Related papers: Ensemble Timestepping Algorithms for the Heat Equa…

We consider optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. Using the sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems.…

Statistical post-processing techniques are now widely used to correct systematic biases and errors in calibration of ensemble forecasts obtained from multiple runs of numerical weather prediction models. A standard approach is the ensemble…

Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long time prediction of the evolution of the unknown system. Training a DNN with low…

Although by now the ensemble-based probabilistic forecasting is the most advanced approach to weather prediction, ensemble forecasts still might suffer from lack of calibration and/or display systematic bias, thus require some…

This work addresses the challenge of providing consistent explanations for predictive models in the presence of model indeterminacy, which arises due to the existence of multiple (nearly) equally well-performing models for a given dataset…

State-of-the-art weather forecasts usually rely on ensemble prediction systems, accounting for the different sources of uncertainty. As ensembles are typically uncalibrated, they should get statistically postprocessed. Several multivariate…

One of the primal challenges faced by utility companies is ensuring efficient supply with minimal greenhouse gas emissions. The advent of smart meters and smart grids provide an unprecedented advantage in realizing an optimised supply of…

Ensemble forecasts of weather and climate are subject to systematic biases in the ensemble mean and variance, leading to inaccurate estimates of the forecast mean and variance. To address these biases, ensemble forecasts are post-processed…

Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but also used in probabilistic forecasting, clustering and estimating generative adversarial…

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,…

Characterizing uncertainty is a common issue in nuclear measurement and has important implications for reliable physical discovery. Traditional methods are either insufficient to cope with the heterogeneous nature of uncertainty or…

We study the one-dimensional stochastic heat equation in the mild form driven by a general stochastic measure $\mu$, for $\mu$ we assume only $\sigma$-additivity in probability. The time averaging of the equation is considered, uniform a.…

Ensemble learning combines several individual models to obtain a better generalization performance. In this work we present a practical method for estimating the joint power of several classifiers. It differs from existing approaches which…

Student performance prediction is a critical research problem to understand the students' needs, present proper learning opportunities/resources, and develop the teaching quality. However, traditional machine learning methods fail to…

All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition…

Motion forecasting has become an increasingly critical component of autonomous robotic systems. Onboard compute budgets typically limit the accuracy of real-time systems. In this work we propose methods of improving motion forecasting…

Obtaining accurate estimates of uncertainty in climate scenarios often requires generating large ensembles of high-resolution climate simulations, a computationally expensive and memory intensive process. To address this challenge, we train…

In the real world, one almost never knows the parameters of a thermodynamic process to infinite precision. Reflecting this, here we investigate how to extend stochastic thermodynamics to systems with uncertain parameters, including…

Ensembles of forecasts are typically employed to account for the forecast uncertainties inherent in predictions of future weather states. However, biases and dispersion errors often present in forecast ensembles require statistical…

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…