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Article

Bittracher, Andreas and Mollenhauer, Mattes and Koltai, Péter and Schütte, Ch. (2023) Optimal Reaction Coordinates: Variational Characterization and Sparse Computation. Multiscale Modeling & Simulation, 21 (2). ISSN ISSN (print): 1540-3459 ISSN (online): 1540-3467

Blömker, Dirk and Schillings, Claudia and Wacker, Philipp (2018) A strongly convergent numerical scheme from ensemble Kalman inversion. SIAM Journal on Numerical Analysis, 56 (4).

Blömker, Dirk and Schillings, Claudia and Wacker, Philipp and Weissmann, Simon (2022) Continuous time limit of the stochastic ensemble Kalman inversion: Strong convergence analysis. SIAM Journal on Numerical Analysis, 60 (6). pp. 3181-3215.

Borzì, Alfio and Schulz, Volker H. and Schillings, Claudia and von Winckel, Gregory (2010) On the treatment of distributed uncertainties in PDE‐constrained optimization. GAMM-Mitteilungen, 33 (2). pp. 230-246.

Chada, Neil and Schillings, Claudia and Tong, Xin and Weissmann, Simon (2022) Consistency analysis of bilevel data-driven learning in inverse problems. Communications in Mathematical Sciences, 20 (1). pp. 123-164.

Chada, Neil and Schillings, Claudia and Weissmann, Simon (2019) On the incorporation of box-constraints for ensemble Kalman inversion. Foundations of Data Science, 1 (4). pp. 433-456.

Eigel, Martin and Gruhlke, Robert and Sommer, David (2024) Less interaction with forward models in Langevin dynamics: Enrichment and Homotopy Martin , Robert , David. arXiv To appear in SIADS . (Submitted)

Ernst, Oliver and Nobile, Fabio and Schillings, Claudia and Sullivan, Tim (2020) Uncertainty quantification. Oberwolfach Reports, 16 (1). pp. 695-772.

Gruhlke, Robert and Nouy, Anthony and Trunschke, Philipp (2024) Optimal sampling for stochastic and natural gradient descent Robert Gruhlke, ,. arXiv . (Submitted)

Guth, Philipp A. and Kaarnioja, Vesa (2024) Generalized dimension truncation error analysis for high-dimensional numerical integration: lognormal setting and beyond. to appear in SIAM Journal on Numerical Analysis . (Submitted)

Guth, Philipp A. and Kaarnioja, Vesa (2024) Uncertainty quantification for random domains using periodic random variables. Numerische Mathematik, 156 . pp. 273-317.

Guth, Philipp A. and Kaarnioja, Vesa and Kuo, Frances Y. and Schillings, Claudia and Sloan, Ian H. (2021) A Quasi-Monte Carlo Method for Optimal Control Under Uncertainty. SIAM/ASA Journal on Uncertainty Quantification, 9 (2). pp. 354-383.

Guth, Philipp A. and Kaarnioja, Vesa and Kuo, Frances Y. and Schillings, Claudia and Sloan, Ian H. (2019) A quasi-Monte Carlo method for an optimal control problem under uncertainty. ArXiv .

Guth, Philipp A. and Kaarnioja, Vesa and Kuo, Frances Y. and Sloan, Ian H. (2022) Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration. arXiv preprint arXiv:2208.02767 . (Submitted)

Guth, Philipp A. and Schillings, Claudia and Weissmann, Simon (2020) Ensemble Kalman filter for neural network-based one-shot inversion. ArXiv . (Submitted)

Hajian, Soheil and Hintermüller, Michael and Schillings, Claudia and Strogtes, Michael (2018) A Bayesian approach to parameter identification in gas networks. Preprint : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2537 .

Hanu, Matei and Hesser, Jürgen and Kanschat, Guido and Moviglia, Javier and Schillings, Claudia and Stallkamp, Jan (2023) Ensemble Kalman Inversion for Image Guided Guide Wire Navigation in Vascular Systems. arXiv . (Submitted)

Hanu, Matei and Latz, J. and Schillings, Claudia (2023) Subsampling in ensemble Kalman inversion. Inverse Problems, 39 (9).

Hiptmair, R. and Scarabosio, L. and Schillings, Claudia and Schwab, Ch. (2018) Large deformation shape uncertainty quantification in acoustic scattering. Advances in Computational Mathematics, 44 . pp. 1475-1518.

John, David N. and Stohrer, Livia and Schillings, Claudia and Schick, Michael and Heuveline, Vincent (2021) Hierarchical surrogate-based Approximate Bayesian Computation for an electric motor test bench. . . (Submitted)

Jung, S. and Schwedhelm, J.C. and Schillings, Claudia and Keuper, M. (2023) Happy People--Image Synthesis as Black-Box Optimization Problem in the Discrete Latent Space of Deep Generative Models. arXiv . (Submitted)

Kaarnioja, Vesa and Rupp, Andreas (2024) Quasi-Monte Carlo and discontinuous Galerkin. arXiv . (Submitted)

Li, Z. and Meunier, D. and Mollenhauer, M. and Gretton, A. (2023) Towards Optimal Sobolev Norm Rates for the Vector-Valued Regularized Least-Squares Algorithm. arXiv . (Submitted)

Li, Z. and Meunier, D. and Mollenhauer, Mattes and Gretton, A. (2023) Optimal Rates for Regularized Conditional Mean Embedding Learning. Advances in Neural Information Processing Systems (NeurIPS), 36 . (Submitted)

Liu, Dishi and Litvinenko, Alexander and Schillings, Claudia and Schulz, Volker (2017) Quantification of airfoil geometry-induced aerodynamic uncertainties---comparison of approaches. SIAM/ASA Journal on Uncertainty Quantification, 5 (1).

Mollenhauer, Mattes and Klus, Stefan and Schütte, Christof and Koltai, Péter (2022) Kernel autocovariance operators of stationary processes: Estimation and convergence. Journal of Machine Learning Research, 23 (327). pp. 1-34.

Mollenhauer, Mattes and Mücke, Nicole and Sullivan, T.J. (2022) Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem. arXiv . (Submitted)

Mollenhauer, Mattes and Schillings, Claudia (2023) On the concentration of subgaussian vectors and positive quadratic forms in Hilbert spaces. arXiv . (Submitted)

Mollenhauer, Mattes and Schuster, Ingmar and Klus, Stefan and Schütte, Christof (2020) Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces. Advances in Dynamics, Optimization and Computation . pp. 109-131.

Oesting, Marco and Schlather, Martin and Schillings, Claudia (2019) Sampling sup‐normalized spectral functions for Brown–Resnick processes. Stat, 8 (1).

Schillings, Claudia and Guth, Philipp A. and Weissmann, Simon (2021) A General Framework for Machine Learning based Optimization Under Uncertainty. . . (Submitted)

Schillings, Claudia and Schulz, Volker (2014) On the influence of robustness measures on shape optimization with stochastic uncertainties. Optimization and Engineering, 16 . pp. 347-386. ISSN 1573-2924; Print 1389-4420

Schillings, Claudia and Schwab, Christoph (2016) Scaling limits in computational Bayesian inversion. ESAIM: Mathematical Modelling and Numerical Analysis, 50 (6). pp. 1825-1856. ISSN 2822-7840; eISSN = 2804-7214

Schillings, Claudia and Schwab, Christoph (2013) Sparse, adaptive Smolyak quadratures for Bayesian inverse problems. Inverse Problems, 29 (6).

Schillings, Claudia and Schwab, Christoph (2014) Sparsity in Bayesian inversion of parametric operator equations. Inverse Problems, 30 (6).

Schillings, Claudia and Schwab, Christoph (2013) A note on sparse, adaptive Smolyak quadratures for Bayesian inverse problems. SAM Research Report, 06 .

Schillings, Claudia and Sprungk, Björn and Wacker, Philipp (2020) On the convergence of the Laplace approximation and noise-level-robustness of Laplace-based Monte Carlo methods for Bayesian inverse problems. Numerische Mathematik, 145 . pp. 915-971.

Schillings, Claudia and Sprungk, Björn and Wacker, Philipp (2020) On the convergence of the Laplace approximation and noise-level-robustness of Laplace-based Monte Carlo methods for Bayesian inverse problems. Numerische Mathematik, 145 (1). pp. 915-971.

Schillings, Claudia and Stuart, Andrew M. (2017) Convergence Analysis of the Ensemble Kalman Filter for Inverse Problems: the Noisy Case. ArXiv .

Schillings, Claudia and Stuart, Andrew M. (2017) Convergence analysis of ensemble Kalman inversion: the linear, noisy case. arXiv . (Submitted)

Schillings, Claudia and Sunnåker, Mikael and Stelling, Jörg and Schwab, Christoph (2015) Efficient characterization of parametric uncertainty of complex (bio) chemical networks. PLOS Computational Biology .

Schillings, Claudia and Totzeck, Claudia and Wacker, Philipp (2023) Ensemble-based gradient inference for particle methods in optimization and sampling. SIAM/ASA Journal on Uncertainty Quantification, 11 (3). pp. 757-787.

Schwab, Christoph and Schillings, Claudia (2012) Sparse, adaptive Smolyak algorithms for Bayesian inverse problems. Research Report No. 2012-37 .

Sloan, Ian H. and Kaarnioja, Vesa Doubling the rate – improved error bounds for orthogonal projection in Hilbert spaces. arXiv . (Submitted)

Weissmann, Simon and Chada, Neil and Schillings, Claudia and Tong, Xin (2022) Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion. Inverse Problems, 38 (4).

von Kleist, M. and Raharinirina, Alexia and Gubela, Nils and Börnigen, Daniela and Smith, Maureen and Oh, Djin-Ye and Budt, Matthias and Mache, Christin and Schillings, Claudia and Fuchs, Stephan and Dürrwald, Ralf and Wolff, Thorsten and Hoelzer, Martin and Sofia, Paraskevopoulou (2023) SARS-CoV-2 Evolution on a Dynamic Immune Landscape. Biological Sciences . (Submitted)

Book Section

Gantner, Robert N. and Schillings, Claudia and Schwab, Christoph (2016) Binned Multilevel Monte Carlo for Bayesian Inverse Problems with Large Data. In: Domain Decomposition Methods in Science and Engineering XXII. Springer, pp. 511-519. ISBN 978-3-319-18826-3

Guth, Philipp A. and Kaarnioja, Vesa (2024) Application of dimension truncation error analysis to high-dimensional function approximation To appear in: 2022. Springer Verlag, 2024. In: Monte Carlo and Quasi-Monte Carlo Methods. Springer Verlag. (Submitted)

Hansen, Markus and Schillings, Claudia and Schwab, Christoph (2014) Sparse approximation algorithms for high dimensional parametric initial value problems. In: Modeling, Simulation and Optimization of Complex Processes - HPSC 2012. Proceedings of the Fifth International Conference on High Performance Scientific Computing, March 5-9, 2012, Hanoi, Vietnam . Springer Cham, pp. 63-81. ISBN 978-3-319-09062-7

Kaarnioja, Vesa and Kuo, Frances Y. and Sloan, Ian H. (2024) Lattice-based kernel approximation and serendipitous weights for parametric PDEs in very high dimensions. In: Monte Carlo and Quasi-Monte Carlo Methods 2022. Springer Verlag. (Submitted)

Schulz, Volker and Schillings, Claudia (2013) Optimal aerodynamic design under uncertainty. In: Management and Minimisation of Uncertainties and Errors in Numerical Aerodynamics. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 122 . Springer, Berlin, Heidelberg, pp. 297-338. ISBN 978-3-642-36184-5 Online: 978-3-642-36185-2

Conference or Workshop Item

Gantner, Robert N. and Schillings, Claudia and Schwab, Christoph (2014) Multilevel Monte Carlo for Bayesian Inverse Problems. In: Swiss Numerics Day 2014, April 2014, Universität Zürich.

Royset, Johannes and Ruthotto, Lars and Schillings, Claudia and Surowiec, Thomas M. (2023) Workshop Report 21w5167 Optimization under Uncertainty: Learning and Decision Making in 2021. In: held virtually hosted by the, Feb 8 - 12, 2023, Banff International Research Station for Mathematical Innovation and Discovery (BIRS).

Schuster, Ingmar and Mollenhauer, Mattes and Klus, Stefan and Muandet, K. (2020) Kernel Conditional Density Operators. In: 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), August 26 - 28, 2020, Online.

Schwab, Christoph and Schillings, Claudia (2013) Sparse Quadrature Approach to Bayesian Inverse Problems. In: SIAM Conference on Computational Science and Engineering.

Book

Schillings, Claudia and Schmidt, Stephan and Schulz, Volker (2011) Efficient shape optimization for certain and uncertain aerodynamic design. Elsevier, pp. 78-87.