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05/23/2023
Subsampling Error in Stochastic Gradient Langevin Diffusions
The Stochastic Gradient Langevin Dynamics (SGLD) are popularly used to a...
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02/22/2023
Subsampling in ensemble Kalman inversion
We consider the Ensemble Kalman Inversion which has been recently introd...
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02/08/2023
Can Physics-Informed Neural Networks beat the Finite Element Method?
Partial differential equations play a fundamental role in the mathematic...
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09/08/2022
Losing momentum in continuous-time stochastic optimisation
The training of deep neural networks and other modern machine learning m...
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08/11/2022
Joint reconstruction-segmentation on graphs
Practical image segmentation tasks concern images which must be reconstr...
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03/22/2022
Gradient flows and randomised thresholding: sparse inversion and classification
Sparse inversion and classification problems are ubiquitous in modern da...
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12/07/2021
A Continuous-time Stochastic Gradient Descent Method for Continuous Data
Optimization problems with continuous data appear in, e.g., robust machi...
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10/27/2020
Classification and image processing with a semi-discrete scheme for fidelity forced Allen–Cahn on graphs
This paper introduces a semi-discrete implicit Euler (SDIE) scheme for t...
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08/14/2020
Error analysis for probabilities of rare events with approximate models
The estimation of the probability of rare events is an important task in...
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04/15/2020
Analysis of Stochastic Gradient Descent in Continuous Time
Stochastic gradient descent is an optimisation method that combines clas...
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03/06/2020
Generalized Parallel Tempering on Bayesian Inverse Problems
In the current work we present two generalizations of the Parallel Tempe...
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01/24/2020
Certified and fast computations with shallow covariance kernels
Many techniques for data science and uncertainty quantification demand e...
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09/17/2019
Multilevel Sequential Importance Sampling for Rare Event Estimation
The estimation of the probability of rare events is an important task in...
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04/27/2019
Multilevel adaptive sparse Leja approximations for Bayesian inverse problems
Deterministic interpolation and quadrature methods are often unsuitable ...
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02/26/2019
On the well-posedness of Bayesian inverse problems
The subject of this article is the introduction of a weaker concept of w...
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07/23/2018
A practical example for the non-linear Bayesian filtering of model parameters
In this tutorial we consider the non-linear Bayesian filtering of static...
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05/08/2018
Bayesian parameter identification in Cahn-Hilliard models for biological growth
In this paper we consider the identification of internal parameters in a...
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04/30/2018
Fast sampling of parameterised Gaussian random fields
Gaussian random fields are popular models for spatially varying uncertai...
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09/27/2017