Research reports

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Nr.	PDF	Authors and Title
2019-69	PDFfile_download	Y. Maday and C. Marcati Analyticity and hp discontinuous Galerkin approximation of nonlinear Schrödinger eigenproblems
2019-68	PDFfile_download	C. Marcati and M. Rakhuba and Ch. Schwab Tensor Rank bounds for Point Singularities in R³
2019-67	PDFfile_download	R. Alaifari and M. Wellershoff Stability estimates for phase retrieval from discrete Gabor measurements Revised 1: November 2020
2019-66	PDFfile_download	R. Alaifari and I. Daubechies and Ph. Grohs and R. Yin Stable Phase Retrieval in Infinite Dimensions
2019-65	PDFfile_download	R. Alaifari and X. Cheng and L.B. Pierce and S. Steinerberger On Matrix Rearrangement Inequalities
2019-64	PDFfile_download	P. Cheridito and A. Jentzen and F. Rossmannek Efficient approximation of high-dimensional functions with deep neural networks
2019-63	PDFfile_download	M. Hutzenthaler and A. Jentzen and Th. Kruse Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities Revised 1: January 2020
2019-62	PDFfile_download	D. Casati and R. Hiptmair and J. Smajic Coupling Finite Elements and Auxiliary Sources for Electromagnetic Wave Propagation Revised 1: May 2020
2019-61	PDFfile_download	L. Gonon and Ph. Grohs and A. Jentzen and D. Kofler and D. Šiška Uniform error estimates for artificial neural network approximations for heat equations
2019-60	PDFfile_download	S. Becker and P. Cheridito and A. Jentzen and T. Welti Solving high-dimensional optimal stopping problems using deep learning
2019-59	PDFfile_download	M. Giles and A. Jentzen and T. Welti Generalised multilevel Picard approximations
2019-58	PDFfile_download	M. Hutzenthaler and A. Jentzen and F. Lindner and P. Pušnik Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations
2019-57	PDFfile_download	Ch. Beck and A. Jentzen and B. Kuckuck Full error analysis for the training of deep neural networks
2019-56	PDFfile_download	T. S. Koltukluoglu Fourier Spectral Dynamic Data Assimilation: Interlacing CFD with 4D Flow MRI
2019-55	PDFfile_download	T. S. Koltukluoglu and G. Cvijetic and R. Hiptmair Harmonic Balance Techniques in Cardiovascular Fluid Mechanics
2019-54	PDFfile_download	K. Lye and S. Mishra and R. Molinaro A Multi-level procedure for enhancing accuracy of machine learning algorithms
2019-53	PDFfile_download	S. Mazzonetto and D. Salimova Existence, uniqueness, and numerical approximations for stochastic Burgers equations Revised 1: September 2019
2019-52	PDFfile_download	Y. Liu and W. Ren and H. Ammari Robust reconstruction of fluorescence molecular tomography with an optimized illumination pattern
2019-51	PDFfile_download	S. Lanthaler and S. Mishra and C. Parés-Pulido Statistical solutions of the incompressible Euler equations
2019-50	PDFfile_download	Ph. Grohs and A. Jentzen and D. Salimova Deep neural network approximations for Monte Carlo algorithms
2019-49	PDFfile_download	A. Jentzen and F. Lindner and P. Pušnik Spatial Sobolev regularity for stochastic Burgers equations with additive trace class noise
2019-48	PDFfile_download	Ph. Grohs and F. Hornung and A. Jentzen and Ph. Zimmermann Space-time error estimates for deep neural network approximations for differential equations
2019-47	PDFfile_download	Ch. Beck and L. Gonon and M. Hutzenthaler and A. Jentzen On existence and uniqueness properties for solutions of stochastic fixed point equations
2019-46	PDFfile_download	M. Hutzenthaler and A. Jentzen and Th. Kruse and T. Nguyen and Ph. von Wurstemberger Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equations
2019-45	PDFfile_download	D. Casati and R. Hiptmair Coupling FEM with a Multiple-Subdomain Trefftz Method Revised 1: January 2020
2019-44	PDFfile_download	R. Hiptmair and C. Urzua-Torres Preconditioning the EFIE on Screens
2019-43	PDFfile_download	F. Henriquez and Ch. Schwab Shape Holomorphy of the Calderón Projector for the Laplacean in R2
2019-42	PDFfile_download	M. Hutzenthaler and A. Jentzen and Ph. von Wurstemberger Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risks
2019-41	PDFfile_download	L. Herrmann and M. Keller and Ch. Schwab Quasi-Monte Carlo Bayesian estimation under Besov priors in elliptic inverse problems
2019-40	PDFfile_download	Ch. Beck and F. Hornung and M. Hutzenthaler and A. Jentzen and Th. Kruse Overcoming the curse of dimensionality in the numerical approximation of Allen--Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations
2019-39	PDFfile_download	Ch. Beck and S. Becker and P. Cheridito and A. Jentzen and A. Neufeld Deep splitting method for parabolic PDEs
2019-38	PDFfile_download	H. Ammari and B. Li and J. Zou Mathematical analysis of electromagnetic plasmonic metasurfaces
2019-37	PDFfile_download	H. Ammari and K. Imeri and N. Nigam Optimization of Steklov-Neumann eigenvalues
2019-36	PDFfile_download	S. Blanes and V. Gradinaru High Order Efficient Splittings for the SemiclassicalTime–Dependent Schrödinger Equation Revised 1: December 2019
2019-35	PDFfile_download	J. A. A. Opschoor and Ch. Schwab and J. Zech Exponential ReLU DNN expression of holomorphic maps in high dimension Revised 1: August 2020 Revised 2: May 2021
2019-34	PDFfile_download	H. Ammari and O. Bruno and K. Imeri and N. Nigam Wave Enhancement through Optimization of Boundary Conditions
2019-33	PDFfile_download	D. Casati and J. Smajic and R. Hiptmair H-$\Phi$ Field Formulation with Lumped Sources and Unbounded Domains Revised 1: October 2019
2019-32	PDFfile_download	L. Herrmann and K. Kirchner and Ch. Schwab Multilevel approximation of Gaussian random fields: fast simulation Revised 1: October 2019
2019-31	PDFfile_download	H. Ammari and B. Davies and E.O. Hiltunen and S. Yu Topologically protected edge modes in one-dimensional chains of subwavelength resonators
2019-30	PDFfile_download	M. Rakhuba Robust alternating direction implicit solver in quantized tensor formats for a three-dimensional elliptic PDE Revised 1: July 2020
2019-29	PDFfile_download	H. Gietler and H. Ammari and H. Zangl Electromagnetic Near-Field based Pose Estimation for Autonomous Systems Revised 1: June 2019
2019-28	PDFfile_download	U. S. Fjordholm and K. Lye and S. Mishra and F. Weber Statistical solutions of hyperbolic systems of conservation laws: numerical approximation
2019-27	PDFfile_download	S. Mishra and C. Parés-Pulido and K. Pressel Arbitrarily high-order (weighted) essentially non-oscillatory finite difference schemes for anelastic flows on staggered meshes Revised 1: July 2020 Revised 2: October 2020
2019-26	PDFfile_download	J. Berner and D. Elbrächter and P. Grohs and A. Jentzen Towards a regularity theory for ReLU networks -- chain rule and global error estimates
2019-25	PDFfile_download	H. Ammari and M. Putinar and A. Steenkamp and F. Triki Reconstruction of domains with algebraic boundaries from generalized polarization tensors
2019-24	PDFfile_download	A. Jentzen and B. Kuckuck and T. Müller-Gronbach and L. Yaroslavtseva On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values
2019-23	PDFfile_download	S. G. Cox and K. Kirchner Regularity and convergence analysis in Sobolev and Hölder spaces for generalized Whittle-Matérn fields
2019-22	PDFfile_download	H. Ammari and E. Orvehed Hiltunen and S. Yu Subwavelength guided modes for acoustic waves in bubbly crystals with a line defect
2019-21	PDFfile_download	B. Fehrman and B. Gess and A. Jentzen Convergence rates for the stochastic gradient descent method for non-convex objective functions
2019-20	PDFfile_download	H. Ammari and B. Davies Modelling the active cochlea as a fully-coupled system of subwavelength Hopf resonators Revised 1: April 2019
2019-19	PDFfile_download	D. Casati and L. Codecasa and R. Hiptmair and F. Moro Trefftz Co-chain Calculus Revised 1: August 2019
2019-18	PDFfile_download	R. Hiptmair and C. Pechstein Regular Decompositions of Vector Fields - Continuous, Discrete, and Structure-Preserving
2019-17	PDFfile_download	S. Lanthaler and S. Mishra On the convergence of the spectral viscosity method for the incompressible Euler equations with rough initial data
2019-16	PDFfile_download	L. Baldassari Time-Dependent Polarization Tensors: Derivation of Asymptotic Expansions for the Transient Wave Equation
2019-15	PDFfile_download	M. Beccari and M. Hutzenthaler and A. Jentzen and R. Kurniawan and F. Lindner and D. Salimova Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearities
2019-14	PDFfile_download	A. Scapin Electrocommunication for weakly electric fish
2019-13	PDFfile_download	K. Lye and S. Mishra and R. Deep Deep learning observables in computational fluid dynamics Revised 1: March 2019 Revised 2: December 2019
2019-12	PDFfile_download	C. Marcati and Ch. Schwab Analytic Regularity for the incompressible Navier-Stokes Equations in polygons Revised 1: April 2020
2019-11	PDFfile_download	H. Ammari and A. Dabrowski and B. Fitzpatrick and P. Millien and M. Sini Subwavelength resonant dielectric nanoparticles with high refractive indices
2019-10	PDFfile_download	M. Hutzenthaler and A. Jentzen and Th. Kruse and T. A. Nguyen A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
2019-09	PDFfile_download	H. Ammari and B. Davies A fully-coupled subwavelength resonance approach to modelling the passive cochlea Revised 1: March 2019
2019-08	PDFfile_download	S. Cox and A. Jentzen and F. Lindner Weak convergence rates for temporal numerical approximations of stochastic wave equations with multiplicative noise
2019-07	PDFfile_download	J. A. A. Opschoor and P. C. Petersen and Ch. Schwab Deep ReLU Networks and High-Order Finite Element Methods Revised 1: September 2019 Revised 2: December 2019
2019-06	PDFfile_download	L. Herrmann and Ch. Schwab Multilevel quasi-Monte Carlo uncertainty quantification for advection-diffusion-reaction Revised 1: June 2019 Revised 2: March 2021
2019-05	PDFfile_download	V.H. Hoang and J.H. Quek and Ch. Schwab Analysis of multilevel MCMC-FEM for Bayesian inversion of log-normal diffusions Revised 1: June 2019
2019-04	PDFfile_download	R. Aylwin and C. Jerez-Hanckes and C. Schwab and J. Zech Domain Uncertainty Quantification in Computational Electromagnetics
2019-03	PDFfile_download	A. Hudde and M. Hutzenthaler and A. Jentzen and S. Mazzonetto On the Itô-Alekseev-Gröbner formula for stochastic differential equations
2019-02	PDFfile_download	A. Jentzen and F. Lindner and P. Pušnik Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions
2019-01	PDFfile_download	H. Ammari and E. Orvehed Hiltunen and S. Yu A high-frequency homogenization approach near the Dirac points in bubbly honeycomb crystals

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