Related papers: A Big-Data Approach to Handle Process Variations: …

Accurate assessment of systematic uncertainties is an increasingly vital task in physics studies, where large, high-dimensional datasets, like those collected at the Large Hadron Collider, hold the key to new discoveries. Common approaches…

Despite the massive advancements in large language models (LLMs), they still suffer from producing plausible but incorrect responses. To improve the reliability of LLMs, recent research has focused on uncertainty quantification to predict…

In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the Generalized Multiscale Finite Element Method (GMsFEM). In order…

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…

Many problems in science and engineering require uncertainty quantification that accounts for observed data. For example, in computational neuroscience, Neural Population Models (NPMs) are mechanistic models that describe brain physiology…

Stochastic simulation has been widely used to analyze the performance of complex stochastic systems and facilitate decision making in those systems. Stochastic simulation is driven by the input model, which is a collection of probability…

Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the…

This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any…

We consider the problem of estimating the expected outcomes of Monte Carlo processes whose outputs are described by multidimensional random variables. We tightly characterize the quantum query complexity of this problem for various choices…

Deep Learning methods are known to suffer from calibration issues: they typically produce over-confident estimates. These problems are exacerbated in the low data regime. Although the calibration of probabilistic models is well studied,…

Stochastic collocation methods for approximating the solution of partial differential equations with random input data (e.g., coefficients and forcing terms) suffer from the curse of dimensionality whereby increases in the stochastic…

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…

Nowadays, with the availability of massive amount of trade data collected, the dynamics of the financial markets pose both a challenge and an opportunity for high frequency traders. In order to take advantage of the rapid, subtle movement…

A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the…

In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…

In this work, we describe a Bayesian framework for reconstructing the boundaries of piecewise smooth regions in the X-ray computed tomography (CT) problem in an infinite-dimensional setting. In addition to the reconstruction, we are also…

In the framework of uncertainty quantification, we consider a quantity of interest which depends non-smoothly on the high-dimensional parameter representing the uncertainty. We show that, in this situation, the multilevel Monte Carlo…

In the Multiple Measurements Vector (MMV) model, measurement vectors are connected to unknown, jointly sparse signal vectors through a linear regression model employing a single known measurement matrix (or dictionary). Typically, the…

We consider the problem of quantifying uncertainty regarding the output of an electromagnetic field problem in the presence of a large number of uncertain input parameters. In order to reduce the growth in complexity with the number of…