Related papers: Inverse problems and uncertainty quantification

A common task in experimental sciences is to fit mathematical models to real-world measurements to improve understanding of natural phenomenon (reverse-engineering or inverse modeling). When complex dynamical systems are considered, such as…

Uncertainty quantification (UQ) techniques are frequently used to ascertain output variability in systems with parametric uncertainty. Traditional algorithms for UQ are either system-agnostic and slow (such as Monte Carlo) or fast with…

As machine learning-based prediction systems are increasingly used in high-stakes situations, it is important to understand how such predictive models will perform upon deployment. Distribution-free uncertainty quantification techniques…

Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that…

Motivation: Recent work has demonstrated the feasibility of using non-numerical, qualitative data to parameterize mathematical models. However, uncertainty quantification (UQ) of such parameterized models has remained challenging because of…

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…

Estimating posteriors and the associated model evidences, with desired accuracy and affordable computational cost, is a core issue of Bayesian model updating, and can be of great challenge given expensive-to-evaluate models and posteriors…

Machine learning (ML) is often viewed as a powerful data analysis tool that is easy to learn because of its black-box nature. Yet this very nature also makes it difficult to quantify confidence in predictions extracted from ML models, and…

We present a computational framework for estimating the uncertainty in the numerical solution of linearized infinite-dimensional statistical inverse problems. We adopt the Bayesian inference formulation: given observational data and their…

If Uncertainty Quantification (UQ) is crucial to achieve trustworthy Machine Learning (ML), most UQ methods suffer from disparate and inconsistent evaluation protocols. We claim this inconsistency results from the unclear requirements the…

The Parallel C++ Statistical Library for the Quantification of Uncertainty for Estimation, Simulation and Optimization, Queso, is a collection of statistical algorithms and programming constructs supporting research into the quantification…

Inverse problems, particularly those governed by Partial Differential Equations (PDEs), are prevalent in various scientific and engineering applications, and uncertainty quantification (UQ) of solutions to these problems is essential for…

Uncertainty Quantification (UQ) is an essential step in computational model validation because assessment of the model accuracy requires a concrete, quantifiable measure of uncertainty in the model predictions. The concept of UQ in the…

Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

Epistemic uncertainty quantification (UQ) identifies where models lack knowledge. Traditional UQ methods, often based on Bayesian neural networks, are not suitable for pre-trained non-Bayesian models. Our study addresses quantifying…

A nonparametric Bayesian approach is developed to determine quantum potentials from empirical data for quantum systems at finite temperature. The approach combines the likelihood model of quantum mechanics with a priori information over…

This paper provides a tutorial about uncertainty quantification (UQ) for those who have no background but are interested in learning more in this area. It exploits many very simple examples, which are understandable to undergraduates, to…

Deep learning-based surrogate models have demonstrated remarkable advantages over classical solvers in terms of speed, often achieving speedups of 10 to 1000 times over traditional partial differential equation (PDE) solvers. However, a…

Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…

Uncertainty quantification in image retrieval is crucial for downstream decisions, yet it remains a challenging and largely unexplored problem. Current methods for estimating uncertainties are poorly calibrated, computationally expensive,…