Related papers: Bayesian Covariance Uncertainty for Adaptive Pilot…

We propose a multi-fidelity neural network surrogate sampling method for the uncertainty quantification of physical/biological systems described by ordinary or partial differential equations. We first generate a set of low/high-fidelity…

Probabilistic prediction of sequences from images and other high-dimensional data is a key challenge, particularly in risk-sensitive applications. In these settings, it is often desirable to quantify the uncertainty associated with the…

Many probabilistic models of interest in scientific computing and machine learning have expensive, black-box likelihoods that prevent the application of standard techniques for Bayesian inference, such as MCMC, which would require access to…

We consider the problem of Bayesian regression with trustworthy uncertainty quantification. We define that the uncertainty quantification is trustworthy if the ground truth can be captured by intervals dependent on the predictive…

Testing and evaluation are expensive but critical steps in the development of connected and automated vehicles (CAVs). In this paper, we develop an adaptive sampling framework to efficiently evaluate the accident rate of CAVs, particularly…

A multi-fidelity simulator is a numerical model, in which one of the inputs controls a trade-off between the realism and the computational cost of the simulation. Our goal is to estimate the probability of exceeding a given threshold on a…

Aircraft design relies heavily on solving challenging and computationally expensive Multidisciplinary Design Optimization problems. In this context, there has been growing interest in multi-fidelity models for Bayesian optimization to…

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…

Bayesian optimization is a popular tool for data-efficient optimization of expensive objective functions. In real-life applications like engineering design, the designer often wants to take multiple objectives as well as input uncertainty…

A Bayesian analytics framework that precisely quantifies uncertainty offers a significant advance for financial risk management. We develop an integrated approach that consistently enhances the handling of risk in market volatility…

We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward…

This study is devoted to the construction of a multifidelity Monte Carlo (MFMC) method for the uncertainty quantification of a nonlocal, non-mass-conserving Cahn-Hilliard model for phase transitions with an obstacle potential. We are…

There is a lack of simple and scalable algorithms for uncertainty quantification. Bayesian methods quantify uncertainty through posterior and predictive distributions, but it is difficult to rapidly estimate summaries of these…

Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often…

While generally considered computationally expensive, Uncertainty Quantification using Monte Carlo sampling remains beneficial for applications with uncertainties of high dimension. As an extension of the naive Monte Carlo method, the…

Sampling-based approaches are widely used in systems without analytic models to estimate risk or find optimal control. However, gathering sufficient data in such scenarios can be prohibitively costly. On the other hand, in many situations,…

We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or…

Parameters in climate models are usually calibrated manually, exploiting only small subsets of the available data. This precludes both optimal calibration and quantification of uncertainties. Traditional Bayesian calibration methods that…

Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…

Inverse uncertainty quantification (UQ) tasks such as parameter estimation are computationally demanding whenever dealing with physics-based models, and typically require repeated evaluations of complex numerical solvers. When partial…