Related papers: Faster Uncertainty Quantification for Inverse Prob…

Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing…

This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches -- which typically assume full knowledge of the forward model or access to paired degraded and…

Learned inverse problem solvers exhibit remarkable performance in applications like image reconstruction tasks. These data-driven reconstruction methods often follow a two-step scheme. First, one trains the often neural network-based…

Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This…

In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…

Consistency models imitate the multi-step sampling of score-based diffusion in a single forward pass of a neural network. They can be learned in two ways: consistency distillation and consistency training. The former relies on the true…

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…

In this article, we propose a novel method for sampling potential functions based on noisy observation data of a finite number of observables in quantum canonical ensembles, which leads to the accurate sampling of a wide class of test…

Computer vision research has long aimed to build systems that are robust to spatial transformations found in natural data. Traditionally, this is done using data augmentation or hard-coding invariances into the architecture. However, too…

In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…

Constructing first principles models is a challenging task for nonlinear and complex systems such as a wastewater treatment unit. In recent years, data-driven models are widely used to overcome the complexity. However, they often suffer…

Predictive estimation, which comprises model calibration, model prediction, and validation, is a common objective when performing inverse uncertainty quantification (UQ) in diverse scientific applications. These techniques typically require…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Many important problems in science and engineering involve inferring a signal from noisy and/or incomplete observations, where the observation process is known. Historically, this problem has been tackled using hand-crafted regularization…

In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…

Solving multiphysics-based inverse problems for geological carbon storage monitoring can be challenging when multimodal time-lapse data are expensive to collect and costly to simulate numerically. We overcome these challenges by combining…