The subject of this article is the introduction of a new concept of the well-posedness of Bayesian
inverse problems. The conventional concept of (Lipschitz, Hellinger) well-posedness in […

Stochastic gradient descent is an optimisation method that combines classical gradient
descent with random subsampling within the target functional. In this work, we introduce the …

Partial differential equations play a fundamental role in the mathematical modelling of many
processes and systems in physical, biological and other sciences. To simulate such …

Inverse problems describe the task of blending a mathematical model with observational
data---a fundamental task in many scientific and engineering disciplines. The solvability of such …

In image reconstruction, an accurate quantification of uncertainty is of great importance for
informed decision making. Here, the Bayesian approach to inverse problems can be used: the …

ODE solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical
systems, differential equations with low regularity, and, implicitly, in stochastic optimisation…

The identification of parameters in mathematical models using noisy observations is a common
task in uncertainty quantification. We employ the framework of Bayesian inversion: we …

Gaussian random fields are popular models for spatially varying uncertainties, arising for
instance in geotechnical engineering, hydrology or image processing. A Gaussian random field …

Sparse inversion and classification problems are ubiquitous in modern data science and
imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, …

The estimation of the probability of rare events is an important task in reliability and risk
assessment. We consider failure events that are expressed in terms of a limit state function, …