Related papers: Inverse problems and uncertainty quantification
Inverse problems play a key role in modern image/signal processing methods. However, since they are generally ill-conditioned or ill-posed due to lack of observations, their solutions may have significant intrinsic uncertainty. Analysing…
Additive manufacturing (AM) technology is being increasingly adopted in a wide variety of application areas due to its ability to rapidly produce, prototype, and customize designs. AM techniques afford significant opportunities in regard to…
The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
In the context of Monte Carlo (MC) simulation of particle transport Uncertainty Quantification (UQ) addresses the issue of predicting non statistical errors affecting the physical results, i.e. errors deriving mainly from uncertainties in…
We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian…
There are essentially three kinds of approaches to Uncertainty Quantification (UQ): (A) robust optimization, (B) Bayesian, (C) decision theory. Although (A) is robust, it is unfavorable with respect to accuracy and data assimilation. (B)…
Deep learning is gaining increasing popularity for spatiotemporal forecasting. However, prior works have mostly focused on point estimates without quantifying the uncertainty of the predictions. In high stakes domains, being able to…
This paper outlines a methodology for Bayesian multimodel uncertainty quantification (UQ) and propagation and presents an investigation into the effect of prior probabilities on the resulting uncertainties. The UQ methodology is adapted…
Due to the importance of uncertainty quantification (UQ), Bayesian approach to inverse problems has recently gained popularity in applied mathematics, physics, and engineering. However, traditional Bayesian inference methods based on Markov…
Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…
This paper introduces a novel hierarchical Bayesian model specifically designed to address challenges in Inverse Uncertainty Quantification (IUQ) for time-dependent problems in nuclear Thermal Hydraulics (TH) systems. The unique…
Bayesian quadrature (BQ) is a model-based numerical integration method that is able to increase sample efficiency by encoding and leveraging known structure of the integration task at hand. In this paper, we explore priors that encode…
In inverse problems, distribution-free uncertainty quantification (UQ) aims to obtain error bars with coverage guarantees that are independent of any prior assumptions about the data distribution. In the context of mass mapping,…
Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian…
Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…
This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual…
Uncertainty quantification (UQ) methods for Large Language Models (LLMs) encompass a variety of approaches, with two major types being particularly prominent: information-based, which focus on model confidence expressed as token…
We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…
Uncertainty quantification (UQ) is an important component of molecular property prediction, particularly for drug discovery applications where model predictions direct experimental design and where unanticipated imprecision wastes valuable…