Ranked Probability Score Research Articles

Probabilistic prediction with locally weighted jackknife predictive system

Probabilistic predictions for regression problems are more popular than point predictions and interval predictions, since they contain more information for test labels. Conformal predictive system is a recently proposed non-parametric method to do reliable probabilistic predictions, which is computationally inefficient due to its learning process. To build faster conformal predictive system and make full use of training data, this paper proposes the predictive system based on locally weighted jackknife prediction approach. The theoretical property of our proposed method is proved with some regularity assumptions in the asymptotic setting, which extends our earlier theoretical researches from interval predictions to probabilistic predictions. In the experimental section, our method is implemented based on our theoretical analysis and its comparison with other predictive systems is conducted using 20 public data sets. The continuous ranked probability scores of the predictive distributions and the performance of the derived prediction intervals are compared. The better performance of our proposed method is confirmed with Wilcoxon tests. The experimental results demonstrate that the predictive system we proposed is not only empirically valid, but also provides more information than the other comparison predictive systems.

On the Combination of Physical Parameterization Schemes for Tropical Cyclone Track and Intensity Forecasts in the Context of Uncertainty

AbstractThe selection of physical parameterization schemes for tropical cyclone (TC) forecasts has required a substantial amount of effort. In general, the evaluation of physical parameterization schemes and their combined performance was based solely on the deterministic forecast, which had inherent limitations in representing the overall performance of physical parameterization schemes due to the model uncertainty. This study introduces an uncertainty‐informed framework of evaluating and selecting the combination of physical parameterization schemes for TC forecasts, based on the ensemble forecast that could include the model uncertainty roles. The performance ranking of the scheme combination based on the ensemble mean error is found to be distinct from that based on the deterministic forecast error. Moreover, differences in both ensemble mean errors and ensemble spreads for various scheme combinations highlight the importance of considering two metrics concurrently, that is, via the quality of the forecast distribution as a whole, to assess the forecast performance. Consequently, the ensemble Continuous Ranked Probability Score (eCRPS) is used to quantify the performance of the scheme combinations, and it is demonstrated that the performance is more comprehensive than that in the deterministic context. Finally, the well‐performed scheme combination for the forecasts of six intense TCs is chosen from the evaluated schemes in the context of model uncertainty, based on the overall quality of TC track and intensity forecast distributions.

Scale‐dependent blending of ensemble rainfall nowcasts and numerical weather prediction in the open‐source pysteps library

AbstractFlash flood early warning requires accurate rainfall forecasts with a high spatial and temporal resolution. As the first few hours ahead are already not sufficiently well captured by the rainfall forecasts of numerical weather prediction (NWP) models, radar rainfall nowcasting can provide an alternative. Because this observation‐based method quickly loses skill after the first 2 hr of the forecast, it needs to be combined with NWP forecasts to extend the skillful lead time of short‐term rainfall forecasts, which should increase decision‐making times. We implemented an adaptive scale‐dependent ensemble blending method in the open‐source pysteps library, based on the Short‐Term Ensemble Prediction System scheme. In this implementation, the extrapolation (ensemble) nowcast, (ensemble) NWP, and noise components are combined with skill‐dependent weights that vary per spatial scale level. To constrain the (dis)appearance of rain in the ensemble members to regions around the rainy areas, we have developed a Lagrangian blended probability matching scheme and incremental masking strategy. We describe the implementation details and evaluate the method using three heavy and extreme (July 2021) rainfall events in four Belgian and Dutch catchments. We benchmark the results of the 48‐member blended forecasts against the Belgian NWP forecast, a 48‐member nowcast, and a simple 48‐member linear blending approach. Both on the radar domain and catchment scale, the introduced blending approach predominantly performs similarly or better than only nowcasting (in terms of event‐averaged continuous ranked probability score and critical success index values) and adds value compared with NWP for the first hours of the forecast, although the difference, particularly with the linear blending method, reduces when we focus on catchment‐average cumulative rainfall sums instead of instantaneous rainfall rates. By properly combining observations and NWP forecasts, blending methods such as these are a crucial component of seamless prediction systems.

A novel criterion based on continuous ranked probability score for performance evaluation of control charts

AbstractRun length distributions are generally used to characterize the performance of a control chart in signaling alarms when a process is out‐of‐control. Since it is usually difficult to directly compare distributions, statistics of the run length distribution are commonly adopted as the performance criteria in practice. Particularly, the average run length (ARL) and its extended versions play a dominant role. However, due to the skewness of the run length distribution, the ARL cannot accurately reflect the central tendency and may be misleading in some cases. In order to comprehensively summarize the information of the run length distribution, a novel criterion is proposed based on the continuous ranked probability score (CRPS). The CRPS‐based criterion measures the difference between the run length distribution and the ideal constant value 0 for the run length. It has advantages of easy computation and good interpretability. Furthermore, theoretical properties and geometric representation guarantee that the CRPS‐based criterion is statistically consistent, informative of both first and second moments of the run length distribution, and robust to extreme values. Results of numerical experiments show that the proposed criterion favors control charts with higher probability to detect outliers earlier, and is a superior metric for characterizing the run length distribution.

CT texture analysis in predicting treatment response and survival in patients with hepatocellular carcinoma treated with transarterial chemoembolization using random forest models

BackgroundUsing texture features derived from contrast-enhanced computed tomography (CT) combined with general imaging features as well as clinical information to predict treatment response and survival in patients with hepatocellular carcinoma (HCC) who received transarterial chemoembolization (TACE) treatment.MethodsFrom January 2014 to November 2022, 289 patients with HCC who underwent TACE were retrospectively reviewed. Their clinical information was documented. Their treatment-naïve contrast-enhanced CTs were retrieved and reviewed by two independent radiologists. Four general imaging features were evaluated. Texture features were extracted based on the regions of interest (ROIs) drawn on the slice with the largest axial diameter of all lesions using Pyradiomics v3.0.1. After excluding features with low reproducibility and low predictive value, the remaining features were selected for further analyses. The data were randomly divided in a ratio of 8:2 for model training and testing. Random forest classifiers were built to predict patient response to TACE treatment. Random survival forest models were constructed to predict overall survival (OS) and progress-free survival (PFS).ResultsWe retrospectively evaluated 289 patients (55.4 ± 12.4 years old) with HCC treated with TACE. Twenty features, including 2 clinical features (ALT and AFP levels), 1 general imaging feature (presence or absence of portal vein thrombus) and 17 texture features, were included in model construction. The random forest classifier achieved an area under the curve (AUC) of 0.947 with an accuracy of 89.5% for predicting treatment response. The random survival forest showed good predictive performance with out-of-bag error rate of 0.347 (0.374) and a continuous ranked probability score (CRPS) of 0.170 (0.067) for the prediction of OS (PFS).ConclusionsRandom forest algorithm based on texture features combined with general imaging features and clinical information is a robust method for predicting prognosis in patients with HCC treated with TACE, which may help avoid additional examinations and assist in treatment planning.

Dynamic line rating forecasting algorithm for a secure power system network

This research aimed to enhance the capacity of transmission lines by developing an algorithm to predict Dynamic Line Rating (DLR) to avert the curtailment of renewable energy sources. This will help meet electricity demand, prevent power outages, reduce costs, and protect equipment and personnel. The proposed algorithm was trained by analyzing the correlation between sequential hourly DLR calculations derived from historical weather data and line physical parameters. The proposed algorithm used k-means clustering and Monte Carlo simulation to predict hourly DLR, considering the temporal correlation of historical DLR values for each month. The model's accuracy was verified through statistical tests and was compared to other forecasting methods such as ensemble forecasting, quantile regression, and recurrent neural networks. It was found that the proposed model demonstrated performance that is comparable or superior to existing methods, as seen in forecast skill ranging from 91 to 98%, a Continuous Ranked Probability Score (CRPS) between 0.02 and 0.05, and probabilistic ratings that are 48–70% higher than traditional Static Line Rating (SLR).

Local scale invariance and robustness of proper scoring rules

Averages of proper scoring rules are often used to rank probabilistic forecasts. In many cases, the individual terms in these averages are based on observations and forecasts from different distributions. We show that some of the most popular proper scoring rules, such as the continuous ranked probability score (CRPS), give more importance to observations with large uncertainty, which can lead to unintuitive rankings. To describe this issue, we define the concept of local scale invariance for scoring rules. A new class of generalized proper kernel scoring rules is derived and as a member of this class we propose the scaled CRPS (SCRPS). This new proper scoring rule is locally scale invariant and, therefore, works in the case of varying uncertainty. Like the CRPS, it is computationally available for output from ensemble forecasts, and does not require the ability to evaluate densities of forecasts. We further define robustness of scoring rules, show why this also can be an important concept for average scores unless one is specifically interested in extremes, and derive new proper scoring rules that are robust against outliers. The theoretical findings are illustrated in three different applications from spatial statistics, stochastic volatility models and regression for count data.

The suitability of a seasonal ensemble hybrid framework including data-driven approaches for hydrological forecasting

Abstract. Hydrological forecasts are important for operational water management and near-future planning, even more so in light of the increased occurrences of extreme events such as floods and droughts. Having a forecasting framework, which is flexible in terms of input forcings and forecasting locations (local, regional, or national) that can deliver this information in fast and computational efficient manner, is critical. In this study, the suitability of a hybrid forecasting framework, combining data-driven approaches and seasonal (re)forecasting information from dynamical models, to predict hydrological variables was explored. Target variables include discharge and surface water levels for various stations at a national scale, with the Netherlands as the focus. Five different machine learning (ML) models, ranging from simple to more complex and trained on historical observations of discharge, precipitation, evaporation, and seawater levels, were run with seasonal (re)forecast data, including the European Flood Awareness System (EFAS) and ECMWF seasonal forecast system (SEAS5), of these driver variables in a hindcast setting. The results were evaluated using the evaluation metrics, i.e. anomaly correlation coefficient (ACC), continuous ranked probability (skill) score (CRPS and CRPSS), and Brier skill score (BSS), in comparison to a climatological reference hindcast. Aggregating the results of all stations and ML models revealed that the hindcasting framework outperformed the climatological reference forecasts by roughly 60 % for discharge predictions (80 % for surface water level predictions). Skilful prediction for the first lead month, independently of the initialization month, can be made for discharge. The skill extends up to 2–3 months for spring months due to snowmelt dynamic captured in the training phase of the model. Surface water level hindcasts showed similar skill and skilful lead times. While the different ML models showed differences in performance during a testing and training phase using historical observations, running the ML framework in a hindcast setting showed only minor differences between the models, which is attributed to the uncertainty in seasonal forecasts. However, despite being trained on historical observations, the hybrid framework used in this study shows similar skilful predictions to previous large-scale forecasting systems. With our study, we show that a hybrid framework is able to bring location-specific skilful seasonal forecast information with global seasonal forecast inputs. At the same time, our hybrid approach is flexible and fast, and as such, a hybrid framework could be adapted to make it even more interesting to water managers and their needs, for instance, as part of a fast model-predictive control framework.

Pairing ensemble numerical weather prediction with ensemble physical model chain for probabilistic photovoltaic power forecasting

Under the two-step framework of photovoltaic (PV) power forecasting, that is, forecasting first the irradiance and then converting it to PV power, there are two chief ways in which one can account for the uncertainty embedded in the final PV power forecast. One of those is to produce probabilistic irradiance forecast through, for example, ensemble numerical weather prediction (NWP), and the other is to pass the irradiance forecast through a collection of different irradiance-to-power conversion sequences, which are known as model chains. This work investigates, for the first time, into the question: Whether pairing ensemble NWP with ensemble model chain is better than leveraging any individual method alone? Using data from 14 utility-scale ground-mounted PV plants in Hungary and the state-of-the-art global mesoscale NWP model of the European Centre for Medium-Range Weather Forecasts, it is herein demonstrated that the best probabilistic PV power forecast needs to consider both ensemble NWP and ensemble model chain. Furthermore, owing to the higher-quality probabilistic forecasts, the point forecast accuracy is also improved substantially through pairing. Overall, the recommended paring strategy achieves a mean-normalized continuous ranked probability score and a root mean square error of 18.4% and 42.1%, respectively.

Probabilistic Intraday PV Power Forecast Using Ensembles of Deep Gaussian Mixture Density Networks

There is a growing interest of estimating the inherent uncertainty of photovoltaic (PV) power forecasts with probability forecasting methods to mitigate accompanying risks for system operators. This study aims to advance the field of probabilistic PV power forecast by introducing and extending deep Gaussian mixture density networks (MDNs). Using the sum of the weighted negative log likelihood of multiple Gaussian distributions as a minimizing objective, MDNs can estimate flexible uncertainty distributions with nearly all neural network structures. Thus, the advantages of advances in machine learning, in this case deep neural networks, can be exploited. To account for the epistemic (e.g., model) uncertainty as well, this study applies two ensemble approaches to MDNs. This is particularly relevant for industrial applications, as there is often no extensive (manual) adjustment of the forecast model structure for each site, and only a limited amount of training data are available during commissioning. The results of this study suggest that already seven days of training data are sufficient to generate significant improvements of 23.9% in forecasting quality measured by normalized continuous ranked probability score (NCRPS) compared to the reference case. Furthermore, the use of multiple Gaussian distributions and ensembles increases the forecast quality relatively by up to 20.5% and 19.5%, respectively.

Combining predictive distributions of electricity prices. Does minimizing the CRPS lead to optimal decisions in day-ahead bidding?

Probabilistic price forecasting has recently gained attention in power trading because decisions based on such predictions can yield significantly higher profits than those made with point forecasts alone. At the same time, methods are being developed to combine predictive distributions, since no model is perfect and averaging generally improves forecasting performance. In this article, we address the question of whether using CRPS learning, a novel weighting technique minimizing the continuous ranked probability score (CRPS), leads to optimal decisions in day-ahead bidding. To this end, we conduct an empirical study using hourly day-ahead electricity prices from the German EPEX market. We find that increasing the diversity of an ensemble can have a positive impact on accuracy. At the same time, the higher computational cost of using CRPS learning compared to an equal-weighted aggregation of distributions is not offset by higher profits, despite significantly more accurate predictions.

Drifting Streaming Peaks-Over-Threshold-Enhanced Self-Evolving Neural Networks for Short-Term Wind Farm Generation Forecast

This paper investigates the short-term wind farm generation forecast. It is observed from the real wind farm generation measurements that wind farm generation exhibits distinct features, such as the non-stationarity and the heterogeneous dynamics of ramp and non-ramp events across different classes of wind turbines. To account for the distinct features of wind farm generation, we propose a Drifting Streaming Peaks-over-Threshold (DSPOT)-enhanced self-evolving neural networks-based short-term wind farm generation forecast. Using DSPOT, the proposed method first classifies the wind farm generation data into ramp and non-ramp datasets, where time-varying dynamics are taken into account by utilizing dynamic ramp thresholds to separate the ramp and non-ramp events. We then train different neural networks based on each dataset to learn the different dynamics of wind farm generation by the NeuroEvolution of Augmenting Topologies (NEAT), which can obtain the best network topology and weighting parameters. As the efficacy of the neural networks relies on the quality of the training datasets (i.e., the classification accuracy of the ramp and non-ramp events), a Bayesian optimization-based approach is developed to optimize the parameters of DSPOT to enhance the quality of the training datasets and the corresponding performance of the neural networks. Based on the developed self-evolving neural networks, both distributional and point forecasts are developed. The experimental results show that compared with other forecast approaches, the proposed forecast approach can substantially improve the forecast accuracy, especially for ramp events. The experiment results indicate that the accuracy improvement in a 60 min horizon forecast in terms of the mean absolute error (MAE) is at least 33.6% for the whole year data and at least 37% for the ramp events. Moreover, the distributional forecast in terms of the continuous rank probability score (CRPS) is improved by at least 35.8% for the whole year data and at least 35.2% for the ramp events.

Inferring surface energy fluxes using drone data assimilation in large eddy simulations

Abstract. Spatially representative estimates of surface energy exchange from field measurements are required for improving and validating Earth system models and satellite remote sensing algorithms. The scarcity of flux measurements can limit understanding of ecohydrological responses to climate warming, especially in remote regions with limited infrastructure. Direct field measurements often apply the eddy covariance method on stationary towers, but recently, drone-based measurements of temperature, humidity, and wind speed have been suggested as a viable alternative to quantify the turbulent fluxes of sensible (H) and latent heat (LE). A data assimilation framework to infer uncertainty-aware surface flux estimates from sparse and noisy drone-based observations is developed and tested using a turbulence-resolving large eddy simulation (LES) as a forward model to connect surface fluxes to drone observations. The proposed framework explicitly represents the sequential collection of drone data, accounts for sensor noise, includes uncertainty in boundary and initial conditions, and jointly estimates the posterior distribution of a multivariate parameter space. Assuming typical flight times and observational errors of light-weight, multi-rotor drone systems, we first evaluate the information gain and performance of different ensemble-based data assimilation schemes in experiments with synthetically generated observations. It is shown that an iterative ensemble smoother outperforms both the non-iterative ensemble smoother and the particle batch smoother in the given problem, yielding well-calibrated posterior uncertainty with continuous ranked probability scores of 12 W m−2 for both H and LE, with standard deviations of 37 W m−2 (H) and 46 W m−2 (LE) for a 12 min vertical step profile by a single drone. Increasing flight times, using observations from multiple drones, and further narrowing the prior distributions of the initial conditions are viable for reducing the posterior spread. Sampling strategies prioritizing space–time exploration without temporal averaging, instead of hovering at fixed locations while averaging, enhance the non-linearities in the forward model and can lead to biased flux results with ensemble-based assimilation schemes. In a set of 18 real-world field experiments at two wetland sites in Norway, drone data assimilation estimates agree with independent eddy covariance estimates, with root mean square error values of 37 W m−2 (H), 52 W m−2 (LE), and 58 W m−2 (H+LE) and correlation coefficients of 0.90 (H), 0.40 (LE), and 0.83 (H+LE). While this comparison uses the simplifying assumptions of flux homogeneity, stationarity, and flat terrain, it is emphasized that the drone data assimilation framework is not confined to these assumptions and can thus readily be extended to more complex cases and other scalar fluxes, such as for trace gases in future studies.

Distributional regression and its evaluation with the CRPS: Bounds and convergence of the minimax risk

The theoretical advances in the properties of scoring rules over the past decades have broadened the use of scoring rules in probabilistic forecasting. In meteorological forecasting, statistical postprocessing techniques are essential to improve the forecasts made by deterministic physical models. Numerous state-of-the-art statistical postprocessing techniques are based on distributional regression evaluated with the continuous ranked probability score (CRPS). However, the theoretical properties of such evaluations with the CRPS have solely considered the unconditional framework (i.e. without covariates) and infinite sample sizes. We extend these results and study the rate of convergence in terms of the CRPS of distributional regression methods. We find the optimal minimax rate of convergence for a given class of distributions and show that the k-nearest neighbor method and the kernel method reach this optimal minimax rate.

On the verification of ensemble precipitation forecasts over the Godavari River basin

The ensemble forecasts from Numerical Weather Prediction (NWP) models are considered as essential elements for operational hydrologic forecasting. However, these forecasts are burdened with significant inherent biases and cannot be used directly for hydrologic forecasting. Therefore, the present study examines the capability of ensemble precipitation forecasts obtained from two NWP models i.e., a 20-member ensemble from the National Center for Environmental Prediction (NCEP) and a 50-member ensemble from the European center for Medium-term Weather Forecasts (ECMWF). The skill of 70-member multi-model grand ensemble (MME) generated from the NCEP and ECMWF forecasts is also verified in this study. Furthermore, post-processing of the raw ensemble members was carried out using two methods (Quantile Mapping (QM) and Quantile Regression Forests (QRF)) in order to minimize the inherent biases. The analysis was performed over subbasins of an Indian river basin namely the Godavari River Basin. Here, a set of deterministic and probabilistic verification measures (forecast error box plots, correlation coefficient, Relative Mean Error, mean Continuous Ranked Probability Score, spread-skill relationship, rank histograms, reliability diagram, Area under Relative Operating Characteristic Curve) were employed to assess various quality attributes of the forecasts. The findings from the study suggests that QRF post-processed NCEP and MME forecasts are comparatively better than other forecasts in terms of all employed verification measures over all subbasins. The QRF post-processed forecasts were found to be superior than QM post-processed and raw forecasts over all subbasins. The adopted post-processing methods resulted in improved forecasts at shorter lead times. However, the skill of both raw and post-processed forecasts declines at higher lead times over all subbasins.

Probabilistic Forecast of Visibility at Gimpo, Incheon, and Jeju International Airports Using Weighted Model Averaging

In this study, weighted model averaging (WMA) was applied to calibrating ensemble forecasts generated using Limited-area ENsemble prediction System (LENS). WMA is an easy-to-implement post-processing technique that assigns a greater weight to the ensemble member forecast that exhibits better performance; it is used to provide probabilistic visibility forecasting in the form of a predictive probability density function for ensembles. The predictive probability density function is a mixture of discrete point mass and two-sided truncated normal distribution components. Observations were obtained at Gimpo, Incheon, and Jeju International Airports, and 13 ensemble member forecasts were obtained using LENS, for the period of December 2018 to June 2019. Prior to applying WMA, a reliability analysis was conducted using rank histograms and reliability diagrams to identify the statistical consistency between the ensembles and the corresponding observations. The WMA method was then applied to each raw ensemble model, and a weighted predictive probability density function was proposed. Performances were evaluated using the mean absolute error, the continuous ranked probability score, the Brier score, and the probability integral transform. The results showed that the proposed method provided improved performance compared with the raw ensembles, indicating that the raw ensembles were well calibrated using the predicted probability density function.

A Gramian angular field-based data-driven approach for multiregion and multisource renewable scenario generation

Scenario generation is a pivotal method for providing system operators with a reasonable quantity of power scenarios that are capable of reflecting uncertainties and spatiotemporal processes to make exact and effective decisions for power systems. Aiming at improving the forecasting performance of renewable generation and capturing uncertainty as well as dependency over renewable site groups in different regions, this paper proposes a data-driven approach for parallel scenario generation. To capture the complex spatiotemporal dynamics of renewable energy sources (RESs), the proposed approach utilizes Gramian angular field (GAF) to process time sequences and constructs style-based super-resolution models that correspond with the idea of multi-model ensembles. Thereafter, a two-stage stochastic optimization strategy is adopted to accomplish scenario forecasting using point forecasts and historical error information as input. Based on two real-world datasets from the National Renewable Energy Laboratory (NREL) and the Belgian transmission operator ELIA, the effectiveness of the proposed approach is verified by methods including statistical analysis, spatiotemporal correlations, power system scheduling, and out-of-sample evaluations. Compared with three advanced benchmarks, the proposed approach has superior forecasting performance and spatiotemporal dynamic capture capability. At a 24-h lead time, the proposed model achieves continuous ranked probability scores (CRPSs) of 4–14% over the other models with consistent performance during the economic dispatching of actual power system operations.

Seamless streamflow forecasting at daily to monthly scales: MuTHRE lets you have your cake and eat it too

Abstract. Subseasonal streamflow forecasts inform a multitude of water management decisions, from early flood warning to reservoir operation. Seamless forecasts, i.e. forecasts that are reliable and sharp over a range of lead times (1–30 d) and aggregation timescales (e.g. daily to monthly) are of clear practical interest. However, existing forecast products are often non-seamless, i.e. developed and applied for a single timescale and lead time (e.g. 1 month ahead). If seamless forecasts are to be a viable replacement for existing non-seamless forecasts, it is important that they offer (at least) similar predictive performance at the timescale of the non-seamless forecast. This study compares forecasts from two probabilistic streamflow post-processing (QPP) models, namely the recently developed seamless daily Multi-Temporal Hydrological Residual Error (MuTHRE) model and the more traditional (non-seamless) monthly QPP model used in the Australian Bureau of Meteorology's dynamic forecasting system. Streamflow forecasts from both post-processing models are generated for 11 Australian catchments, using the GR4J hydrological model and pre-processed rainfall forecasts from the Australian Community Climate and Earth System Simulator – Seasonal (ACCESS-S) numerical weather prediction model. Evaluating monthly forecasts with key performance metrics (reliability, sharpness, bias, and continuous ranked probability score skill score), we find that the seamless MuTHRE model achieves essentially the same performance as the non-seamless monthly QPP model for the vast majority of metrics and temporal stratifications (months and years). As such, MuTHRE provides the capability of seamless daily streamflow forecasts with no loss of performance at the monthly scale – the modeller can proverbially “have their cake and eat it too”. This finding demonstrates that seamless forecasting technologies, such as the MuTHRE post-processing model, are not only viable but also a preferred choice for future research development and practical adoption in streamflow forecasting.

Ensemble probabilistic wind power forecasting with multi-scale features

The uncertainty of wind power forecasting has a significant impact on the decision-making process of power system operators. Herein, to comprehensively characterize this uncertainty, a novel ensemble probabilistic forecasting model is developed in this study. First, the best model inputs were selected to forecast future wind power based on the value of maximum information coefficient, which measures both linear and nonlinear relationships between two random variables. Second, to extract sufficient and useful features from historical wind power data, a multi-scale feature extraction module based on average pooling, convolutional neural network, bidirectional long short-term memory, and attention mechanism was proposed. Third, five multi-scale deep density neural networks with different distribution-based loss functions and the proposed multi-scale feature extraction module were designed as base probabilistic forecasters to characterize the uncertainty from various aspects. Finally, an ensemble framework that combines five multi-scale deep density neural networks was built to determine the optimal ensemble weights for all base forecasters by simultaneously minimizing the pinball loss and continuous ranked probability score. The proposed ensemble model was implemented on four real-world wind power datasets. The results demonstrated the effectiveness of the proposed ensemble strategy and the designed multi-scale feature extraction module for probabilistic wind power forecasting.

Self-Attention-Based Machine Theory of Mind for Electric Vehicle Charging Demand Forecast

The popularization of electric vehicles (EVs) and charging stations has been threatening the distribution network’s reliability and efficiency. The prediction of EV charging demand can benefit the optimization of the operation of energy-transportation nexus and improve social welfare toward a low carbon future. In this article, a short-term probabilistic charging demand forecast model is proposed to estimate the quantiles of future charging demand of a charging station 15 min ahead, i.e., the self-attention-based machine theory of mind (SAMToM). The SAMToM has considered both the users’ historical charging habits (schedules) and the current trend of charging demand variation using the framework of machine theory of mind (MToM), and real-world-data-based case studies have verified its superiority in EV charging demand forecast over state-of-the-arts. Moreover, analyses show that the advantage of SAMToM lies in the following aspects. 1) The self-attention layers have mitigated the long-range forgetting in SAMToM. 2) The MToM architecture enables SAMToM to balance historical charging habits and current charging demand variation trends well. 3) Using a quantile forecast evaluation metric as the loss function, i.e., the continuous ranked probability score (CRPS), enables SAMToM to aim directly at the highest quality of forecasted quantiles.