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The costs for drilling offshore wells are high and hydrocarbons are often located in complex reservoir formations. To effectively produce from such reservoirs and reduce costs, optimized well placement in real-time (geosteering) is crucial.…
Software testing is one of the important ways to ensure the quality of software. It is found that testing cost more than 50% of overall project cost. Effective and efficient software testing utilizes the minimum resources of software.…
This paper presents a simple, general technique to prove finite element method (FEM) pressure stability and convergence. Typically, pressure estimates are ignored in the literature. However, full reliability of a numerical method is not…
This paper derives a posteriori error estimators for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on the results of [14] for…
The definition of partial differential equation (PDE) models usually involves a set of parameters whose values may vary over a wide range. The solution of even a single set of parameter values may be quite expensive. In many cases, e.g.,…
We present the checkpoint ensembles method that can learn ensemble models on a single training process. Although checkpoint ensembles can be applied to any parametric iterative learning technique, here we focus on neural networks. Neural…
The applications of artificial intelligence (AI) are rapidly evolving, and they are also commonly used in safety-critical domains, such as autonomous driving and medical diagnosis, where functional safety is paramount. In AI-driven systems,…
This paper proposes a new interpretation of sparse penalties such as the elastic-net and the group-lasso. Beyond providing a new viewpoint on these penalization schemes, our approach results in a unified optimization strategy. Our…
Deep Ensembles are a simple, reliable, and effective method of improving both the predictive performance and uncertainty estimates of deep learning approaches. However, they are widely criticised as being computationally expensive, due to…
Uncertainty quantification by ensemble learning is explored in terms of an application from computational optical form measurements. The application requires to solve a large-scale, nonlinear inverse problem. Ensemble learning is used to…
Ensemble forecasting is a technique devised to palliate sensitivity to initial conditions in nonlinear dynamical systems. The basic idea to avoid this sensitivity is to run the model many times under several slightly-different initial…
This paper is devoted to studying the stationary solutions of a general constrained optimization problem through its associated unconstrained penalized problems. We aim to answer the question, "what do the stationary solutions of a…
Ensemble learning improves classification performance by combining multiple base classifiers. While increasing the number of classifiers generally enhances accuracy, excessively large ensembles can lead to computational inefficiency and…
Ensemble-based methods are highly popular approaches that increase the accuracy of a decision by aggregating the opinions of individual voters. The common point is to maximize accuracy; however, a natural limitation occurs if incremental…
Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in…
In this paper, we propose, analyze, and test an efficient algorithm for computing ensemble average of incompressible magnetohydrodynamics (MHD) flows, where instances/members correspond to varying kinematic viscosity, magnetic diffusivity,…
Speech classification has attracted increasing attention due to its wide applications, particularly in classifying physical and mental states. However, these tasks are challenging due to the high variability in speech signals. Ensemble…
To increase the reliability of simulations by particle methods for incompressible viscous flow problems, convergence studies and improvements of accuracy are considered for a fully explicit particle method for incompressible Navier--Stokes…
People tend to behave inconsistently over time due to an inherent present bias. As this may impair performance, social and economic settings need to be adapted accordingly. Common tools to reduce the impact of time-inconsistent behavior are…
This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principles are proved under suitable `mixing' conditions on random…