geometry of domains (on which PDEs and their approximations act). We will develop analytical and numerical tools to understand, utilise and control geometry, also touching upon dynamically changing geometries and structural connections between different mathematical concepts, such as PDE solution manifolds, analysis of pattern formation, and geometry. online |
| Project membership Mathematics Münster | C: Models and Approximations C4: Geometry-based modelling, approximation, and reduction |
| Current Talks | • Locally conservative Reduced Basis methods. 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics GAMM 2019, Universität Wien, Wien, Österreich Slides Link to event |
| Current Publications | • Haasdonk B, Kleikamp H, Ohlberger M, Schindler F, Wenzel T A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs. SIAM Journal on Scientific Computing Vol. 45 (3), 2023 online • Wenzel, Tizian; Haasdonk, Bernard; Kleikamp, Hendrik; Ohlberger, Mario; Schindler, Felix Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling. , 2023 online • Keil Tim, Ohlberger Mario, Schindler Felix Adaptive Localized Reduced Basis Methods for Large Scale Parameterized Systems. , 2023 online • Gavrilenko Pavel, Haasdonk Bernard, Iliev Oleg, Ohlberger Mario, Schindler Felix, Toktaliev Pavel, Wenzel Tizian, Youssef Maha A full order, reduced order and machine learning model pipeline for efficient prediction of reactive flows. Large-Scale Scientific ComputingLecture Notes in Computer Science (LNCS), 2022, pp 378-386 online • Banholzer S, Keil T, Mechelli L, Ohlberger M, Schindler F, Volkwein S An adaptive projected Newton non-conforming dual approach for trust-region reduced basis approximation of PDE-constrained parameter optimization. Pure and Applied Functional Analysis Vol. 7 (5), 2022 online • Fokina, D, Iliev O, Toktaliev P, Oseledets I, Schindler F On the Performance of Machine Learning Methods for Breakthrough Curve Prediction. arXiv [physics.flu-dyn] Vol. 2204.11719, 2022 online • Haasdonk B, Ohlberger M, Schindler F An adaptive model hierarchy for data-augmented training of kernel models for reactive flow. MATHMOD 2022 Discussion Contribution VolumearXiv [math.NA] Vol. ARGESIM Report, 2022 online • Gavrilenko Pavel, Haasdonk Bernard, Iliev Oleg, Ohlberger Mario, Schindler Felix, Toktaliev Pavel, Wenzel Tizian, Youssef Maha A full order, reduced order and machine learning model pipeline for efficient prediction of reactive flows. Large-Scale Scientific ComputingLecture Notes in Computer Science (LNCS), 2022, pp 378-386 online • Banholzer S, Keil T, Mechelli L, Ohlberger M, Schindler F, Volkwein S An adaptive projected Newton non-conforming dual approach for trust-region reduced basis approximation of PDE-constrained parameter optimization. Pure and Applied Functional Analysis Vol. 7 (5), 2022 online |
| Current Projects | • ML-MORE: Machine learning and model order reduction to predict the efficiency of catalytic filters. Subproject 1: Model Order Reduction Reaktiver Stofftransport in porösen Medien in Verbindung mit katalytischen Reaktionen ist die Grundlage für viele industrielle Prozesse und Anlagen, wie z.B. Brennstoffzellen, Photovoltaikzellen, katalytische Filter für Abgase, etc. Die Modellierung und Simulation der Prozesse auf der Porenskala kann bei der Optimierung des Designs von katalytischen Komponenten und der Prozessführung helfen, ist jedoch derzeit dadurch eingeschränkt, dass solche Simulationen zu grossen Datenmengen führen, zeitaufwändig sind und von einer grossen Anzahl von Parametern abhängen. Außerdem werden auf diese Weise die im Laufe der Jahre gesammelten Versuchsdaten nicht wiederverwendet. Die Entwicklung von Lösungsansätzen für die Vorhersage der chemischen Konversionsrate mittels moderner datenbasierter Methoden des Maschinellen Lernens (ML) ist essenziell, um zu schnellen, zuverlässigen prädiktiven Modellen zu gelangen. Hierzu sind verschiedene Methodenklassen erforderlich. Neben den experimentellen Daten sind voll aufgelöste Simulationen auf der Porenskala notwendig. Diese sind jedoch zu teuer, um einen umfangreichen Satz an Trainingsdaten zu generieren. Daher ist die Modellordnungsreduktion (MOR) zur Beschleunigung entscheidend. Es werden reduzierte Modelle fur den betrachteten instationären reaktiven Transport entwickelt, um große Mengen an Trainingsdaten zu simulieren. Als ML-Methodik werden mehrschichtige Kern-basierte Lernverfahren entwickelt, um die heterogenen Daten zu kalibrieren und nichtlineare prädiktive Modelle zur Effizienzvorhersage zu entwickeln.Hierbei werden große Daten (bzgl. Dimensionalität und Sample-Zahl) zu behandeln sein, was Datenkompression und Parallelisierung des Trainings erfordern wird. Das Hauptziel des Projekts ist es, alle oben genannten Entwicklungen in einem prädiktiven ML-Tool zu integrieren, das die Industrie bei der Entwicklung neuer katalytischer Filter unterstützt und auf viele andere vergleichbare Prozesse übertragbar ist. online • EXC 2044 - C4: Geometry-based modelling, approximation, and reduction In mathematical modelling and its application to the sciences, the notion of geometry enters in multiple related but different flavours: the geometry of the underlying space (in which e.g. data may be given), the geometry of patterns (as observed in experiments or solutions of corresponding mathematical models), or the geometry of domains (on which PDEs and their approximations act). We will develop analytical and numerical tools to understand, utilise and control geometry, also touching upon dynamically changing geometries and structural connections between different mathematical concepts, such as PDE solution manifolds, analysis of pattern formation, and geometry. online • Localized Reduced Basis Methods for PDE-constrained Parameter Optimization This projects is concerned with model reduction for parameter optimization of nonlinear elliptic partial differential equations (PDEs). The goal is to develop a new paradigm for PDE-constrained optimization based on adaptive online enrichment. The essential idea is to design a localized version of the reduced basis (RB) method which is called Localized Reduced Basis Method (LRBM). online | felix.schindler@wwu.de |
| Phone | +49 251 83-35051 |
| FAX | +49 251 83-32729 |
| Room | 120.023 |
| Secretary | Sekretariat Wernke Frau Silvia Wernke Telefon +49 251 83-35052 Fax +49 251 83-32729 Zimmer 120.001 |
| Address | Dr. Felix Schindler Angewandte Mathematik Münster: Institut für Analysis und Numerik Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62 48149 Münster Deutschland |
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