Related papers: Ensemble Averaging for Dynamical Systems under Fas…

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…

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…

The space weather community has begun to use frontier methods such as data assimilation, machine learning, and ensemble modeling to advance current operational forecasting efforts. This was highlighted by a multi-disciplinary session at the…

In this work, we demonstrate how to reliably estimate epistemic uncertainty while maintaining the flexibility needed to capture complicated aleatoric distributions. To this end, we propose an ensemble of Normalizing Flows (NF), which are…

Mesoscale forecasts are now routinely performed as elements of operational forecasts and their outputs do appear convincing. However, despite their realistic appearance at times the comparison to observations is less favorable. At the grid…

Complex systems may be subject to various uncertainties. A great effort has been concentrated on predicting the dynamics under uncertainty in initial conditions. In the present work, we consider the well-known Burgers equation with random…

Neural network (NN) ensembles can reduce large prediction variance of NN and improve prediction accuracy. For highly nonlinear problems with insufficient data set, the prediction accuracy of NN models becomes unstable, resulting in a…

Ensemble prediction systems are an invaluable tool for weather forecasting. Practically, ensemble predictions are obtained by running several perturbations of the deterministic control forecast. However, ensemble prediction is associated…

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…

We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression…

Empirical evidence shows that ensembles, such as bagging, boosting, random and rotation forests, generally perform better in terms of their generalization error than individual classifiers. To explain this performance, Schapire et al.…

We prove a fractional averaging principle for interacting slow-fast systems. The mode of convergence is in H\"older norm in probability. The main technical result is a quenched ergodic theorem on the conditioned fractional dynamics. We also…

This paper investigates an expected average error for distributed averaging problems under asynchronous updates. The asynchronism in this context implies no existence of a global clock as well as random characteristics in communication…

Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…

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…

Meteorological ensembles are a collection of scenarios for future weather delivered by a meteorological center. Such ensembles form the main source of valuable information for probabilistic forecasting which aims at producing a predictive…

We present the validity of stochastic averaging principle for non-autonomous slow-fast stochastic differential equations (SDEs) whose fast motions admit random periodic solutions. Our investigation is motivated by some problems arising from…

A new statistical ensemble is examined using the example of classical one-component simple fluid. It's logical to call it an open ensemble, because its peculiarity is the inclusion in the consideration some surrounding area. Calculations…

Techniques of hybridisation and ensemble learning are popular model fusion techniques for improving the predictive power of forecasting methods. With limited research that instigates combining these two promising approaches, this paper…

Motivated by applications to mathematical biology, we study the averaging problem for slow-fast systems, {\em in the case in which the fast dynamics is a stochastic process with multiple invariant measures}. We consider both the case in…