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Full-Waveform Inversion (FWI) has now become a widely accepted tool to obtain high-resolution velocity models from seismic data. Typically, the velocity model in its discrete form is represented on a rectangular grid, and we solve for the…

When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…

This paper is concerned with the numerical solution of model-based, Bayesian inverse problems. We are particularly interested in cases where the cost of each likelihood evaluation (forward-model call) is expensive and the number of un-…

We present a Newton-like method to solve inverse problems and to quantify parameter uncertainties. We apply the method to parameter reconstruction in optical scatterometry, where we take into account a priori information and measurement…

Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown…

Realisation of experiments even on small and medium-scale quantum computers requires an optimisation of several parameters to achieve high-fidelity operations. As the size of the quantum register increases, the characterisation of quantum…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

This study investigates an inverse problem associated with a time-fractional HIV infection model incorporating nonlinear diffusion. The model describes the dynamics of uninfected target cells, infected cells, and free virus particles, where…

This paper introduces an infinite-dimensional Bayesian framework for acoustic seabed tomography, leveraging wave scattering to simultaneously estimate the seabed and its roughness. Tomography is considered an ill-posed problem where…

We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by differential equations. We construct physics-informed…

This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…

Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…

Ptychography is a scanning coherent diffractive imaging technique that enables imaging nanometer-scale features in extended samples. One main challenge is that widely used iterative image reconstruction methods often require significant…

The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial…

In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of…

Empirical Bayes methods are widely used for large-scale inference, yet most classical approaches assume homoscedastic observations and focus primarily on posterior mean estimation. We develop a nonparametric empirical Bayes framework for…

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 successfully applied for the quantification of uncertainties…

We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…

When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…

Through the Bayesian lens of data assimilation, uncertainty on model parameters is traditionally quantified through the posterior covariance matrix. However, in modern settings involving high-dimensional and computationally expensive…