57 citations · 113 across the 21 of their papers we have counts for
26 papers
Mixture-Weighted Ensemble Kalman Filter with Quasi-Monte Carlo Transport
Ilja Klebanov, Claudia Schillings, Dana Wrischnig
The Bootstrap Particle Filter (BPF) and the Ensemble Kalman Filter (EnKF) are two widely used methods for sequential Bayesian filtering: the BPF is asymptotically exact but can suf…
Quasi-Monte Carlo for Bayesian shape inversion governed by the Poisson problem subject to Gevrey regular domain deformations
Ana Djurdjevac, Vesa Kaarnioja, Max Orteu +1
We consider the application of a quasi-Monte Carlo cubature rule to Bayesian shape inversion subject to the Poisson equation under Gevrey regular parameterizations of domain uncert…
Uncertainty quantification for stationary and time-dependent PDEs subject to Gevrey regular random domain deformations
Ana Djurdjevac, Vesa Kaarnioja, Claudia Schillings +1
We study uncertainty quantification for partial differential equations subject to domain uncertainty. We parameterize the random domain using the model recently considered by Chern…
Lattice Rules Meet Kernel Cubature
Vesa Kaarnioja, Ilja Klebanov, Claudia Schillings +1
Rank-1 lattice rules are a class of equally weighted quasi-Monte Carlo methods that achieve essentially linear convergence rates for functions in a reproducing kernel Hilbert space…
A Gauss-Newton Method for ODE Optimal Tracking Control
Vicky Holfeld, Michael Burger, Claudia Schillings
This paper introduces and analyses a continuous optimization approach to solve optimal control problems involving ordinary differential equations (ODEs) and tracking type objective…
Quasi-Monte Carlo for Bayesian design of experiment problems governed by parametric PDEs
Vesa Kaarnioja, Claudia Schillings
This paper contributes to the study of optimal experimental design for Bayesian inverse problems governed by partial differential equations (PDEs). We derive estimates for the para…
Happy People -- Image Synthesis as Black-Box Optimization Problem in the Discrete Latent Space of Deep Generative Models
Steffen Jung, Jan Christian Schwedhelm, Claudia Schillings +1
In recent years, optimization in the learned latent space of deep generative models has been successfully applied to black-box optimization problems such as drug design, image gene…
On the concentration of subgaussian vectors and positive quadratic forms in Hilbert spaces
Mattes Mollenhauer, Claudia Schillings
In these notes, we investigate the tail behaviour of the norm of subgaussian vectors in a Hilbert space. The subgaussian variance proxy is given as a trace class operator, allowing…
Subsampling in ensemble Kalman inversion
Matei Hanu, Jonas Latz, Claudia Schillings
We consider the Ensemble Kalman Inversion which has been recently introduced as an efficient, gradient-free optimisation method to estimate unknown parameters in an inverse setting…
Ensemble-based gradient inference for particle methods in optimization and sampling
Claudia Schillings, Claudia Totzeck, Philipp Wacker
We propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information of objective functions {from a given ensemble of partic…
Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration
Philipp A. Guth, Vesa Kaarnioja, Frances Y. Kuo +2
We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal control problems subject to parabolic partial differential equation (PDE) constraints un…
One-shot Learning of Surrogates in PDE-constrained Optimization Under Uncertainty
Philipp A. Guth, Claudia Schillings, Simon Weissmann
We propose a general framework for machine learning based optimization under uncertainty. Our approach replaces the complex forward model by a surrogate, which is learned simultane…
Adaptive Tikhonov strategies for stochastic ensemble Kalman inversion
Simon Weissmann, Neil K. Chada, Claudia Schillings +1
Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this…
Continuous time limit of the stochastic ensemble Kalman inversion: Strong convergence analysis
Dirk Blömker, Claudia Schillings, Philipp Wacker +1
The Ensemble Kalman inversion (EKI) method is a method for the estimation of unknown parameters in the context of (Bayesian) inverse problems. The method approximates the underlyin…
Hierarchical surrogate-based Approximate Bayesian Computation for an electric motor test bench
David N. John, Livia Stohrer, Claudia Schillings +2
Inferring parameter distributions of complex industrial systems from noisy time series data requires methods to deal with the uncertainty of the underlying data and the used simula…
Consistency analysis of bilevel data-driven learning in inverse problems
Neil K. Chada, Claudia Schillings, Xin T. Tong +1
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization,…
Ensemble Kalman filter for neural network based one-shot inversion
Philipp A. Guth, Claudia Schillings, Simon Weissmann
We study the use of novel techniques arising in machine learning for inverse problems. Our approach replaces the complex forward model by a neural network, which is trained simulta…
A quasi-Monte Carlo Method for an Optimal Control Problem Under Uncertainty
Philipp A. Guth, Vesa Kaarnioja, Frances Y. Kuo +2
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a…
On the Incorporation of Box-Constraints for Ensemble Kalman Inversion
Neil K. Chada, Claudia Schillings, Simon Weissmann
The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been…
Sampling Sup-Normalized Spectral Functions for Brown-Resnick Processes
Marco Oesting, Martin Schlather, Claudia Schillings
Sup-normalized spectral functions form building blocks of max-stable and Pareto processes and therefore play an important role in modeling spatial extremes. For one of the most pop…
On the Convergence of the Laplace Approximation and Noise-Level-Robustness of Laplace-based Monte Carlo Methods for Bayesian Inverse Problems
Claudia Schillings, Björn Sprungk, Philipp Wacker
The Bayesian approach to inverse problems provides a rigorous framework for the incorporation and quantification of uncertainties in measurements, parameters and models. We are int…
Well Posedness and Convergence Analysis of the Ensemble Kalman Inversion
Dirk Blömker, Claudia Schillings, Philipp Wacker +1
The ensemble Kalman inversion is widely used in practice to estimate unknown parameters from noisy measurement data. Its low computational costs, straightforward implementation, an…
A strongly convergent numerical scheme from Ensemble Kalman inversion
Dirk Blömker, Claudia Schillings, Philipp Wacker
The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differen…
Convergence Analysis of Ensemble Kalman Inversion: The Linear, Noisy Case
Claudia Schillings, Andrew Stuart
We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to estab…