List of publications

Publications

• 2026
• 2025
• 2024
• 2023
• 2022
• 2021
• 2020
• 2019
• 2018
• 2017
• 2016
• 2015
• 2014
• 2013
• 2012
• 2011
• 2010
• 2009
• 2008
• 2007
• 2006
• 2005
• 2004
• 2003
• 2002
• 2001
• 2000
• 1999
• 1998
• 1997
• 1996
• 1995
• 1993
• 1991
• 1990
• 1980
• 1979
• 1978
• 1977
• 1976
• 1975

2026

Published

• Maggiorelli, Eleonora, Riva, Filippo, and Tolotti, Giovanni Edoardo. 2026. “A free boundary approach to the quasistatic evolution of debonding models.” Mathematical Models and Methods in Applied Sciences Online. doi: 10.1142/S0218202526500363.
• Seis, Christian, and Winkler, Dominik. 2026. “Stability of traveling waves for doubly nonlinear equations.” Tunisian Journal of Mathematics 8 (1): 157–170. doi: 10.2140/tunis.2026.8.157.
• Seis, Christian, Wiedemann, Emil, and Woźnicki, Jakub. 2026. “Strong convergence of vorticities in the 2D viscosity limit on a bounded domain.” Preprint. Journal of Nonlinear Science 36 (22). doi: 10.1007/s00332-026-10239-x.
• Navarro-Fernández, Víctor, and Seis, Christian. 2026. “Exponential mixing by random cellular flows.” Journal of Functional Analysis 290 (2). doi: 10.1016/j.jfa.2025.111227.
• Klein, Benedikt, and Ohlberger, Mario. 2026. “Multi-fidelity Learning of Reduced Order Models for Parabolic PDE Constrained Optimization.” Advances in Computational Mathematics 52 (19): 1–36. doi: 10.1007/s10444-026-10296-6.
• Seis, Christian. 2026. “Infinite Prandtl number convection with Navier-slip boundary conditions.” Preprint. Communications in Mathematical Physics 407 (125). doi: 10.1007/s00220-026-05637-x.
• Scheel, Arnd, and Stevens, Angela. 2026. “Reversible switching due to attraction and repulsion: clusters, gaps, sorting, and mixing.” SIAM Journal on Applied Dynamical Systems 25 (3): 2022–2043. doi: 10.1137/25M177744X.
• Wirth, Benedikt. 2026. “Convergence of spectral discretization for the flow of diffeomorphisms.” Preprint. Numerische Mathematik tba. doi: 10.1007/s00211-026-01538-2.
• Chandra, A., de, Lima Feltes G., and Weber, H. 2026. “A priori bounds for the generalised parabolic Anderson model.” Communications on Pure and Applied Mathematics 79 (5): 1315–1394. doi: 10.1002/cpa.70025.

accepted / in Press (not yet published)

• Gander, Martin J, Ohlberger, Mario, and Rave, Stephan. in Kürze. “A Parareal algorithm without Coarse Propagator?” Preprint. in Domain Decomposition Methods in Science and Engineering XXVIII, Vol. 155 of Lecture Notes in Computational Science and Engineering, edited by Petter Bjørstad, Xiao-Chuan Cai, Victorita Dolean, David E. Keyes, Ralf Kornhuber, Jinchao Xu and Xiao-Chuan Cai. Cham: Springer Publishing. doi: 10.48550/arXiv.2409.02673.

Submitted / Under Review

• Klein, Benedikt, Ohlberger, Mario, and Schuster, Thomas. 2026. “Adaptive Reduced-Basis Trust-Region Methods for Defect Identification in Elastic Materials.” Preprint. arXiv doi: 10.48550/arXiv.2605.19896.
• Kotowski, Dawid, and Ohlberger, Mario. 2026. “A New Adaptive Deep Learning based Reduced Order Model for Hybrid-Type Parabolic PDEs: Rigorous Error Analysis and Applications.” Preprint. arXiv doi: 10.48550/arXiv.2604.22512.
• Kabanov, Dmitry I., Rave, Stephan, and Ohlberger, Mario. 2026. “MaRDI Open Interfaces for Interoperable Nonlinear Optimization.” Preprint. arXiv doi: 10.48550/arXiv.2606.20410.
• Kabanov, Dmitry I., Rave, Stephan, and Ohlberger, Mario. 2026. “Software package MaRDI Open Interfaces for improved interoperability in numerical optimization.” Preprint. arXiv doi: 10.48550/arXiv.2606.20490.

2025

Published

• Kartmann, Michael, Klein, Benedikt, Ohlberger, Mario, Schuster, Thomas, and Volkwein, Stefan. 2025. “Adaptive Reduced Basis Trust Region Methods for Parabolic Inverse Problems.” Inverse Problems 41 (12): 1–36. doi: 10.1088/1361-6420/ae2a66.
• Marquardt, N, Hengsbach, T, Mauritz, M, Wirth, B, and Schäfers, K. 2025. “Motion simulation of radio-labeled cells in whole-body positron emission tomography.” IEEE Transactions on Medical Imaging 45 (3): 919–930. doi: 10.1109/TMI.2025.3614767.
• Kleikamp, Hendrik, and Renelt, Lukas. 2025. “Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems.” Journal of Scientific Computing 104 (78). doi: 10.1007/s10915-025-02988-w.
• Mori, Y., Perthame, B., and Stevens, A., eds. 2025. Lecture Notes on Mathematical Modelling in the Life Sciences, Vol. 1, Dynamics of Physiological Control. Contributions in Honor of Michael C. Mackey Cham, Switzerland: Springer. doi: 10.1007/978-3-031-82396-1.
• Budde, Ilka, Schlichting, André, Ing, David, Schimmelpfennig, Sandra, Kuntze, Anna, Fels, Benedikt, Romac, Joelle M.-J., Swain, Sandip M., Liddle, Rodger A., Stevens, Angela, Schwab, Albrecht, and Pethő, Zoltán. 2025. “Piezo1-induced durotaxis of pancreatic stellate cells depends on TRPC1 and TRPV4 channels.” Journal of Cell Science online first. doi: 10.1242/jcs.263846.
• Kleikamp, Hendrik, Lazar, Martin, and Molinari, Cesare. 2025. “Be greedy and learn: efficient and certified algorithms for parametrized optimal control problems.” Preprint. ESAIM: Mathematical Modelling and Numerical Analysis 59 (1): 291–330. doi: 10.1051/m2an/2024074.
• Schembera, Björn, Wübbeling, Frank, Kleikamp, Hendrik, Schmidt, Burkhard, Shehu, Aurela, Reidelbach, Marco, Biedinger, Christine, Fiedler, Jochen, Koprucki, Thomas, Iglezakis, Dorothea, and Göddeke, Dominik. 2025. “Towards a Knowledge Graph for Models and Algorithms in Applied Mathematics.” in Proceedings of the 18th International Conference on Metadata and Semantics Research 2024, Communications in Computer and Information Science, edited by Michalis Sfakakis, Emmanouel Garoufallou, Matthew Damigos, Athena Salaba and Christos Papatheodorou. Cham: Springer. doi: 10.1007/978-3-031-81974-2_8.
• Kleikamp, Hendrik, and Ohlberger, Mario. 2025. “Adaptive Model Hierarchies for Multi-Query Scenarios.” Preprint. in MATHMOD 2025 - Discussion Contribution Volume, edited by Andreas Körner, Andreas Kugi, Wolfgang Kemmetmüller, Andreas Deutschmann-Olek, Andreas Steinböck, Christian Hartl-Nesic and Lukasz Piotr Jadachowski. Wien: ARGESIM Verlag. doi: 10.34726/9007.
• Song, Chunqiu, Weber, Hendrik, and Wulkenhaar, Raimar. 2025. “Stochastic quantization of λϕ^4_2-theory in 2-d Moyal space.” Preprint. arXiv doi: 10.48550/arXiv.2502.02355.
• Lazzaroni, Giuliano; Wozniak, Piotr; Zeppieri, Caterina Ida. 2025. “Strong approximation of special functions of bounded variation functions with prescribed jump direction.” Mathematical News / Mathematische Nachrichten 298 (1): 312–327. doi: 10.1002/mana.202300346.
• Mauritz, Marco, and Wirth, Benedikt. 2025. “Convergence of Poisson point processes and of optimal transport regularization with application in variational analysis of PET reconstruction.” Inverse Problems 41 035002. doi: 10.1088/1361-6420/ada97a.
• Meyer, David, Niebel, Lukas, and Seis, Christian. 2025. “Steady bubbles and drops in inviscid fluids.” Calculus of Variations and Partial Differential Equations 64 (299). doi: 10.1007/s00526-025-03144-w.
• Klein, Benedikt, and Ohlberger, Mario. 2025. “A Trust Region RB-ML-ROM Approach for Parabolic PDE Constrained Optimization.” Preprint. in MATHMOD 2025 - Discussion Contribution Volume, edited by Andreas Körner, Andreas Kugi, Wolfgang Kemmetmüller, Andreas Deutschmann-Olek, Andreas Steinböck, Christian Hartl-Nesic and Lukasz Piotr Jadachowski. Wien: ARGESIM Verlag. doi: 10.34726/9000.
• Kabanov, Dmitry I., Rave, Stephan, and Ohlberger, Mario. 2025. “Improving Interoperability in Scientific Computing via MaRDI Open Interfaces.” Journal of Open Research Software 13 (1) 29. doi: 10.5334/jors.569.
• Dzikonski, Dustin, Bekker, Elena, Zamboni, Riccardo, Ciechanska, Dominika, Schwab, Albrecht, Denz, Cornelia, and Imbrock, Jörg. 2025. “Hybrid Microfluidic Chip Design with Two-Photon Polymerized Protein-Based Hydrogel Microstructures for Single Cell Experiments.” Advanced Materials Technologies 10 2401571 . doi: 10.1002/admt.202401571.
• Huang, Ruojun, Matetski, Konstantin, and Weber, Hendrik. 2025. “Scaling limit of a weakly asymmetric simple exclusion process in the framework of regularity structures.” Preprint. arXiv doi: 10.48550/arXiv.2505.00621.
• Stevens, A. 2025. “Laudatio zur Verleihung der Georg-Cantor-Medaille an Felix Otto.” Mitteilungen der Deutschen Mathematiker-Vereinigung 33 (1): 7–9. doi: 10.1515/dmvm-2025-0006.
• Bauerschmidt, Roland, Dagallier, Benoit, and Weber, Hendrik. 2025. “Holley--Stroock uniqueness method for the φ42 dynamics.” Preprint. arXiv doi: 10.48550/arXiv.2504.08606.
• Tempelmayr, Markus, and Weber, Hendrik. 2025. “A priori bounds for stochastic porous media equations via regularity structures.” Preprint. arXiv doi: 10.48550/arXiv.2507.03575.
• Bourne, David, Schmitzer, Bernhard, and Wirth, Benedikt. 2025. “Semi-discrete unbalanced optimal transport and quantization.” Preprint. European Journal of Applied Mathematics FirstView: 1–43. doi: 10.1017/S0956792525100144.
• Kunisch, Manuel, Beutler, Sascha, Pilger, Christian, Kiefer, Friedemann, Huser, Thomas, and Wirth, Benedikt. 2025. “Active Axial Motion Compensation in Multiphoton-Excited Fluorescence Microscopy.” Optics Express 33 (2): 3620–3636. doi: 10.1364/OE.547244.
• Lohmann, Julius, Schmitzer, Bernhard, and Wirth, Benedikt. 2025. “Formulas for the h-mass on 1-currents with coefficients in R^m.” Calculus of Variations and Partial Differential Equations 64 288. doi: 10.1007/s00526-025-03151-x.
• Tolotti, Giovanni Edoardo. 2025. “On the Hierarchy of Plate Models for a Singularly Perturbed Multi-Well Nonlinear Elastic Energy.” Preprint. Journal of Nonlinear Science 35 77. doi: 10.1007/s00332-025-10174-3.
• Tolotti, Giovanni Edoardo. 2025. “Stability of the Von Kármán regime for thin plates under Neumann boundary conditions.” Preprint. ESAIM: Control, Optimisation and Calculus of Variations 31 61. doi: 10.1051/cocv/2025050.

Submitted / Under Review

• Engwer, Christian, Ohlberger, Mario, and Renelt, Lukas. 2025. “Sectional Kolmogorov N-widths for parameter-dependent function spaces: A general framework with application to parametrized Friedrichs' systems.” Preprint. arXiv doi: 10.48550/arXiv.2507.00678.
• Gander, Martin J, Ohlberger, Mario, and Rave, Stephan. 2025. “A Parareal Algorithm with Spectral Coarse Solver.” Preprint. arXiv doi: 10.48550/arXiv.2508.08873.

2024

Published

• Otto, Felix, Sauer, Jonas, Smith, Scott, and Weber, Hendrik. 2024. “A priori bounds for quasi-linear SPDEs in the full sub-critical regime.” Journal of the European Mathematical Society 27: 71–118. doi: 10.4171/jems/1574.
• Esquivel Calzada, Salvador Cesar, and Weber, Hendrik. 2024. “A priori bounds for the dynamic fractional Φ4 model on T3 in the full subcritical regime.” Preprint. arXiv e-prints
• Engwer, Christian, Ohlberger, Mario, and Renelt, Lukas. 2024. “Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems.” SIAM Journal on Scientific Computing 46 (5): A3205–A3229. doi: 10.1137/23M1613402.
• Kartmann, Michael, Keil, Tim, Ohlberger, Mario, Volkwein, Stephan, and Kaltenbacher, Barbara. 2024. “Adaptive Reduced Basis Trust Region Methods for Parameter Identification Problems.” Computational Science and Engineering 1 (3): 1–30. doi: 10.1007/s44207-024-00002-z.
• Engwer, Christian, Ohlberger, Mario, and Renelt, Lukas. 2024. “Construction of local reduced spaces for Friedrichs' systems via randomized training.” contribution to the Central-European Conference on Scientific Computing, ALGORITMY, Podbanské
• Budde, Ilka, Schlichting, André, Ing, David, Schimmelpfennig, Sandra, Kuntze, Anna, Fels, Benedikt, Romac, Joelle M.-J., Swain, Sandip M., Liddle, Rodger A., Stevens, Angela, Schwab, Albrecht, and Pethő, Zoltán. 2024. “Piezo1-induced durotaxis of pancreatic stellate cells depends on TRPC1 and TRPV4 channels.” Preprint. bioRxiv Cold Spring Harbor Laboratory. doi: 10.1101/2023.12.22.572956.
• Kleikamp, Hendrik. 2024. “Application of an adaptive model hierarchy to parametrized optimal control problems.” Preprint. in Proceedings of the Conference Algoritmy 2024, edited by P. Frolkovič and K.Mikula and D. Ševčovič. Bratislava: Jednota slovenských matematikov a fyzikov.
• de Lima Feltes, Guilherme, and Weber, Hendrik. 2024. “Brownian particle in the curl of 2-d stochastic heat equations.” Preprint. Journal of Statistical Physics 191 16. doi: 10.1007/s10955-023-03224-1.
• Keil, Tim, and 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.
• Meyer, David, and Seis, Christian. 2024. “Propagation of regularity for transport equations. A Littlewood-Paley approach.” Preprint. Indiana University Mathematics Journal 73 (2): 445–473.
• Ceci, Stefano, and Seis, Christian. 2024. “On the dynamics of vortices in viscous 2D flows.” Preprint. Mathematische Annalen 388: 1937–1967. doi: 10.1007/s00208-023-02568-z.
• Seis, Christian, and Winkler, Dominik. 2024. “Invariant Manifolds for the Thin Film Equation.” Preprint. Archive for Rational Mechanics and Analysis 248 (2). doi: 10.1007/s00205-024-01968-y.
• Wenzel, Tizian, Haasdonk, Bernard, Kleikamp, Hendrik, Ohlberger, Mario, and Schindler, Felix. 2024. “Application of Deep Kernel Models for Certified and Adaptive RB-ML-ROM Surrogate Modeling.” Preprint. in Large-Scale Scientific Computations, Vol. 13952 of Lecture Notes in Computer Science, edited by I. Lirkov and S. Margenov. Cham: Springer Nature. doi: 10.1007/978-3-031-56208-2_11.
• Keil, Tim, Ohlberger, Mario, and Schindler, Felix. 2024. “Adaptive Localized Reduced Basis Methods for Large Scale PDE-constrained Optimization.” Preprint. in Large-Scale Scientific Computations, Vol. 13952 of Lecture Notes in Computer Science, edited by I Lirkov and S Margenov. Cham: Springer Nature. doi: 10.1007/978-3-031-56208-2_10.
• Baumann, Lena, and Pirner, Marlies. 2024. “Linear Landau damping for a two-species Vlasov-Poisson system for electrons and ions.” in Hyperbolic Problems: Theory, Numerics, Applications. Volume II : HYP2022, Málaga, Spain, June 20-24, 2022, Vol. 35 of SEMA SIMAI Springer Series, edited by Carlos Parés, Manuel Castro, Tomas Morales de Luna and Maria Luz Muñoz-Ruiz. Cham: Springer Nature. doi: 10.1007/978-3-031-55264-9_22.
• Choi, Beomjun, and Seis, Christian. 2024. “Finite-dimensional leading order dynamics for the fast diffusion equation near extinction.” Preprint. Discrete and Continuous Dynamical Systems - Series A 44 (9): 2697–2712. doi: 10.3934/dcds.2024043.
• Schembera, Björn, Wübbeling, Frank, Kleikamp, Hendrik, Biedinger, Christine, Fiedler, Jochen, Reidelbach, Marco, Shehu, Aurela, Schmidt, Burkhard, Koprucki, Thomas, Iglezakis, Dorothea, and Göddeke, Dominik. 2024. “Ontologies for Models and Algorithms in Applied Mathematics and Related Disciplines.” in Metadata and Semantic Research - 17th Research Conference, MTSR 2023, Milan, Italy, October 25–27, 2023, Revised Selected Papers, Vol. 2048 of Communications in Computer and Information Science, edited by Emmanouel Garoufallou and Fabio Sartori. Cham: Springer. doi: 10.1007/978-3-031-65990-4_14.
• Seis, Christian, and Winkler, Dominik. 2024. “Fine large-time asymptotics for the axisymmetric Navier-Stokes equations.” Preprint. Journal of Evolution Equations 24 72. doi: 10.1007/s00028-024-01001-5.
• Holler, Martin, and Wirth, Benedikt. 2024. “Exact reconstruction and reconstruction from noisy data with anisotropic total variation.” SIAM Journal on Mathematical Analysis 56 (3): 2938–2967. doi: 10.1137/22M1508571.
• Braunsmann, Juliane, Rajković, Marko, Rumpf, Martin, and Wirth, Benedikt. 2024. “Convergent Autoencoder Approximation of Low Bending and Low Distortion Manifold Embeddings.” ESAIM: Mathematical Modelling and Numerical Analysis 58 (1): 335–361. doi: 10.1051/m2an/2023088.
• Chevyrev, I., Gerasimovičs, A., and Weber, H. 2024. “Feature Engineering with Regularity Structures.” Journal of Scientific Computing 98 (13). doi: 10.1007/s10915-023-02401-4.
• Esposito, A, Patacchini, FS, and Schlichting, A. 2024. “On a Class of Nonlocal Continuity Equations on Graphs.” European Journal of Applied Mathematics 35 (1): 109–126. doi: 10.1017/S0956792523000128.
• Holler, Martin, Schlüter, Alexander, and 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.
• Chandra, Ajay, de Lima Feltes, Guilherme, and Weber, Hendrik. 2024. “A priori bounds for 2-d generalised Parabolic Anderson Model.” Preprint. arXiv doi: 10.48550/arXiv.2402.05544.
• de Nitti, Nicola, Meyer, David, and Seis, Christian. 2024. “Optimal Regularity for the 2D Euler Equations in the Yudovich class.” Preprint. Journal de Mathématiques Pures et Appliquées 191. doi: 10.1016/j.matpur.2024.103631.
• Pirner, Marlies. 2024. “A consistent kinetic Fokker-Planck model for gas mixtures.” Journal of Statistical Physics 191 (11) 143. doi: 10.1007/s10955-024-03361-1.
• Singh, A, Thale, S, Leibner, T, Lamparter, L, Ricker, A, Nüsse, H, Klingauf, J, Galic, M, Ohlberger, M, and Matis, M. 2024. “Dynamic interplay of microtubule and actomyosin forces drive tissue extension.” Nature Communications 15 (1): 3198–3198. doi: 10.1038/s41467-024-47596-8.
• Tim, Keil, Mario, Ohlberger, Felix, Schindler, and Julia, Schleuß. 2024. “Local training and enrichment based on a residual localization strategy.” Preprint. in Proceedings of the Conference Algoritmy 2024, Vol. 8 of Proceedings of the Conference Algoritmy, edited by P Frolkovič, K Mikula and D Ševčovič. Bratislava: Jednota slovenských matematikov a fyzikov.
• Mauritz, Marco, Schmitzer, Bernhard, and Wirth, Benedikt. 2024. “A Bayesian model for dynamic mass reconstruction from PET listmode data.” SIAM Journal on Mathematical Analysis 56 (5): 5840–5880. doi: 10.1137/23M161923X.
• Grazieschi, Paolo, Matetski, Konstantin, and Weber, Hendrik. 2024. “The dynamical Ising-Kac model in 3D converges to Φ4/3.” Probability Theory and Related Fields 190 (1-2). doi: 10.1007/s00440-024-01316-x.
• Grazieschi, Paolo, Matetski, Konstantin, and Weber, Hendrik. 2024. “Martingale-driven integrals and singular SPDEs.” Preprint. Probability Theory and Related Fields 190: 1063–1120. doi: 10.1007/s00440-024-01311-2.
• Balduf, P, and Thürigen, J. 2024. “Primitive asymptotics in $\phi^4$ vector theory.” Preprint. arXiv.org doi: 10.48550/arXiv.2412.08617.
• Ben Achour, J, Benedetti, D, Bojowald, M, Brandenberger, R, Butera, S, Ferrero, R, Giacomini, F, Giesel, K, Goeller, C, Haas, T, Höhn, P, Kirklin, J, Marchetti, L, Oriti, D, Percacci, R, Pereira, A, Pithis, A, Sakellariadou, M, Steinhaus, S, and Thürigen, J. 2024. “Quantum Gravity, Hydrodynamics and Emergent Cosmology: A Collection of Perspectives.” General Relativity and Gravitation 57 2. doi: 10.1007/s10714-024-03335-4.

Submitted / Under Review

• Kleikamp, Hendrik, and Wenzel, Tizian. 2024. “Kernel Methods in the Deep Ritz framework: Theory and practice.” Preprint. arXiv doi: 10.48550/arXiv.2410.03503.
• Fischer, J, Hensel, S, Laux, T, and Simon, T.M. 2024. “A weak-strong uniqueness principle for the Mullins-Sekerka equation.” Preprint. arXiv doi: 10.48550/arXiv.2404.02682.
• Muratov, C.B., Simon, T.M., and Slastikov, V.V. 2024. “Existence of higher degree minimizers in the magnetic skyrmion problem.” Preprint. arXiv doi: 10.48550/arXiv.2409.07205.

2023

Published

• Boussange, V., Becker, S., Jentzen, A., Kuckuck, B., and Pellissier, L. 2023. “Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions.” Preprint. SN Partial Differential Equations and Applications 4 51. doi: 10.1007/s42985-023-00244-0.
• Renelt, Lukas, Ohlberger, Mario, and Engwer, Christian. 2023. “An optimally stable approximation of reactive transport using discrete test and infinite trial spaces.” Preprint. in Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems, Springer Proceedings in Mathematics & Statistics, edited by Emmanuel Franck, Jürgen Fuhrmann, Michel-Dansac Victor and Laurent Navoret. Cham: Springer. doi: 10.1007/978-3-031-40860-1_30.
• Friedrich, Manuel, and Machill, Lennart. 2023. “One-dimensional viscoelastic von Kármán theories derived from nonlinear thin-walled beams.” Preprint. Calculus of Variations and Partial Differential Equations 62 (7) 190. doi: 10.1007/s00526-023-02525-3.
• Haasdonk, B, Kleikamp, H, Ohlberger, M, Schindler, F, and Wenzel, T. 2023. “A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs.” SIAM Journal on Scientific Computing 45 (3): A1039–1065. doi: 10.1137/22M1493318.
• Chandra, Ajay, Moinat, Augustin, and Weber, Hendrik. 2023. “A Priori Bounds for the Φ4 Equation in the Full Sub-critical Regime.” Archive for Rational Mechanics and Analysis 247 (3) 48. doi: 10.1007/s00205-023-01876-7.
• Eberle, Simon, Jentzen, Arnulf, Riekert, Adrian, and 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 (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, and Repple, Jonathan. 2023. “Towards a network control theory of electroconvulsive therapy response.” PNAS Nexus 2 (2). doi: 10.1093/pnasnexus/pgad032.
• Beck, C, Hutzenthaler, M, Jentzen, A, and Kuckuck, B. 2023. “An overview on deep learning-based approximation methods for partial differential equations.” Discrete and Continuous Dynamical Systems - Series B 28 (6): 3697–3746. doi: 10.3934/dcdsb.2022238.
• Choi, Beomjun, McCann, Robert J., and Seis, Christian. 2023. “Asymptotics near extinction for nonlinear fast diffusion on a bounded domain.” Preprint. Archive for Rational Mechanics and Analysis 247 16. doi: 10.1007/s00205-023-01850-3.
• Navarro-Fernández, V, and Schlichting, A. 2023. “Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients.” ESAIM: Mathematical Modelling and Numerical Analysis 57 (4): 2131–2158. doi: 10.1051/m2an/2023035.
• Jentzen, A, and 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 (2) 126601. doi: 10.1016/j.jmaa.2022.126601.
• Hutzenthaler, M, Jentzen, A, Kruse, T, and Nguyen, TA. 2023. “Overcoming the curse of dimensionality in the numerical approximation of backward stochastic differential equations.” Journal of Numerical Mathematics 31 (2): 1–28. doi: 10.1515/jnma-2021-0111.
• Grohs, P, Hornung, F, Jentzen, A, and Zimmermann, P. 2023. “Space-time error estimates for deep neural network approximations for differential equations.” Advances in Computational Mathematics 49 (1) 4. doi: 10.1007/s10444-022-09970-2.
• Becker, S, Gess, B, Jentzen, A, and Kloeden, PE. 2023. “Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen--Cahn equations.” Stochastics and Partial Differential Equations: Analysis and Computations 11 (1): 211–268. doi: 10.1007/s40072-021-00226-6.
• Keil, Tim, and Rave, Stephan. 2023. “An Online Efficient Two-Scale Reduced Basis Approach for the Localized Orthogonal Decomposition.” SIAM Journal on Scientific Computing 45 (4). doi: 10.1137/21M1460016.
• Landstorfer, M, Ohlberger, M, Rave, S, and Tacke, M. 2023. “A Modeling Framework for Efficient Reduced Order Simulations of Parametrized Lithium-Ion Battery Cells.” European Journal of Applied Mathematics 34 (3): 554–591. doi: 10.1017/S0956792522000353.
• Herzing, Tobias, Klingenberg, Christian, and Pirner, Marlies. 2023. “Hypocoercivity of the linearized BGK equation with stochastic coefficients.” Methods and Applications of Analysis 30(3): 113–128. doi: 10.4310/MAA.2023.v30.n3.a2.
• Bae, Gi-Chan, Klingenberg, Christian, Pirner, Marlies, and Yun, Seok-Bae. 2023. “BGK model for two-component gases near a global Maxwellian.” SIAM Journal on Mathematical Analysis 55 (2). doi: 10.1137/22M1469535.
• Favre, Gianluca, Pirner, Marlies, and Schmeiser, Christian. 2023. “Hypocoercivity and reaction-diffusion limit for a non-linear generation-recombination model.” Archive for Rational Mechanics and Analysis 247 (4) 72. doi: 10.1007/s00205-023-01902-8.
• Monteil, A, Muratov, C.B., Simon, T.M., and Slastikov, V.V. 2023. “Magnetic skyrmions under confinement.” Preprint. Communications in Mathematical Physics 404: 1571–1605. doi: 10.1007/s00220-023-04864-w.
• Rüland, A., and Simon, T.M. 2023. “On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation.” Preprint. Journal of Elasticity 153: 455–475. doi: 10.1007/s10659-023-10011-2.
• Medani, Takfarinas, Garcia-Prieto, Juan, Tadel, Francois, Antonakakis, Marios, Erdbrügger, Tim, Höltershinken, Malte, Mead, Wayne, Schrader, Sophie, Joshi, Anand, Engwer, Christian, Wolters, Carsten H., Mosher, John C., and Leahy, Richard M. 2023. “Brainstorm-DUNEuro: An integrated and user-friendly Finite Element Method for modeling electromagnetic brain activity.” NeuroImage 267 119851. doi: 10.1016/j.neuroimage.2022.119851.
• Ohlberger, M., Banholzer, S., Haasdonk, B., Keil, T.Kleikamp H., Mechelli, L., Oguntola, M, Schindler F., Volkwein, S., and Wenzel, T. 2023. “Model Reduction and Learning for PDE Constrained Optimization.” contribution to the Oberwolfach Workshop on Optimization Problems for PDEs in Weak Space-Time Form, Oberwolfach doi: 10.4171/OWR/2023/13.
• Guastini, Mara, Rajković, Marko, Rumpf, Martin, and Wirth, Benedikt. 2023. “The variational approach to the flow of Sobolev-diffeomorphisms model.” in Scale Space and Variational Methods in Computer Vision, Lecture Notes in Computer Science, edited by Luca Calatroni, Marco Donatelli, Serena Morigi, Marco Prato and Matteo Santacesaria. Cham: Springer. doi: 10.1007/978-3-031-31975-4_42.
• Sassen, Josua, Hildebrandt, Klaus, Rumpf, Martin, and Wirth, Benedikt. 2023. “Parametrizing product shape manifolds by composite networks.” contribution to the International Conference on Learning Representations (ICLR 2023), Kigali
• Beck, Lisa, Cinti, Eleonora, and Seis, Christian. 2023. “Optimal regularity of isoperimetric sets with Hölder densities.” Preprint. Calculus of Variations and Partial Differential Equations 62 (214). doi: 10.1007/s00526-023-02542-2.
• Schleuß, Julia, Smetana, Kathrin, and ter Maat, Lukas. 2023. “Randomized quasi-optimal local approximation spaces in time.” SIAM Journal on Scientific Computing 45 (3). doi: 10.1137/22M1481002.
• Himpe, Christian, and Grundel, sara. 2023. “System Order Reduction for Gas and Energy Networks.” contribution to the 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Aachen doi: 10.1002/pamm.202200201.
• Hahn, Bernadette, and Wirth, Benedikt. 2023. “Convex reconstruction of moving particles with inexact motion model.” Proceedings in Applied Mathematics and Mechanics n/a e202300054. doi: 10.1002/pamm.202300054.
• Bernand-Mantel, A., Fondet, A, Barnova, S., Simon, T.M., and Muratov, C.B. 2023. “Theory of magnetic field-stabilized compact skyrmions in thin film ferromagnets.” Physical Review B 2023 L161405. doi: 10.1103/PhysRevB.108.L161405.
• Tolomeo, Leonardo, and Weber, Hendrik. 2023. “Phase transition for invariant measures of the focusing Schrödinger equation.” Preprint. arXiv doi: 10.48550/arXiv.2306.07697.
• Luckhaus, Stephan, and Stevens, Angela. 2023. “A free boundary problem-in time-for the spread of Covid-19.” Journal of Mathematical Biology 86 (45). doi: 10.1007/s00285-023-01881-0.
• Erdbrügger, T., Westhoff, A., Höltershinken, M., Radecke, J.-O., Buschermöhle, Y., Buyx, A., Wallois, F., Pursiainen, S., Gross, J., Lencer, R., Engwer, C., and Wolters, C.H. 2023. “CutFEM forward modeling for EEG source analysis.” Frontiers in Human Neuroscience 17 1216758. doi: 10.3389/fnhum.2023.1216758.
• Luckhaus, Stephan, and Stevens, Angela. 2023. “A two level contagion process and its deterministic McKendrick limit with relevance for the Covid epidemic.” Ensaios Matemáticos 38: 343–358. doi: 10.21711/217504322023/em3813.
• Bach, A.; Marziani, R.; Zeppieri, C.I.. 2023. “Γ-convergence and stochastic homogenisation of singularly-perturbed elliptic functionals.” Calculus of Variations and Partial Differential Equations 62 (199).
• Bach, A.; Esposito, T.; Marziani, R; Zeppieri, C.I.. 2023. “Gradient Damage Models for Heterogeneous Materials.” SIAM Journal on Mathematical Analysis 55 (4). doi: 10.1137/22M1499145.
• Ruf, Matthias; Zeppieri, Caterina Ida. 2023. “Stochastic homogenization of degenerate integral functionals with linear growth.” Calculus of Variations and Partial Differential Equations 62 (138) 138. doi: 10.1007/s00526-023-02476-9.
• D'Onofrio, C.; Zeppieri, C.I.. 2023. “Gamma-convergence and stochastic homogenisation of degenerate integral functionals in weighted Sobolev spaces.” Proceedings of the Royal Society of Edinburgh: Section A Mathematics 153 (2).
• Pellet, X.; Scardia, L.; Zeppieri, C.I.. 2023. “Stochastic homogenisation of free-discontinuity functionals in randomly perforated domains.” Advances in Calculus of Variations 17 (3). doi: 10.1515/acv-2022-0052.

accepted / in Press (not yet published)

• Jentzen, A, and Riekert, A. in Kürze. “Strong overall error analysis for the training of artificial neural networks via random initializations.” Communications in Mathematics and Statistics. doi: 10.1007/s40304-022-00292-9.
• Grohs, P, Ibragimov, S, Jentzen, A, and Koppensteiner, S. in Kürze. “Lower bounds for artificial neural network approximations: A proof that shallow neural networks fail to overcome the curse of dimensionality.” Journal of Complexity 101746. doi: 10.1016/j.jco.2023.101746.

Submitted / Under Review

• Gonon, L., Graeber, R., and Jentzen, A. 2023. “The necessity of depth for artificial neural networks to approximate certain classes of smooth bounded functions without the curse of dimensionality.” Preprint. arXiv.org
• Jentzen, A., Riekert, A., and von Wurstemberger, P. 2023. “Algorithmically Designed Artificial Neural Networks (ADANNs): Higher order deep operator learning for parametric partial differential equations.” Preprint. arXiv.org
• Dereich, S., Jentzen, A., and Kassing, S. 2023. “On the existence of minimizers in shallow residual ReLU neural network optimization landscapes.” Preprint. arXiv.org
• Beck, C., Jentzen, A., Kleinberg, K., and Kruse, T. 2023. “Nonlinear Monte Carlo methods with polynomial runtime for Bellman equations of discrete time high-dimensional stochastic optimal control problems.” Preprint. arXiv.org
• Julia, Schleuß, and Kathrin, Smetana. 2023. “DEIM vs. leverage scores for time-parallel construction of problem-adapted basis functions.” Preprint. arXiv doi: 10.48550/arXiv.2302.00348.

2022

Published

• Keil, T, Kleikamp, H, Lorentzen, R, Oguntola, M, and Ohlberger, M. 2022. “Adaptive machine learning based surrogate modeling to accelerate PDE-constrained optimization in enhanced oil recovery.” Advances in Computational Mathematics 2022 (48) 73. doi: 10.1007/s10444-022-09981-z.
• Peletier, Mark A., and Schlichting, André. 2022. “Cosh gradient systems and tilting.” Nonlinear Analysis: Theory, Methods and Applications 2203 113094. doi: 10.1016/j.na.2022.113094.
• Leibner, Tobias. 2022. “Model reduction for kinetic equations: moment approximations and hierarchical approximate proper orthogonal decomposition.” Dissertation thesis, Universität Münster.
• Friedrich, Manuel, and Machill, Lennart. 2022. “Derivation of a one-dimensional von Kármán theory for viscoelastic ribbons.” Nonlinear Differential Equations and Applications 29 (2): 1–42. doi: 10.1007/s00030-021-00745-0.
• Schlichting, André, and Seis, Christian. 2022. “The Scharfetter-Gummel scheme for aggregation-diffusion equations.” IMA Journal of Numerical Analysis 42 (3). doi: 10.1093/imanum/drab039.
• Seis, C. 2022. “Bounds on the rate of enhanced dissipation.” Communications in Mathematical Physics Online first. doi: 10.1007/s00220-022-04588-3.
• Nobili, Camilla, and Seis, Christian. 2022. “Renormalization and energy conservation for axisymmetry fluid flows.” Mathematische Annalen 382: 1–36. doi: 10.1007/s00208-020-02050-0.
• Menz, G, Schlichting, A, Tang, W, and Wu, T. 2022. “Ergodicity of the infinite swapping algorithm at low temperature.” Stochastic Processes and their Applications 151: 519–552. doi: 10.1016/j.spa.2022.06.015.
• Dirks, C, and Wirth, B. 2022. “An adaptive finite element approach for lifted branched transport problems.” in Optimization and Control for Partial Differential Equations: Uncertainty quantification, open and closed-loop control, and shape optimization, edited by Herzog Roland, Heinkenschloss Matthias, Kalise Dante, Stadler Georg and Trélat Emmanuel. Berlin, Boston: De Gruyter.
• Gavrilenko, Pavel, Haasdonk, Bernard, Iliev, Oleg, Ohlberger, Mario, Schindler, Felix, Toktaliev, Pavel, Wenzel, Tizian, and Youssef, Maha. 2022. “A full order, reduced order and machine learning model pipeline for efficient prediction of reactive flows.” in Large-Scale Scientific Computing, Vol. 13127 of Lecture Notes in Computer Science (LNCS), edited by Ivan Lirkov and Svetozar Margenov. Cham: Springer VDI Verlag. doi: 10.1007/978-3-030-97549-4_43.
• Keil, Tim, and Ohlberger, Mario. 2022. “Model Reduction for Large Scale Systems.” in Large-Scale Scientific Computing, Vol. 13127 of Lecture Notes in Computer Science (LNCS), edited by Ivan Lirkov and Svetozar Margenov. Cham: Springer International Publishing. doi: 10.1007/978-3-030-97549-4_2.
• Gander, Martin Rave Stephan. 2022. “Localized Reduced Basis Additive Schwarz Methods.” in Domain Decomposition Methods in Science and Engineering XXVI, edited by Susanne C. Brenner Brenner, Eric Chung, Axel Klawonn, Felix Kwok, Jinchao Xu and Jun Zou. Cham: Springer International Publishing. doi: 10.1007/978-3-030-95025-5_52.
• Niethammer, Barbara, Pego, Robert L., Schlichting, André, and Velázquez, Juan J. L. 2022. “Oscillations in a Becker-Döring model with injection and depletion.” SIAM Journal on Applied Mathematics 82 (4): 1194–1219. doi: 10.1137/20M1398664.
• Navarro-Fernández, V, Schlichting, A, and Seis, C. 2022. “Optimal stability estimates and a new uniqueness result for advection-diffusion equations.” Pure and Applied Analysis 4 (3): 571–596. doi: 10.2140/paa.2022.4.571.
• Gonon, Lukas, Grohs, Philipp, Jentzen, Arnulf, Kofler, Dvid, and Šiška, David. 2022. “Uniform error estimates for artificial neural network approximations for heat equations.” IMA Journal of Numerical Analysis 42 (3): 1991–2054. doi: 10.1093/imanum/drab027.
• Hutzenthaler, M, Jentzen, A, and Kruse, T. 2022. “Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities.” Foundations of Computational Mathematics 22 (4): 905–966. doi: 10.1007/s10208-021-09514-y.
• Cheridito, P, Jentzen, A, and Rossmannek, F. 2022. “Efficient approximation of high-dimensional functions with neural networks.” IEEE Transactions on Neural Networks and Learning Systems 33 (7): 3079–3093. doi: 10.1109/TNNLS.2021.3049719.
• Jentzen, A, Kuckuck, B, Müller-Gronbach, T, and Yaroslavtseva, L. 2022. “Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven SDEs with smooth drift coefficient functions with at most polynomially growing derivatives.” Discrete and Continuous Dynamical Systems - Series B 27 (7): 3707–3724. doi: 10.3934/dcdsb.2021203.
• E, W., Han, J., and Jentzen, A. 2022. “Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning.” Nonlinearity 35 (1): 278–310. doi: 10.1088/1361-6544/ac337f.
• Effland, A, Heeren, B, Rumpf, M, and Wirth, B. 2022. “Consistent Curvature Approximation on Riemannian Shape Spaces.” IMA Journal of Numerical Analysis 42 (1): 78–106.
• Banholzer, S, Keil, T, Mechelli, L, Ohlberger, M, Schindler, F, and Volkwein, S. 2022. “An adaptive projected Newton non-conforming dual approach for trust-region reduced basis approximation of PDE-constrained parameter optimization.” Pure and Applied Functional Analysis 7 (5): 1561–1596.
• Potthoff, Jonas, and Wirth, Benedikt. 2022. “Optimal fine-scale structures in compliance minimization for a uniaxial load in three space dimensions.” ESAIM: Control, Optimisation and Calculus of Variations 28 27.
• Striewski, Paul, and Wirth, Benedikt. 2022. “Elastic 3D-2D Image Registration.” Journal of Mathematical Imaging and Vision 64: 443–462.
• Kleikamp, Hendrik, Ohlberger, Mario, and Rave, Stephan. 2022. “Nonlinear Model Order Reduction using Diffeomorphic Transformations of a Space-Time Domain.” in MATHMOD 2022 - Discussion Contribution Volume, Vol. 17 of ARGESIM Report, edited by Felix Breitenecker, Wolfgang Kemmetmüller, Andreas Körner, Andreas Kugi and Inge Troch. Wien: ARGESIM Verlag. doi: 10.11128/arep.17.a17129.
• Brecher, C, Buchmeiser, MR, Burkert, A, Busemeyer, MR, Conermann, S, Ertl, T, Friedrich, M, Helmig, R, Hohmann, V, Johnston, AJ, Kollmeier, B, Larkum, M, Louis, J, Menges, A, Morgner, U, Müller, J, Niessen, C, Ohlberger, M, Schäffner, W, Schmidt, P, Schmitz, D, Seeger, W, Stammer, D, Thomas, A, Traninger, A, Wegener, M, Colomb, J, Hermann, S, Kopsch-Xhema, J, Range, J, and Flemisch, B. 2022. “Commitment zu aktivem Daten- und -softwaremanagement in großen Forschungsverbünden: Commitment to active data and software management in large research alliances.” Bausteine Forschungsdatenmanagement 1: 121–123.. doi: 10.17192/bfdm.2022.1.8412.
• Himpe, C, Grundel, S, and Benner, P. 2022. “Efficient Gas Network Simulations.” in German Success Stories in Industrial Mathematics, Vol. 35 of Mathematics in Industry, edited by HG Bock, KH Küfer, P Maass, A Milde and V Schulz. doi: 10.1007/978-3-030-81455-7_4.
• Jentzen, A, and Riekert, A. 2022. “On the existence of global minima and convergence analyses for gradient descent methods in the training of deep neural networks.” Journal of Machine Learning 1 (2): 141–246. doi: 10.4208/jml.220114a.
• Jentzen, Arnulf, and Riekert, Adrian. 2022. “A proof of convergence for the gradient descent optimization method with random initializations in the training of neural networks with ReLU activation for piecewise linear target functions.” Journal of Machine Learning Research 23 (260): 1–50.
• Jentzen, Arnulf, and Riekert, Adrian. 2022. “A proof of convergence for stochastic gradient descent in the training of artificial neural networks with ReLU activation for constant target functions.” Zeitschrift für Angewandte Mathematik und Physik 73 (5) 188. doi: 10.1007/s00033-022-01716-w.
• Cheridito, P, Jentzen, A, and Rossmannek, F. 2022. “Landscape analysis for shallow neural networks: complete classification of critical points for affine target functions.” Journal of Nonlinear Science 32 (5) 64. doi: 10.1007/s00332-022-09823-8.
• Cheridito, Patrick, Jentzen, Arnulf, Riekert, Adrian, and Rossmannek, Florian. 2022. “A proof of convergence for gradient descent in the training of artificial neural networks for constant target functions.” Journal of Complexity 72 101646. doi: 10.1016/j.jco.2022.101646.
• Beck, C, Jentzen, A, and Kuckuck, B. 2022. “Full error analysis for the training of deep neural networks.” Infinite Dimensional Analysis, Quantum Probability and Related Topics 25 (2) 2150020. doi: 10.1142/S021902572150020X.
• Grohs, P, Jentzen, A, and Salimova, D. 2022. “Deep neural network approximations for solutions of PDEs based on Monte Carlo algorithms.” SN Partial Differential Equations and Applications 3 (4) 45. doi: 10.1007/s42985-021-00100-z.
• Elbrächter, D., Grohs, P., Jentzen, A., and Schwab, C. 2022. “DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing.” Constructive Approximation 55 (1): 3–71. doi: 10.1007/s00365-021-09541-6.
• Abgrall, R, Öffner, P, and Ranocha, H. 2022. “Reinterpretation and Extension of Entropy Correction Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure Preserving Discretization.” Journal of Computational Physics 2022: 110955.. doi: 10.1016/j.jcp.2022.110955.
• Ranocha, H, Schlottke-Lakemper, M, Winters, AR, Faulhaber, E, Chan, J, and Gassner, G. 2022. “Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing.” Proceedings of the JuliaCon Conferences 1 (1): 77.. doi: 10.21105/jcon.00077.
• Lohmann, Julius, Schmitzer, Bernhard, and Wirth, Benedikt. 2022. “Formulation of branched transport as geometry optimization.” Journal de Mathématiques Pures et Appliquées 163: 739–779. doi: 10.1016/j.matpur.2022.05.021.
• Haasdonk, B, Ohlberger, M, and Schindler, F. 2022. “An adaptive model hierarchy for data-augmented training of kernel models for reactive flow.” in MATHMOD 2022 Discussion Contribution Volume, edited by Felix Breitenecker, Wolfgang Kemmetmüller, Andreas Körner, Andreas Kugi and Inge Troch. Vienna: ARGESIM Verlag. doi: 10.11128/arep.17.a17155.
• Ceci, S, and Seis, C. 2022. “On the dynamics of point vortices for the 2D Euler equation with Lp vorticity.” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380 (2226). doi: 10.1098/rsta.2021.0046.
• Benner, P., Burger, M., Göddeke, D., Himpe, C., Hintermüller, M., Heiland, J., Koprucki, T., Ohlberger, M., Rave, S., Reidelbach, M., Saak, J., Schöbel, A., and Tabelow, K. 2022. “Die Mathematische Forschungsdateninitiative in der NFDI: MaRDI (Mathematical Research Data Initiative).” GAMM Rundbrief 1/2022: 40–43.
• Pirner, Marlies, and Warnecke, Sandra. 2022. “A review on a general multi-species BGK model: modelling, theory and numerics.” in From Kinetik Theory to Turbulence Modeling : The Legacy of Carlo Cercignani, Springer INdAM Series, edited by Paolo Barbante, Francesco Belgiorno, Silvia Lorenzani and Lorenzo Valdettaro. Singapur: Springer. doi: 10.1007/978-981-19-6462-6_17.
• Favre, Gianluca, Pirner, Marlies, and Schmeiser, Christian. 2022. “Thermalization of a rarefied gas with total energy conservation: existence, hypocoercivity, macroscopic limit.” Kinetic and Related Models 15 (5): 823–841. doi: 10.3934/krm.2022015.
• Haack, Jeff, Hauck, Cory, Klingenberg, Christian, Pirner, Marlies, and Warnecke, Sandra. 2022. “Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency.” Journal of Computational Physics 473 111729. doi: 10.1016/j.jcp.2022.111729.
• Keil, Tim. 2022. “Adaptive Reduced Basis Methods for Multiscale Problems and Large-scale PDE-constrained Optimization.” Dissertation thesis, WWU Münster. doi: 10.48550/arXiv.2211.09607.
• Lohmann, Julius, Schmitzer, Bernhard, and Wirth, Benedikt. 2022. “Duality in branched transport and urban planning.” Applied Mathematics and Optimization 86 45. doi: 10.1007/s00245-022-09927-3.
• Bruno, Stefano, Gess, Benjamin, and Weber, Hendrik. 2022. “Optimal regularity in time and space for stochastic porous medium equations.” Annals of Probability 50 (6): 2288–2343. doi: 10.1214/22-AOP1583.
• Gunaratnam, Trishen, Oh, Tadahiro, Tzvetkov, Nikolay, and Weber, Hendrik. 2022. “Quasi-invariant Gaussian measures for the nonlinear wave equation in three dimensions.” Probability and Mathematical Physics 3 (2): 343–379. doi: 10.2140/pmp.2022.3.343.
• Chandra, Ajay, Gunaratnam, Trishen S., and Weber, Hendrik. 2022. “Phase Transitions for ϕ^4_3.” Communications in Mathematical Physics 392: 691–782. doi: 10.1007/s00220-022-04353-6.
• Bonnefoi, Timothée, Chandra, Ajay, Moinat, Augustin, and Weber, Hendrik. 2022. “A priori bounds for rough differential equations with a non-linear damping term.” Journal of Differential Equations 318: 58–93. doi: 10.1016/j.jde.2022.02.006.
• Julia, Schleuß, and Kathrin, Smetana. 2022. “Optimal local approximation spaces for parabolic problems.” Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 20 (1). doi: 10.1137/20M1384294.
• Fritze, René, and Rave, Stephan. 2022. “Specification and Validation of Numerical Algorithms with the Gradual Contracts Pattern.” in Testing Software and Systems, Lecture Notes in Computer Science, edited by David Clark, Hector Menendez and Ana Rosa Cavalli. Cham: Springer International Publishing.
• Himpe, Christian, Grundel, Sara, and Benner, Peter. 2022. “Next-Gen Gas Network Simulation.” in Progress in Industrial Mathematics at ECMI 2021, Vol. 39 of Mathematics in Industry, edited by Matthias Ehrhardt and Michael Günther. Cham: Springer. doi: 10.1007/978-3-031-11818-0_15.
• Muratov, C.B., and Simon, T.M. 2022. Correction to: A Nonlocal Isoperimetric Problem with Dipolar Repulsion doi: 10.1007/s00220-022-04426-6.
• Stevens, Angela, and Winkler, Michael. 2022. “Taxis-driven persistent localization in a degenerate Keller-Segel system.” Communications in Partial Differential Equations 47 (12): 2341–2362. doi: 10.1080/03605302.2022.2122836.
• Luckhaus, Stephan, and Stevens, Angela. 2022. “Kermack and McKendrick Models on a Two-Scale Network and Connections to the Boltzmann Equations.” in Mathematics Going Forward. Lecture Notes in Mathematics, vol 2313, Lecture Notes in Mathematics, edited by Jean Michel Morel and Bernard Teissier. Cham: Springer. doi: 10.1007/978-3-031-12244-6_29.
• Cagnetti, Filippo, Dal Maso, Gianni, Scardia, Lucia, and Zeppieri, Caterina Ida. 2022. “A global method for deterministic and stochastic homogenisation in BV.” Annals of PDE 8 (1): 8–8. doi: 10.1007/s40818-022-00119-4.

Submitted / Under Review

• Fokina, D, Iliev, O, Toktaliev, P, Oseledets, I, and Schindler, F. 2022. “On the Performance of Machine Learning Methods for Breakthrough Curve Prediction.” arXiv [physics.flu-dyn] 2204.11719. doi: 10.48550/arXiv.2204.11719.
• Ranocha, H. 2022. A Note on Numerical Fluxes Conserving Harten's Entropies for the Compressible Euler Equations
• Singh, A, Thale, S, Leibner, T, Ricker, A, Nüsse, H, Klingauf, J, Ohlberger, M, and Matis, M. 2022. “Dynamic interplay of protrusive microtubule and contractile actomyosin forces drives tissue extension.” eLife 2022. doi: 10.1101/2022.06.21.496930.
• Ibragimov, Shokhrukh, Jentzen, Arnulf, Kröger, Timo, and Riekert, Adrian. 2022. “On the existence of infinitely many realization functions of non-global local minima in the training of artificial neural networks with ReLU activation.” Preprint. ArXiv doi: 10.48550/arXiv.2202.11481.
• Eberle, Simon, Jentzen, Arnulf, Riekert, Adrian, and Weiss, Georg. 2022. “Normalized gradient flow optimization in the training of ReLU artificial neural networks.” Preprint. ArXiv doi: 10.48550/arXiv.2207.06246.
• Freese, P, Hauck, M, Keil, T, and Peterseim, D. 2022. “A Super-Localized Generalized Finite Element Method.” Preprint. arXiv 2022 doi: 10.48550/arXiv.2211.09461.
• Fischer, J, Hensel, S, Laux, T, and Simon, T.M. 2022. “Local minimizers of the interface length functional based on a concept of local paired calibrations.” Preprint. arXiv doi: 10.48550/arXiv.2212.11840.
• Becker, S., Jentzen, A., and Müller, M. S.von Wurstemberger P. 2022. “Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing.” Preprint. arXiv.org
• Jentzen, A., Kröger, and T.. 2022. “On bounds for norms of reparameterized ReLU artificial neural network parameters: sums of fractional powers of the Lipschitz norm control the network parameter vector.” Preprint. arXiv.org
• Cheridito, P., Jentzen, A., and Rossmannek, F. 2022. “Gradient descent provably escapes saddle points in the training of shallow ReLU networks.” Preprint. arXiv.org
• Beck, C., Becker, S., Cheridito, P., Jentzen, A., and Neufeld, A. 2022. “An efficient Monte Carlo scheme for Zakai equations.” Preprint. arXiv.org
• Gallon, D., Jentzen, A., and Lindner, F. 2022. “Blow up phenomena for gradient descent optimization methods in the training of artificial neural networks.” Preprint. arXiv.org
• Ibragimov, S., Jentzen, A., and Riekert, A. 2022. “Convergence to good non-optimal critical points in the training of neural networks: Gradient descent optimization with one random initialization overcomes all bad non-global local minima with high probability.” Preprint. arXiv.org

2021

Published

• Schlichting, André, and Seis, Christian. 2021. “The Scharfetter–Gummel scheme for aggregation–diffusion equations.” IMA Journal of Numerical Analysis 42 (3): 2361–2402. doi: 10.1093/imanum/drab039.
• Eichenberg, C, and Schlichting, A. 2021. “Self-similar behavior of the exchange-driven growth model with product kernel.” Commun. Partial. Differ. Equ. 46 (3): 498–546. doi: 10.1080/03605302.2020.1845205.
• Esposito, A, Patacchini, F, Schlichting, A, and Slepčev, D. 2021. “Nonlocal-interaction equation on graphs: gradient flow structure and continuum limit.” Arch. Ration. Mech. Anal. 2021. doi: 10.1007/s00205-021-01631-w.
• Seis, Christian. 2021. “A note on the vanishing viscosity limit in the Yudovich class.” Canadian Mathematical Bulletin 64 (1): 112–122. doi: 10.4153/S0008439520000296.
• Bastian, P, Blatt, M, Dedner, A, Dreier, N, Engwer, C, Fritze, R, Gräser, C, Kempf, D, Klöfkorn, R, Ohlberger, M, and Sander, O. 2021. “The DUNE Framework: Basic Concepts and Recent Developments.” Computers & Mathematics with Applications 81: 75–112. doi: 10.1016/j.camwa.2020.06.007.
• Ceci, Stefano, and Seis, Christian. 2021. “Vortex dynamics for 2D Euler flows with unbounded vorticity.” Revista Matematica Iberoamericana 37 (5): 1969–1990. doi: 10.4171/rmi/1255.
• Buhr, Andreas, Iapichino, Laura, Ohlberger, Mario, Rave, Stephan, Schindler, Felix, and Smetana, Kathrin. 2021. “Localized model reduction for parameterized problems.” in Model Order Reduction: Volume 2 Snapshot-Based Methods and Algorithms, edited by P Benner, S Grivet-Talocia, A Quarteroni, G Rozza, W Schilders and L Sileira. doi: 10.1515/9783110671490-006.
• Streitbürger, Florian Engwer Christian, and May, Sandra Nüßing Andreas. 2021. “Monotonicity considerations for stabilized DG cut cell schemes for the unsteady advection equation.” contribution to the ENUMATH2019, Egmond aan Zee, The Netherlands
• Fehr, J, Himpe, C, Rave, S, and Saak, J. 2021. “Sustainable Research Software Hand-Over.” Journal of Open Research Software 9 (1). doi: 10.5334/jors.307/.
• Leibner, T, and Ohlberger, M. 2021. “A new entropy-variable-based discretization method for minimum entropy moment approximations of linear kinetic equations.” ESAIM: Mathematical Modelling and Numerical Analysis 55: 2567–2608.. doi: 10.1051/m2an/2021065.
• Nussenzveig, Lopes H. J., Seis, C, and Wiedemann, E. 2021. “On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity.” Nonlinearity 34 (5): 3112–3121.. doi: 10.1088/1361-6544/abe51f.
• Keil, T, Mechelli, L, Ohlberger, M, Schindler, F, and Volkwein, S. 2021. “A non-conforming dual approach for adaptive Trust-Region Reduced Basis approximation of PDE-constrained optimization.” ESAIM: Mathematical Modelling and Numerical Analysis 55: 1239–1269.. doi: 10.1051/m2an/2021019.
• Dreier, Nils-Arne, and Engwer, Christian. 2021. “Strategies for the vectorized Block Conjugate Gradients method.” contribution to the ENUMATH2019, Egmond aan Zee, The Netherlands
• Schlottke-Lakemper, M, Winters, AR, Ranocha, H, and Gassner, GJ. 2021. “A purely hyperbolic discontinuous Galerkin approach for self-gravitating gas dynamics.” Journal of Computational Physics 2021: 110467.. doi: 10.1016/j.jcp.2021.110467.
• Schrader, S, Westhoff, A, Piastra, MC, Miinalainen, T, Pursiainen, S, Vorwerk, J, Brinck, H, Wolters, CH, and Engwer, C. 2021. “DUNEuro- A software toolbox for forward modeling in bioelectromagnetism.” PloS one 2021. doi: 10.1371/journal.pone.0252431.
• Braunsmann, J, Rajkovic, M, Rumpf, M, and Wirth, B. 2021. “Learning low bending and low distortion manifold embeddings.” in 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), edited by The Computer Vision Foundation. -: Wiley-IEEE Press.
• Dirks, C, Striewski, P, Wirth, B, Aalto, A, and Olguin-Olguin, A. 2021. “A mathematical model for cell polarization in zebrafish primordial germ cells.” IMA Mathematical Medicine and Biology 38 (2): 218–254.
• Mitsotakis, Dimitrios, Ranocha, Hendrik, Ketcheson, David I, and Süli, Endre. 2021. “A conservative fully-discrete numerical method for the regularized shallow water wave equations.” SIAM Journal on Scientific Computing 42. doi: 10.1137/20M1364606.
• LeFloch, PG, and Ranocha, H. 2021. “Kinetic functions for nonclassical shocks, entropy stability, and discrete summation by parts.” Journal of Scientific Computing 87. doi: 10.1007/s10915-021-01463-6.
• Dreier, Nils-Arne. 2021. “Hardware-Oriented Krylov Methods for High-Performance Computing.” Dissertation thesis, WWU Münster. doi: 10.48550/arXiv.2104.02494.
• Ranocha, H, and Nordström, J. 2021. “A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions.” Journal of Scientific Computing 87. doi: 10.1007/s10915-021-01454-7.
• Ranocha, H, Mitsotakis, D, and Ketcheson, DI. 2021. “A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations.” Communications in Computational Physics 29 (4): 979–1029. doi: 10.4208/cicp.OA-2020-0119.
• Ranocha, H. 2021. “On Strong Stability of Explicit Runge-Kutta Methods for Nonlinear Semibounded Operators.” IMA Journal of Numerical Analysis 41 (1): 654–682. doi: 10.1093/imanum/drz070.
• Rojas, D, Boukharfane, R, Dalcin, L, Fernández, DCDR, Ranocha, H, Keyes, DE, and Parsani, M. 2021. “On the robustness and performance of entropy stable discontinuous collocation methods.” Journal of Computational Physics 426: 109891.. doi: 10.1016/j.jcp.2020.109891.
• Beck, C, Hutzenthaler, M, and Jentzen, A. 2021. “On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations.” Stochastics and Dynamics 21 (8): Paper No. 2150048, 68 pp... doi: 10.1142/S0219493721500489.
• Cheridito, P, Jentzen, A, and Rossmannek, F. 2021. “Non-convergence of stochastic gradient descent in the training of deep neural networks.” Journal of Complexity 64: Paper No. 101540, 10 pp...
• Andersson, A, Jentzen, A, and Kurniawan, R. 2021. “Existence, uniqueness, and regularity for stochastic evolution equations with irregular initial values.” Journal of Mathematical Analysis and Applications 495 (1): 124558, 33.. doi: 10.1016/j.jmaa.2020.124558.
• Jentzen, AKuckuck B, and Neufeld, Avon Wurstemberger P. 2021. “Strong error analysis for stochastic gradient descent optimization algorithms.” IMA Journal of Numerical Analysis 41 (1): 455–492. doi: 10.1093/imanum/drz055.
• Cox, S, Hutzenthaler, M, Jentzen, A, Neerven, J, and Welti, T. 2021. “Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensions.” IMA Journal of Numerical Analysis 41 (1): 493–548. doi: 10.1093/imanum/drz063.
• Clason, C, Lorenz, D, Mahler, H, and Wirth, B. 2021. “Entropic regularization of continuous optimal transport problems.” Journal of Mathematical Analysis and Applications 494 (1): 124432..
• Seis, Christian, and Winkler, Dominik. 2021. “A well-posedness result for a system of cross-diffusion equations.” Journal of Evolution Equations 21 (2): 2471–2489.. doi: 10.1007/s00028-021-00690-6.
• Jentzen, A, Salimova, D, and Welti, T. 2021. “A proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients.” Communications in Mathematical Sciences 19 (5): 1167–1205. doi: 10.4310/CMS.2021.v19.n5.a1.
• Jentzen, A, Lindner, F, and Pušnik, P. 2021. “Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noise.” Nonlinear Analysis: Theory, Methods and Applications 210: Paper No. 112310.. doi: 10.1016/j.na.2021.112310.
• Jentzen, A, and Kurniawan, R. 2021. “Weak convergence rates for Euler-type approximations of semilinear stochastic evolution equations with nonlinear diffusion coefficients.” Foundations of Computational Mathematics 21 (2): 445–536. doi: 10.1007/s10208-020-09448-x.
• Jentzen, A, Kuckuck, B, Müller-Gronbach, T, and Yaroslavtseva, L. 2021. “On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values.” Journal of Mathematical Analysis and Applications 502 (2): Paper No. 125240.. doi: 10.1016/j.jmaa.2021.125240.
• Jacobe de Naurois, Ladislas, Jentzen, Arnulf, and Welti, Timo. 2021. “Weak Convergence Rates for Spatial Spectral Galerkin Approximations of Semilinear Stochastic Wave Equations with Multiplicative Noise.” Applied Mathematics and Optimization 84 (suppl. 2): 1187–1217. doi: 10.1007/s00245-020-09744-6.
• E, W, Hutzenthaler, M, Jentzen, A, and Kruse, T. 2021. “Multilevel Picard iterations for solving smooth semilinear parabolic heat equations.” SN Partial Differential Equations and Applications 2 (6): Paper No. 80.. doi: 10.1007/s42985-021-00089-5.
• Becker, S, Cheridito, P, Jentzen, A, and Welti, T. 2021. “Solving high-dimensional optimal stopping problems using deep learning.” European Journal of Applied Mathematics 32 (3): 470–514. doi: 10.1017/S0956792521000073.
• Beck, C, Gonon, L, Hutzenthaler, M, and Jentzen, A. 2021. “On existence and uniqueness properties for solutions of stochastic fixed point equations.” Discrete and Continuous Dynamical Systems - Series B 26 (9): 4927–4962. doi: 10.3934/dcdsb.2020320.
• Beck, C, Becker, S, Grohs, P, Jaafari, N, and Jentzen, A. 2021. “Solving the Kolmogorov PDE by means of deep learning.” Journal of Scientific Computing 88 (3): Paper No. 73.. doi: 10.1007/s10915-021-01590-0.
• Beck, C, Becker, S, Cheridito, P, Jentzen, A, and Neufeld, A. 2021. “Deep splitting method for parabolic PDEs.” SIAM Journal on Scientific Computing 43 (5): A3135–A3154.. doi: 10.1137/19M1297919.
• Clason, C, Tameling, C, and Wirth, B. 2021. “Convex relaxation of discrete vector-valued optimization problems.” SIAM Review 63 (4): 783–821.
• Hardering, H, and Wirth, B. 2021. “Quartic Lp-convergence of cubic Riemannian splines.” IMA Journal of Numerical Analysis 42 (4): 3360–3385. doi: 10.1093/imanum/drab077.
• Ranocha, H, Dalcin, L, Parsani, M, and Ketcheson, DI. 2021. “Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics.” Communications on Applied Mathematics and Computation 2021. doi: 10.1007/s42967-021-00159-w.
• Himpe, C. 2021. “Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms.” in Model Reduction of Complex Dynamical Systems, Vol. 171 of International Series of Numerical Mathematics, edited by P Benner, T Breiten, H Faßbender, M Hinze, T Stykel and R Zimmermann. doi: 10.1007/978-3-030-72983-7_7.
• Himpe, C, Grundel, S, and Benner, P. 2021. “Model Order Reduction for Gas and Energy Networks.” Journal of Mathematics in Industry 11: 13.. doi: 10.1186/s13362-021-00109-4.
• Clees, T, Baldin, A, Benner, P, Grundel, S, Himpe, C, Klaassen, B, Küsters, F, Marheineke, N, Nikitina, L, Nikitin, I, Pade, J, Stahl, N, Strohm, C, Tischendorf, C, and Wirsen, A. 2021. “MathEnergy – Mathematical Key Technologies for Evolving Energy Grids.” in Mathematical Modeling, Simulation and Optimization for Power Engineering and Management, Vol. 34 of Mathematics in Industry, edited by S Göttlich, M Herty and A Milde. doi: 10.1007/978-3-030-62732-4_11.
• Nüßlein, S, Ranocha, H, and Ketcheson, DI. 2021. “Positivity-Preserving Adaptive Runge-Kutta Methods.” Communications in Applied Mathematics and Computational Science 16 (2): 155–179. doi: 10.2140/camcos.2021.16.155.
• Ranocha, H, Luna, M, and Ketcheson, DI. 2021. “On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations.” Partial Differential Equations and Applications 2 (6): 76.. doi: 10.1007/s42985-021-00126-3.
• Simon, and T.M.. 2021. “Quantitative aspects of the rigidity of branching microstructures in shape memory alloys via H-measures.” SIAM Journal on Mathematical Analysis 53 (4). doi: 10.1137/18M1220017.
• Simon, and T.M.. 2021. “Rigidity of branching microstructures in shape memory alloys.” Archive for Rational Mechanics and Analysis 241: 1707–1783. doi: 10.1007/s00205-021-01679-8.
• Bernand-Mantel, A., Muratov, C.B., and Simon, T.M. 2021. “A quantitative description of skyrmions in ultrathin ferromagnetic films and rigidity of degree ±1 harmonic maps from from R² to S².” Archive for Rational Mechanics and Analysis 239: 219–299. doi: 10.1007/s00205-020-01575-7.
• Ranocha, H. 2021. “SummationByPartsOperators.jl: A Julia library of provably stable semidiscretization techniques with mimetic properties.” Journal of Open Source Software 6 (64): 3454.. doi: 10.21105/joss.03454.
• Ranocha, H, and Gassner, GJ. 2021. “Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes.” Communications on Applied Mathematics and Computation 2021. doi: 10.1007/s42967-021-00148-z.
• Ostaszewski, K, Glassmeier, K, Goetz, C, Heinisch, P, Henri, P, Park, SA, Ranocha, H, Richter, I, Rubin, M, and Tsurutani, B. 2021. “Steepening of magnetosonic waves in the inner coma of comet 67P/Churyumov-Gerasimenko.” Annales Geophysicae 39 (4): 721–742. doi: 10.5194/angeo-39-721-2021.
• Brunken, Julia. 2021. “Stable and efficient Petrov-Galerkin methods for certain (kinetic) transport equations.” Dissertation thesis, Universität Münster.
• Pirner, Marlies. 2021. “On multi-species BGK models with velocity dependent collision frequencies.” in Small Collaboration: Modeling Phenomena from Nature by Hyperbolic Partial Differential Equations (hybridmeeting), Vol. 19 of Oberwolfach Report, edited by Christian Klingenberg, Qin Li and Marlies Pirner. Oberwolfach: Mathematisches Forschungsinstitut Oberwolfach. doi: 10.4171/OWR/2021/19.
• Bae, Gi-Chan, Klingenberg, Christian, Pirner, Marlies, and Yun, Seok-Bae. 2021. “BGK model of the multi-species Uehling Uhlenbeck equation.” Kinetic and Related Models 14 (1): 25–44. doi: 10.3934/krm.2020047.
• Haack, Jeff, Hauck, Cory, Klingenberg, Christian, Pirner, Marlies, and Warnecke, Sandra. 2021. “A consistent BGK model with velocity-dependent collision frequency for gas mixtures.” Journal of Statistical Physics 184 (3) 31. doi: 10.1007/s10955-021-02821-2.
• Pirner, Marlies. 2021. “A review on BGK models for gas mixtures of mono and polyatomic molecules.” Fluids 6 (11) 393. doi: 10.3390/fluids6110393.
• Scheel, Arnd, Stevens, Angela, and Tenbrock, Christoph. 2021. “Signaling gradients in surface dynamics as basis for planarian regeneration.” Journal of Mathematical Biology 83 (6). doi: 10.1007/s00285-021-01627-w.
• Scheel, Arnd, and Stevens, Angela. 2021. “Regeneration of Tissue: Lessons Learned from Flatworms.” SIAM News Blog
• Cicalese, M; Focardi, M.; Zeppieri, C.I.. 2021. “Phase-Field Approximation of Functionals Defined on Piecewise-Rigid Maps.” Journal of Nonlinear Science 31 (78).

accepted / in Press (not yet published)

• Beneventano, P, Cheridito, P, Graeber, R, Jentzen, A, and Kuckuck, B. in Kürze. “Deep neural network approximation theory for high-dimensional functions.” Sampling Theory in Signal and Image Processing.
• Cox, S, Hutzenthaler, M, and Jentzen, A. in Kürze. “Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations.” Memoirs of the American Mathematical Society.

Submitted / Under Review

• Jentzen, A, and Kröger, T. 2021. “Convergence rates for gradient descent in the training of overparameterized artificial neural networks with biases.” arXiv.
• Hutzenthaler, M, Jentzen, A, Pohl, K, Riekert, A, and Scarpa, L. 2021. “Convergence proof for stochastic gradient descent in the training of deep neural networks with ReLU activation for constant target functions.” arXiv.
• Hutzenthaler, M, Jentzen, A, Kuckuck, B, and Padgett, JL. 2021. “Strong $L^p$-error analysis of nonlinear Monte Carlo approximations for high-dimensional semilinear partial differential equations.” arXiv.
• Beck, C, Hutzenthaler, M, Jentzen, A, and Magnani, E. 2021. “Full history recursive multilevel Picard approximations for ordinary differential equations with expectations.” arXiv.
• Esposito, A, Gvalani, RS, Schlichting, A, and Schmidtchen, M. 2021. “On a novel gradient flow structure for the aggregation equation.” Preprint. arXiv doi: 10.48550/arXiv.2112.08317.
• Ranocha, H, Schlottke-Lakemper, M, Chan, J, Rueda-Ramírez, AM, Winters, AR, Hindenlang, F, and Gassner, GJ. 2021. Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws
• Ketcheson, DI, and Ranocha, H. 2021. Computing with B-series
• Torlo, D, Öffner, P, and Ranocha, H. 2021. A New Stability Approach for Positivity-Preserving Patankar-type Schemes
• Leibner, T, Matis, M, Ohlberger, M, and Rave, S. 2021. “Distributed model order reduction of a model for microtubule-based cell polarization using HAPOD.” arXiv [math.NA] 2111.00129.

2020

Published

• Hellman, Fredrik, Keil, Tim, and Målqvist, Axel. 2020. “Numerical Upscaling of Perturbed Diffusion Problems.” SIAM Journal on Scientific Computing 2020 (Volume 42, Issue 4): A2014–A2036.. doi: 10.1137/19M1278211.
• Bach, A, and Sommer, L. 2020. “A Gamma-convergence result for fluid-filled fracture propagationDO - 10.1051/m2an/2020016.” ESAIM: Mathematical Modelling and Numerical Analysis 54 (3). doi: 10.1051/m2an/2020016.
• Friedrich, M, and Stefanelli, U. 2020. “Ripples in graphene: A variational approach.” Comm. Math. Phys. 379.
• Friedrich, M, and Stefanelli, U. 2020. “Crystallization in a one-dimensional periodic landscape.” J. Stat.Phys. 179.
• Crismale, V, and Friedrich, M. 2020. “Equilibrium configurations for epitaxially strained films and material voids in three-dimensional linear elasticity.” Arch. Ration. Mech. Anal. 237.
• Heeren, B, Rumpf, M, Wardetzky, M, and Wirth, B. 2020. “Discrete Riemannian calculus on shell space.” in Geometric Partial Differential Equations - Part I, Vol. 21 of Handbook of Numerical Analysis, edited by A Bonito and RH Nochetto. Elsevier. doi: 10.1016/bs.hna.2019.06.005.
• Böttcher, U, and Wirth, B. 2020. “Convex Lifting-Type Methods for Curvature Regularization.” in Handbook of Variational Methods for Nonlinear Geometric Data, edited by P Grohs, M Holler and A Weinmann. Cham: Springer International Publishing. doi: 10.1007/978-3-030-31351-7_7.
• Schmitzer, B, Schäfers, KP, and Wirth, B. 2020. “Dynamic Cell Imaging in PET With Optimal Transport Regularization.” IEEE Transactions on Medical Imaging 39 (5): 1626–1635. doi: 10.1109/TMI.2019.2953773.
• Ferrari, L, Dirks, C, and Wirth, B. 2020. “Phase field approximations of branched transportation problems.” Calculus of Variations and Partial Differential Equations 59 (1): Paper No. 37, 34.. doi: 10.1007/s00526-019-1680-3.
• Wirth, B. 2020. “Green's function for the Neumann-Poisson problem on n-dimensional balls.” American Mathematical Monthly 127 (8): 737–743.
• Jentzen, Avon Wurstemberger P. 2020. “Lower error bounds for the stochastic gradient descent optimization algorithm: Sharp convergence rates for slowly and fast decaying learning rates.” Journal of Complexity 57: 101438.. doi: 10.1016/j.jco.2019.101438.
• Bastian, P, Altenbernd, M, Dreier, N, Engwer, C, Fahlke, J, Fritze, R, Geveler, M, Göddeke, D, Iliev, O, Ippisch, O, Mohring, J, Müthing, S, Ohlberger, M, Ribbrock, D, Shegunov, N, and Turek, S. 2020. “Exa-Dune -- Flexible PDE Solvers, Numerical Methods and Applications.” in Software for Exascale Computing - SPPEXA 2016-2019, Vol. 136 of LNCSE, edited by Hans-Joachim Bungartz, Severin. Uekermann Benjamin Reiz, Philipp Neumann and Wolfgang E Nagel. Cham: Springer International Publishing. doi: 10.1007/978-3-030-47956-5_9.
• Davoli, E, and Friedrich, M. 2020. “Two-well rigidity and multidimensional sharp-interface limits for Solid-Solid phase transitions.” Calc. Var. PDE 59.
• Friedrich, M, and Kreutz, L. 2020. “Finite crystallization and Wulff shape emergence for ionic compounds in the square lattice.” Nonlinearity 33.
• Friedrich, M, and F., Solombrino F. 2020. “Functionals defined on piecewise rigid functions: Integral representation and Gamma-convergence.” Arch. Ration. Mech. Anal. 236.
• Seis, Christian. 2020. “On the Littlewood-Paley spectrum for passive scalar transport equations.” Journal of Nonlinear Science 30 (2): 645–656. doi: 10.1007/s00332-019-09585-w.
• Ohlberger, Mario, Schweizer, Ben, Urban, Maik, and Verfürth, Barbara. 2020. “Mathematical analysis of transmission properties of electromagnetic meta-materials.” Networks and Heterogeneous Media 15 (1): 29–56. doi: 10.3934/nhm.2020002.
• Buchfink, P, Haasdonk, B, and Rave, S. 2020. “PSD-Greedy Basis Generation for Structure-Preserving Model Order Reduction of Hamiltonian Systems.” contribution to the ALGORITMY 2020, Vysoké Tatry
• Schlichting, André. 2020. “The exchange-driven growth model: basic properties and longtime behavior.” Journal of Nonlinear Science 30 (3): 793–830. doi: 10.1007/s00332-019-09592-x.
• Gvalani, RS, and Schlichting, A. 2020. “Barriers of the McKean–Vlasov energy via a mountain pass theorem in the space of probability measures.” Journal of Functional Analysis 279 (11): 108720.. doi: 10.1016/j.jfa.2020.108720.
• Erbar, Matthias, Fathi, Max, and Schlichting, André. 2020. “Entropic curvature and convergence to equilibrium for mean-field dynamics on discrete spaces.” Latin American Journal of Probability and Mathematical Statistics 17 (1): 445–471. doi: 10.30757/alea.v17-18.
• Anzt, H, Bach, F, Druskat, S, Löffler, F, Loewe, A, Renard, B, Seemann, G, Struck, A, Achhammer, E, Aggarwal, P, Appel, F, Bader, M, Brusch, L, Busse, C, Chourdakis, G, Dabrowski, P, Ebert, P, Flemisch, B, Friedl, S, Fritzsch, B, Funk, M, Gast, V, Goth, F, Grad, J, Hermann, S, Hohmann, F, Janosch, S, Kutra, D, Linxweiler, J, Muth, T, Peters-Kottig, W, Rack, F, Raters, F, Rave, S, Reina, G, Reißig, M, Ropinski, T, Schaarschmidt, J, Seibold, H, Thiele, J, Uekermann, B, Unger, S, and Weeber, R. 2020. “An environment for sustainable research software in Germany and beyond: current state, open challenges, and call for action.” F1000Research 9 (295). doi: 10.12688/f1000research.23224.1.
• Schneider, Florian Leibner Tobias. 2020. “First-order continuous- and discontinuous-Galerkin moment models for a linear kinetic equation: Model derivation and realizability theory.” Journal of Computational Physics 416: 109547.. doi: 10.1016/j.jcp.2020.109547.
• Heeren, B, Paulus, S, Goldbach, H, Kuhlmann, H, Mahlein, A-K, Rumpf, M, and Wirth, B. 2020. “Statistical shape analysis of tap roots: a methodological case study on laser scanned sugar beets.” BMC Bioinformatics 21 (335).
• Abgrall, R, Mélédo, El, Öffner, P, and Ranocha, H. 2020. “Error Boundedness of Correction Procedure via Reconstruction/Flux Reconstruction and the Connection to Residual Distribution Schemes.” in Hyperbolic Problems: Theory, Numerics, Applications, Vol. 10 of AIMS on Applied Mathematics, edited by A Bressan, M Lewicka, D Wang and Y Zheng. Springfield: Springer.
• Heinisch, P, Ostaszewski, K, and Ranocha, H. 2020. “Towards Green Computing: A Survey of Performance and Energy Efficiency of Different Platforms using OpenCL.” in Proceedings of the International Workshop on OpenCL, IWOCL '20, April 2020, Munich (Germany) New York, NY, USA: ACM Press. doi: 10.1145/3388333.3403035.
• Ranocha, H. 2020. “Entropy Conserving and Kinetic Energy Preserving Numerical Methods for the Euler Equations Using Summation-by-Parts Operators.” in Spectral and High Order Methods for Partial Differential Equations {ICOSAHOM} 2018, Vol. 134 of Lecture Notes in Computational Science and Engineering, edited by SJ Sherwin, D Moxey, J Peiró, PE Vincent and C Schwab. Cham: Springer. doi: 10.1007/978-3-030-39647-3_42.
• Ranocha, H, Ostaszewski, K, and Heinisch, P. 2020. “Discrete Vector Calculus and Helmholtz Hodge Decomposition for Classical Finite Difference Summation by Parts Operators.” Communications on Applied Mathematics and Computation 2: 581–611. doi: 10.1007/s42967-019-00057-2.
• Ranocha, H, Sayyari, M, Dalcin, L, Parsani, M, and Ketcheson, DI. 2020. “Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations.” SIAM Journal on Scientific Computing 42 (2): A612–A638.. doi: 10.1137/19M1263480.
• Öffner, P, Glaubitz, J, and Ranocha, H. 2020. “Analysis of Artificial Dissipation of Explicit and Implicit Time-Integration Methods.” International Journal of Numerical Analysis and Modeling 17 (3): 332–349.
• Ranocha, H, and Ketcheson, DI. 2020. “Relaxation Runge-Kutta Methods for Hamiltonian Problems.” Journal of Scientific Computing 84 (1). doi: 10.1007/s10915-020-01277-y.
• Ranocha, H, Dalcin, L, and Parsani, M. 2020. “Fully-Discrete Explicit Locally Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations.” Computers and Mathematics with Applications 80 (5): 1343–1359. doi: 10.1016/j.camwa.2020.06.016.
• Ranocha, H, Lóczi, L, and Ketcheson, DI. 2020. “General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes.” Numerische Mathematik 146. doi: 10.1007/s00211-020-01158-4.
• Ketcheson, DI, Parsani, M, Grant, ZJ, Ahmadia, A, and Ranocha, H. 2020. “RK-Opt: A package for the design of numerical ODE solvers.” Journal of Open Source Software 5 (54): 2514.. doi: 10.21105/joss.02514.
• Ranocha, H, and Ketcheson, DI. 2020. “Energy Stability of Explicit Runge-Kutta Methods for Nonautonomous or Nonlinear Problems.” SIAM Journal on Numerical Analysis 58 (6): 3382–3405. doi: 10.1137/19M1290346.
• Ketcheson, DI, Ranocha, H, Parsani, M, Waheed, U, and Hadjimichael, Y. 2020. “NodePy: A package for the analysis of numerical ODE solvers.” Journal of Open Source Software 5 (55): 2515.. doi: 10.21105/joss.02515.
• Hutzenthaler, M, Jentzen, A, Kruse, T, and Nguyen, TA. 2020. “A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations.” SN Partial Differential Equations and Applications 1 (2) 10. doi: 10.1007/s42985-019-0006-9.
• Becker, S, Cheridito, P, and Jentzen, A. 2020. “Pricing and Hedging American-Style Options with Deep Learning.” Journal of Risk and Financial Management 13 (7) 158. doi: 10.3390/jrfm13070158.
• Fehrman, B, Gess, B, and Jentzen, A. 2020. “Convergence rates for the stochastic gradient descent method for non-convex objective functions.” Journal of Machine Learning Research 21: Paper No. 136, 48..
• Jentzen, A, and Pušnik, P. 2020. “Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities.” IMA Journal of Numerical Analysis 40 (2): 1005–1050. doi: 10.1093/imanum/drz009.
• Berner, J, Grohs, P, and Jentzen, A. 2020. “Analysis of the generalization error: empirical risk minimization over deep artificial neural networks overcomes the curse of dimensionality in the numerical approximation of Black-Scholes partial differential equations.” SIAM Journal on Mathematics of Data Science 2 (3): 631–657. doi: 10.1137/19M125649X.
• Hutzenthaler, M., Jentzen, A., and von Wurstemberger, P. 2020. “Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks.” Electronic Journal of Probability 25: Paper No. 101, 73.. doi: 10.1214/20-EJP423.
• Becker, S, Gess, B, Jentzen, A, and Kloeden, PE. 2020. “Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations.” BIT Numerical Mathematics 60 (4): 1057–1073. doi: 10.1007/s10543-020-00807-2.
• Becker, S, Braunwarth, R, Hutzenthaler, M, Jentzen, A, and von, Wurstemberger P. 2020. “Numerical simulations for full history recursive multilevel Picard approximations for systems of high-dimensional partial differential equations.” Communications in Computational Physics 28 (5): 2109–2138. doi: 10.4208/cicp.oa-2020-0130.
• Jentzen, A, Lindner, F, and Pušnik, P. 2020. “Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions.” Numerical Algorithms 85 (4): 1447–1473. doi: 10.1007/s11075-019-00871-y.
• Beck, C, Hornung, F, Hutzenthaler, M, Jentzen, A, and Kruse, T. 2020. “Overcoming the curse of dimensionality in the numerical approximation of Allen-Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations.” Journal of Numerical Mathematics 28 (4): 197–222. doi: 10.1515/jnma-2019-0074.
• Hutzenthaler, M, Jentzen, A, Kruse, T, Nguyen, TA, and von, Wurstemberger P. 2020. “Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 (2244): 630–654. doi: 10.1098/rspa.2019.0630.
• Hutzenthaler, M, and Jentzen, A. 2020. “On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients.” Annals of Probability 48 (1): 53–93. doi: 10.1214/19-AOP1345.
• Repple, J, Mauritz, M, Meinert, S, de, Lange SC, Grotegerd, D, Opel, N, Redlich, R, Hahn, T, Förster, K, Leehr, EJ, Winter, N, Goltermann, J, Enneking, V, Fingas, SM, Lemke, H, Waltemate, L, Nenadic, I, Krug, A, Brosch, K, Schmitt, S, Stein, F, Meller, T, Jansen, A, Steinsträter, O, Baune, BT, Kircher, T, Dannlowski, U*, and van, den Heuvel MP* (*equal contribution). 2020. “Severity of current depression and remission status are associated with structural connectome alterations in major depressive disorder.” Molecular Psychiatry 25. doi: 10.1038/s41380-019-0603-1.
• Fischer, J., Laux, T., and Simon, T.M. 2020. “Convergence rates of the Allen-Cahn equation to mean curvature flow: A short proof based on relative entropies.” SIAM Journal on Mathematical Analysis 52 (6): 6222–6233. doi: 10.1137/20M1322182.
• Bernand-Mantel, A., Muratov, C.B., and Simon, T.M. 2020. “Unraveling the role of dipolar vs. Dzyaloshinskii-Moriya interaction in stabilizing compact magnetic skyrmions.” Physical Review B 101 (4) 045416. doi: 10.1103/PhysRevB.101.045416.
• Crestetto, Anais, Klingenberg, Christian, and Pirner, Marlies. 2020. “Kinetic/fluid micro-macro numerical scheme for a two component gas mixture.” Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal 18 (2). doi: 10.1137/17M1141023.
• Moinat, Augustin, and Weber, Hendrik. 2020. “Space-time localisation for the dynamic Phi-4/3 model.” Communications on Pure and Applied Mathematics 73 (12): 2519–2555. doi: 10.1002/cpa.21925.
• Tsatsoulis, Pavlos, and Weber, Hendrik. 2020. “Exponential loss of memory for the 2-dimensional Allen–Cahn equation with small noise.” Probability Theory and Related Fields 177: 257–322. doi: 10.1007/s00440-019-00945-x.
• Moinat, Augustin, and Weber, Hendrik. 2020. “Local bounds for stochastic reaction diffusion equations.” Electronic Journal of Probability 25: 1–26. doi: 10.1214/19-EJP397.
• Hilhorst, Danielle, Matano, Hiroshi, Nguyen, Thanh Nam, and Weber, Hendrik. 2020. “Generation of Interface for Solutions of the Mass Conserved Allen--Cahn Equation.” SIAM Journal on Mathematical Analysis 52 (3): 2624–2654. doi: 10.1137/18M1204747.
• Kaib, Gunnar, Kang, Kyungkeun, and Stevens, Angela. 2020. “Global minimisers for anisotropic attractive-repulsive interactions.” European Journal of Applied Mathematics 31 (5): 854–870. doi: 10.1017/S0956792519000299.
• Bach, A; Braides, A.; Zeppieri, C.I.. 2020. “Quantitative analysis of finite-difference approximations of free-discontinuity problems.” Interfaces and Free Boundaries 22. doi: 10.4171/IFB/443.
• Zeppieri, C.I.. 2020. “Homogenisation of high-contrast brittle materials.” Mathematics in Engineering 2 (1).