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We describe a convergence acceleration technique for unconstrained optimization problems. Our scheme computes estimates of the optimum from a nonlinear average of the iterates produced by any optimization method. The weights in this average…
Quantifying uncertainty in weather forecasts is critical, especially for predicting extreme weather events. This is typically accomplished with ensemble prediction systems, which consist of many perturbed numerical weather simulations, or…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
Anomaly Detection in multivariate time series is a major problem in many fields. Due to their nature, anomalies sparsely occur in real data, thus making the task of anomaly detection a challenging problem for classification algorithms to…
The purpose of this article is to study the convergence of a low order finite element approximation for a natural convection problem. We prove that the discretization based on P1 polynomials for every variable (velocity, pressure and…
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
Many applications of computational fluid dynamics require multiple simulations of a flow under different input conditions. In this paper, a numerical algorithm is developed to efficiently determine a set of such simulations in which the…
The potential effects of conservation actions on threatened species can be predicted using ensemble ecosystem models by forecasting populations with and without intervention. These model ensembles commonly assume stable coexistence of…
The computational cost as well as the probabilistic skill of ensemble forecasts depends on the spatial resolution of the numerical weather prediction model and the ensemble size. Periodically, e.g. when more computational resources become…
Ensemble learning is a mainstay in modern data science practice. Conventional ensemble algorithms assign to base models a set of deterministic, constant model weights that (1) do not fully account for individual models' varying accuracy…
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…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
Ensemble systems appear frequently in many engineering applications and, as a result, they have become an important research topic in control theory. These systems are best characterized by the evolution of their underlying state…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
Ensembles of neural networks have been shown to give better performance than single networks, both in terms of predictions and uncertainty estimation. Additionally, ensembles allow the uncertainty to be decomposed into aleatoric (data) and…
To mitigate the uncertainty of variable renewable resources, two off-the-shelf machine learning tools are deployed to forecast the solar power output of a solar photovoltaic system. The support vector machines generate the forecasts and the…
In this paper, we first devise an ensemble hybridizable discontinuous Galerkin (HDG) method to efficiently simulate a group of parameterized convection diffusion PDEs. These PDEs have different coefficients, initial conditions, source terms…
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.,…
Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…
We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in an earlier paper by two-scale…