Related papers: Uncertainty quantification through Monte Carlo met…
Spectral clustering is a popular unsupervised learning technique which is able to partition unlabelled data into disjoint clusters of distinct shapes. However, the data under consideration are often experimental data, implying that the data…
CIPM published the Supplement I for GUM in 2008 as not only an alternative approach to estimate the uncertainty for a given calibration measurement but also as a proper uncertainty estimation one, whenever any of the conditions imposed in…
We consider a class of density-driven flow problems. We are particularly interested in the problem of the salinization of coastal aquifers. We consider the Henry saltwater intrusion problem with uncertain porosity, permeability, and…
This article presents a novel approach, named MCMP (Monte Carlo Motion Planning), to the problem of motion planning under uncertainty, i.e., to the problem of computing a low-cost path that fulfills probabilistic collision avoidance…
Spatially referenced datasets have become increasingly prevalent across many fields, largely driven by advances in data collection methods such as satellite remote sensing. In many applications, predictions at unobserved locations are…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
In this paper the application of the multi-level Monte Carlo (MLMC) method on numerical simulations of turbulent flows with uncertain parameters is investigated. Several strategies for setting up the MLMC method are presented, and the…
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (PDE) models, combining model computations at different levels…
Estimating predictive uncertainty is crucial for many computer vision tasks, from image classification to autonomous driving systems. Hamiltonian Monte Carlo (HMC) is an sampling method for performing Bayesian inference. On the other hand,…
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…
Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is…
Practical structural engineering problems are often characterized by significant uncertainties. Historically, one of the prevalent methods to account for this uncertainty has been the standard Monte Carlo (MC) method. Recently, improved…
Knowing the uncertainty associated with the output of a deep neural network is of paramount importance in making trustworthy decisions, particularly in high-stakes fields like medical diagnosis and autonomous systems. Monte Carlo Dropout…
Among the various options to estimate uncertainty in deep neural networks, Monte-Carlo dropout is widely popular for its simplicity and effectiveness. However the quality of the uncertainty estimated through this method varies and choices…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
The examination of uncertainty in the predictions of machine learning (ML) models is receiving increasing attention. One uncertainty modeling technique used for this purpose is Monte-Carlo (MC)-Dropout, where repeated predictions are…
We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the cumulative distribution function of a quantity of interest in problems with random input parameters or initial conditions. Our approach…
This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
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…