Research Areas

Institute for Analysis and Numerics

The institute's research focuses on the development and application of analytical and numerical mathematical methods and on mathematical modelling. Particular areas of interest are partial differential equations, multiscale methods, inverse problems, variational calculus, mathematical imaging, mathematical models in the biosciences, dynamical systems, optimization and scientific computing.

AG Wirth: Verallgemeinerte Bezier-Fläche auf einer Riemannschen Mannigfaltigkeit

AG Ohlberger: detailed simulation of a Li-Ion battery model with the software framework DUNE
© AGO

AG Engwer: A solution of the electroencephalography (EEG) forward problem using implicit level set data within an unfitted discontinuous Galerkin scheme.
© A. Nüßing

AG Zeppieri: Crazing in polymers close to the crack-tip

Interdisciplinary cooperations

Strong interdisciplinary connections exist to medicine and biology. In particular, the teams participate actively in the cluster of excellence Cells in Motion, the collaborative research centre 656 Molekulare kardiovaskuläre Bildgebung (MoBil), the European Institute for Molecular Imaging (EIMI), the centre for Developing Mathematics in Interaction (DEMAIN), the Center for Nonlinear Science (CENOS) of the WWU, the Center for Multiscale Theory and Computation (CMTC) and the forum Competence for Computing in Science (CoCoS) at the University of Münster.

Ongoing projects and recent publications

A selection of ongoing projects and recent publications are listed below.

You can find more projects and publications on the webpages of the groups.

Current Projects
- MONTECARLO – Overcoming the curse of dimensionality through nonlinear stochastic algorithms: Nonlinear Monte Carlo type methods for high-dimensional approximation problems (2023 – 2028)
  EU-Project Hosted at University the of Münster: EC Horizon Europe - ERC Consolidator Grant | Project Number: 101045811
- GE4SPDE – Global Estimates for non-linear stochastic PDEs (2022 – 2027)
  EU-Project Hosted at University the of Münster: EC Horizon Europe - ERC Consolidator Grant | Project Number: 101045082
- MaRDI – Mathematical Research Data Initiative - TA2: Scientific Computing (2021 – 2026)
  Subproject in DFG-Joint Project Hosted outside the University of Münster: DFG - National Research Data Infrastructure | Project Number: NFDI 29 /1
- EXC 2044 - C4: Geometry-based modelling, approximation, and reduction (2019 – 2025)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- EXC 2044 - C1: Evolution and asymptotics (2019 – 2025)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- EXC 2044 - C3: Interacting particle systems and phase transitions (2019 – 2025)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- EXC 2044 - C2: Multi-scale phenomena and macroscopic structures (2019 – 2025)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- Mathematical analysis of bubble rings in ideal fluids (2024 – 2025)
  Individual Granted Project: DFG - Individual Grants Programme | Project Number: SE 2436/5-1
- InterKIWWU – Interdisziplinäres Lehrprogramm zu maschinellem Lernen und künstlicher Intelligenz (2021 – 2025)
  Individual Granted Project: Federal Ministry of Education and Research | Project Number: 16DHBKI049
- Dynamical systems and irregular gradient flows (2021 – 2025)
  Own Resources Project
- CRC 1450 A05 - Targeting immune cell dynamics by longitudinal whole-body imaging and mathematical modelling (2021 – 2024)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1450/1, A05
- CRC 1450 A06 - Improving intravital microscopy of inflammatory cell response by active motion compensation using controlled adaptive optics (2021 – 2024)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1450/1, A06
- DLMATH – Mathematical Theory for Deep Learning (2019 – 2024)
  Own Resources Project
- PDE – Existence, uniqueness, and regularity properties of solutions of partial differential equations (2019 – 2024)
  Own Resources Project
- SDE – Regularity properties and approximations for stochastic ordinary and partial differential equations with non-globally Lipschitz continuous nonlinearities (2019 – 2024)
  Own Resources Project
- CURSEOFDIM – Overcoming the curse of dimensionality: stochastic algorithms for high-dimensional partial differential equations (2019 – 2024)
  Own Resources Project
- PerEpi – Personalised diagnosis and treatment for refractory focal paediatric and adult epilepsy (2021 – 2024)
  EU-Project Hosted at University the of Münster: EC H2020 - ERA-NET Cofund | Project Number: ERAPERMED2020-227
- NIH Grant Number: 1 R01 EB 026299-01 – BrainStorm: Highly Extensible Software for Advanced Electrophysiology and MEG/EEG Imaging (since 2019)
  Own Resources Project
- EXC 2044 – Cluster of Excellence 2044 - Mathematics Münster: Dynamics – Geometry – Structure (2019 – 2025)
  Main DFG-Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- EXC 2044 - B3: Operator algebras & mathematical physics (2019 – 2025)
  Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1
- Reconstruction of epilepsy-characteristic sources by means of a simultaneous evaluation of EEG- and MEG- data using calibrated realistic head models (since 2016)
  Own Resources Project
- Modeling and Simulation of TNF receptor clustering (since 2010)
  Own Resources Project
- CiM-IMPRS – Cells in Motion (CiM) Graduate School and International Max Planck Research School - Molecular Biomedicine (since 2010)
  Individual Granted Project: Federal Ministry of Culture and Science of the Federal State of North Rhine-Westphalia
Latest Publications
2024
- de Lima Feltes, Guilherme; Weber, Hendrik. 2024. ‘Brownian particle in the curl of 2-d stochastic heat equations.’ Journal of Statistical Physics 191: 16. doi: 10.1007/s10955-023-03224-1.
- Keil Tim, Ohlberger Mario. 2024. ‘A Relaxed Localized Trust-Region Reduced Basis Approach for Optimization of Multiscale Problems.’ ESAIM: Mathematical Modelling and Numerical Analysis 58: 79–105. doi: 10.1051/m2an/2023089.
- Ceci, Stefano; Seis, Christian. 2024. ‘On the dynamics of vortices in viscous 2D flows.’ Mathematische Annalen 388: 1937–1967. doi: 10.1007/s00208-023-02568-z.
- Braunsmann, Juliane; Rajković, Marko; Rumpf, Martin; Wirth, Benedikt. 2024. ‘Convergent Autoencoder Approximation of Low Bending and Low Distortion Manifold Embeddings.’ ESAIM: Mathematical Modelling and Numerical Analysis 58, No. 1: 335–361. doi: 10.1051/m2an/2023088.
- Holler, Martin; Schlüter, Alexander; Wirth, Benedikt. 2024. ‘Dimension reduction, exact recovery, and error estimates for sparse reconstruction in phase space.’ Applied and Computational Harmonic Analysis 70: 101631. doi: 10.1016/j.acha.2024.101631.
- Singh A; Thale S; Leibner T; Lamparter L; Ricker A; Nüsse H; Klingauf J; Galic M; Ohlberger M; Matis M. 2024. ‘Dynamic interplay of microtubule and actomyosin forces drive tissue extension.’ Nature Communications 15, No. 1: 3198. doi: 10.1038/s41467-024-47596-8.
- Gardella, Eusebio; Geffen, Shirly; Kranz, Julian; Naryshkin, Petr; Vaccaro, Andrea. 2024. ‘Tracially amenable actions and purely infinite crossed products.’ Mathematische Annalen 2024. doi: https://doi.org/10.1007/s00208-024-02833-9.
- Esposito A; Patacchini FS; Schlichting A. 2024. ‘On a Class of Nonlocal Continuity Equations on Graphs.’ European Journal of Applied Mathematics 35, No. 1: 109–126. doi: 10.1017/S0956792523000128.
- Chevyrev, I.; Gerasimovičs, A.; Weber, H. 2024. ‘Feature Engineering with Regularity Structures.’ Journal of Scientific Computing 98, No. 13. doi: 10.1007/s10915-023-02401-4.
- Chandra, Ajay; de Lima Feltes, Guilherme; Weber, Hendrik. 2024. A priori bounds for 2-d generalised Parabolic Anderson Model arXiv. doi: abs/2402.05544.
2023
- Jamalabadi, Hamidreza; Hahn, Tim; Winter, Nils R.; Nozari, Erfan; Ernsting, Jan; Meinert, Susanne; Leehr, Elisabeth J.; Dohm, Katharina; Bauer, Jochen; Pfarr, Julia-Katharina; Stein, Frederike; Thomas-Odenthal, Florian; Brosch, Katharina; Mauritz, Marco; Gruber, Marius; Repple, Jonathan; Kaufmann, Tobias; Krug, Axel; Nenadic, Igor; Kircher, Tilo; Dannlowski, Udo; Derntl, Birgit. 2023. ‘Interrelated effects of age and parenthood on whole-brain controllability: protective effects of parenthood in mothers.’ Frontiers in Aging Neuroscience 15. doi: 10.3389/fnagi.2023.1085153.
- Renelt, Lukas; Ohlberger, Mario; Engwer, Christian. 2023. ‘An optimally stable approximation of reactive transport using discrete test and infinite trial spaces.’ In Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems, edited by Franck, Emmanuel; Fuhrmann, Jürgen;, Michel-Dansac, Victor; Navoret, Laurent, 289–298. Cham: Springer. doi: 10.1007/978-3-031-40860-1_30.
- Friedrich, Manuel; Machill, Lennart. 2023. ‘One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams.’ Calculus of Variations and Partial Differential Equations 62, No. 7: 190. doi: 10.1007/s00526-023-02525-3.
- Bickmann L; Plagwitz L; Varghese J. 2023. ‘Post Hoc Sample Size Estimation for Deep Learning Architectures for ECG-Classification.’ Studies in Health Technology and Informatics 302: 182–186. doi: 10.3233/SHTI230099.
- Plagwitz L; Vogelsang T; Doldi F; Bickmann L; Fujarski M; Eckardt L; Varghese J. 2023. ‘The Necessity of Multiple Data Sources for ECG-Based Machine Learning Models.’ Studies in Health Technology and Informatics 302: 33–37. doi: 10.3233/SHTI230059.
- Fujarski M; Porschen C; Plagwitz L; Stroth D; Van Alen CM; Sadjadi M; Weiss R; Zarbock A; Von Groote T; Varghese J. 2023. ‘DeepTSE: A Time-Sensitive Deep Embedding of ICU Data for Patient Modeling and Missing Data Imputation.’ Studies in Health Technology and Informatics 302: 237–241. doi: 10.3233/SHTI230110.
- Haasdonk B, Kleikamp H, Ohlberger M, Schindler F, Wenzel T. 2023. ‘A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs.’ SIAM Journal on Scientific Computing 45, No. 3: A1039. doi: 10.1137/22M1493318.
- Chandra, Ajay; Moinat, Augustin; Weber, Hendrik. 2023. ‘A Priori Bounds for the Φ4 Equation in the Full Sub-critical Regime.’ Archive for Rational Mechanics and Analysis 247, No. 3: 48. doi: 10.1007/s00205-023-01876-7.
- Eberle, Simon; Jentzen, Arnulf; Riekert, Adrian; Weiss, Georg S. 2023. ‘Existence, uniqueness, and convergence rates for gradient flows in the training of artificial neural networks with ReLU activation.’ Electronic Research Archive 31, No. 5: 2519–2554. doi: 10.3934/era.2023128.
- Hahn, Tim; Jamalabadi, Hamidreza; Nozari, Erfan; Winter, Nils R.; Ernsting, Jan; Gruber, Marius; Mauritz, Marco J.; Grumbach, Pascal; Fisch, Lukas; Leenings, Ramona; Sarink, Kelvin; Blanke, Julian; Vennekate, Leon Kleine; Emden, Daniel; Opel, Nils; Grotegerd, Dominik; Enneking, Verena; Meinert, Susanne; Borgers, Tiana; Klug, Melissa; Leehr, Elisabeth J.; Dohm, Katharina; Heindel, Walter; Gross, Joachim; Dannlowski, Udo; Redlich, Ronny; Repple, Jonathan. 2023. ‘Towards a network control theory of electroconvulsive therapy response.’ PNAS Nexus 2, No. 2. doi: 10.1093/pnasnexus/pgad032.
- Keil Tim, Rave Stephan. 2023. ‘An Online Efficient Two-Scale Reduced Basis Approach for the Localized Orthogonal Decomposition.’ SIAM Journal on Scientific Computing 45, No. 4. doi: 10.1137/21M1460016.
- Beck C, Hutzenthaler M, Jentzen A, Kuckuck B. 2023. ‘An overview on deep learning-based approximation methods for partial differential equations.’ Discrete and Continuous Dynamical Systems - Series B 28, No. 6: 3697–3746. doi: 10.3934/dcdsb.2022238.
- Jentzen A, Riekert A. 2023. ‘Convergence analysis for gradient flows in the training of artificial neural networks with ReLU activation.’ Journal of Mathematical Analysis and Applications 517, No. 2: 126601. doi: 10.1016/j.jmaa.2022.126601.
- Hutzenthaler M, Jentzen A, Kruse T, Nguyen TA. 2023. ‘Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations.’ Journal of Numerical Mathematics 31, No. 2: 1–28. doi: 10.1515/jnma-2021-0111.
- Grohs P, Hornung F, Jentzen A, Zimmermann P. 2023. ‘Space-time error estimates for deep neural network approximations for differential equations.’ Advances in Computational Mathematics 49, No. 1: 4. doi: 10.1007/s10444-022-09970-2.

Research Areas

Interdisciplinary cooperations

Ongoing projects and recent publications

Current Projects

Latest Publications

2024

2023