We present DEF (\textbf{\ul{D}}iffusion-augmented \textbf{\ul{E}}nsemble \textbf{\ul{F}}orecasting), a novel approach for generating initial condition perturbations. Modern approaches to initial condition perturbations are primarily designed for numerical weather prediction (NWP) solvers, limiting their applicability in the rapidly growing field of machine learning for weather prediction. Consequently, stochastic models in this domain are often developed on a case-by-case basis. We demonstrate that a simple conditional diffusion model can (1) generate meaningful structured perturbations, (2) be applied iteratively, and (3) utilize a guidance term to intuitivey control the level of perturbation. This method enables the transformation of any deterministic neural forecasting system into a stochastic one. With our stochastic extended systems, we show that the model accumulates less error over long-term forecasts while producing meaningful forecast distributions. We validate our approach on the 5.625$^\circ$ ERA5 reanalysis dataset, which comprises atmospheric and surface variables over a discretized global grid, spanning from the 1960s to the present. On this dataset, our method demonstrates improved predictive performance along with reasonable spread estimates.

Ensemble forecasting is crucial for improving weather predictions, especially for forecasts of extreme events. Constructing an ensemble prediction system (EPS) based on conventional NWP models is highly computationally expensive. ML models have emerged as valuable tools for deterministic weather forecasts, providing forecasts with significantly reduced computational requirements and even surpassing the forecast performance of traditional NWP models. However, challenges arise when applying ML models to ensemble forecasting. Recent ML models, such as GenCast and SEEDS model, rely on the ERA5 EDA or operational NWP ensemble members for forecast generation. Their spatial resolution is also considered too coarse for many applications. To overcome these limitations, we introduce FuXi-ENS, an advanced ML model designed to deliver 6-hourly global ensemble weather forecasts up to 15 days. This model runs at a significantly increased spatial resolution of 0.25\textdegree, incorporating 5 atmospheric variables at 13 pressure levels, along with 13 surface variables. By leveraging the inherent probabilistic nature of Variational AutoEncoder (VAE), FuXi-ENS optimizes a loss function that combines the CRPS and the KL divergence between the predicted and target distribution, facilitating the incorporation of flow-dependent perturbations in both initial conditions and forecast. This innovative approach makes FuXi-ENS an advancement over the traditional ones that use L1 loss combined with the KL loss in standard VAE models for ensemble weather forecasting. Results demonstrate that FuXi-ENS outperforms ensemble forecasts from the ECMWF, a world leading NWP model, in the CRPS of 98.1% of 360 variable and forecast lead time combinations. This achievement underscores the potential of the FuXi-ENS model to enhance ensemble weather forecasts, offering a promising direction for further development in this field.

As per the records of theWorld Health Organization, the first formally reported incidence of Zika virus occurred in Brazil in May 2015. The disease then rapidly spread to other countries in Americas and East Asia, affecting more than 1,000,000 people. Zika virus is primarily transmitted through bites of infected mosquitoes of the species Aedes (Aedes aegypti and Aedes albopictus). The abundance of mosquitoes and, as a result, the prevalence of Zika virus infections are common in areas which have high precipitation, high temperature, and high population density.Nonlinear spatio-temporal dependency of such data and lack of historical public health records make prediction of the virus spread particularly challenging. In this article, we enhance Zika forecasting by introducing the concepts of topological data analysis and, specifically, persistent homology of atmospheric variables, into the virus spread modeling. The topological summaries allow for capturing higher order dependencies among atmospheric variables that otherwise might be unassessable via conventional spatio-temporal modeling approaches based on geographical proximity assessed via Euclidean distance. We introduce a new concept of cumulative Betti numbers and then integrate the cumulative Betti numbers as topological descriptors into three predictive machine learning models: random forest, generalized boosted regression, and deep neural network. Furthermore, to better quantify for various sources of uncertainties, we combine the resulting individual model forecasts into an ensemble of the Zika spread predictions using Bayesian model averaging. The proposed methodology is illustrated in application to forecasting of the Zika space-time spread in Brazil in the year 2018.

This work presents ensemble forecasting of monthly electricity demand using pattern similarity-based forecasting methods (PSFMs). PSFMs applied in this study include $k$-nearest neighbor model, fuzzy neighborhood model, kernel regression model, and general regression neural network. An integral part of PSFMs is a time series representation using patterns of time series sequences. Pattern representation ensures the input and output data unification through filtering a trend and equalizing variance. Two types of ensembles are created: heterogeneous and homogeneous. The former consists of different type base models, while the latter consists of a single-type base model. Five strategies are used for controlling a diversity of members in a homogeneous approach. The diversity is generated using different subsets of training data, different subsets of features, randomly disrupted input and output variables, and randomly disrupted model parameters. An empirical illustration applies the ensemble models as well as individual PSFMs for comparison to the monthly electricity demand forecasting for 35 European countries.