Related papers: Evaluation of ensemble methods for quantifying unc…

Ensemble Kalman inversion is a parallelizable derivative-free method to solve inverse problems. The method uses an ensemble that follows the Kalman update formula iteratively to solve an optimization problem. The ensemble size is crucial to…

Uncertainty quantification (UQ) includes the characterization, integration, and propagation of uncertainties that result from stochastic variations and a lack of knowledge or data in the natural world. Monte Carlo (MC) method is a…

Uncertainty quantification (UQ) is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this…

Assessing the quality of aleatoric uncertainty estimates from uncertainty quantification (UQ) deep learning methods is important in scientific contexts, where uncertainty is physically meaningful and important to characterize and interpret…

The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…

Uncertainty Quantification (UQ) is pivotal in enhancing the robustness, reliability, and interpretability of Machine Learning (ML) systems for healthcare, optimizing resources and improving patient care. Despite the emergence of ML-based…

Deep neural networks (DNNs) have achieved tremendous success in computer vision, natural language processing, and scientific and engineering domains. However, DNNs can make unexpected, incorrect, yet overconfident predictions, leading to…

In the current era, known as Noisy Intermediate-Scale Quantum (NISQ), encoding large amounts of data in the quantum devices is challenging and the impact of noise significantly affects the quality of the obtained results. A viable approach…

Seismic inversion is essential for geophysical exploration and geological assessment, but it is inherently subject to significant uncertainty. This uncertainty stems primarily from the limited information provided by observed seismic data,…

Using observation data to estimate unknown parameters in computational models is broadly important. This task is often challenging because solutions are non-unique due to the complexity of the model and limited observation data. However,…

We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression…

This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov-Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure of UQ, enhancing interpretability and robustness in…

The practice of uncertainty quantification (UQ) validation, notably in machine learning for the physico-chemical sciences, rests on several graphical methods (scattering plots, calibration curves, reliability diagrams and confidence curves)…

Effective Uncertainty Quantification (UQ) represents a key aspect for reliable deployment of Large Language Models (LLMs) in automated decision-making and beyond. Yet, for LLM generation with multiple choice structure, the state-of-the-art…

This paper addresses uncertainty quantification (UQ) for problems where scalar (or low-dimensional vector) response quantities are insufficient and, instead, full-field (very high-dimensional) responses are of interest. To do so, an…

We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…

The success of diffusion probabilistic models in generative tasks, such as text-to-image generation, has motivated the exploration of their application to regression problems commonly encountered in scientific computing and various other…

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…

Recent studies have shown that ensemble approaches could not only improve accuracy and but also estimate model uncertainty in deep learning. However, it requires a large number of parameters according to the increase of ensemble models for…

Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…