Real-time state estimation and forecasting is critical for efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for probabilistic forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data, whereas in PhI-GPR, we compute the prior statistics by solving stochastic equations governing power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertain mechanical wind power. Here, we assume that the power-grid dynamic is governed by the swing equations, and we treat the unknown terms in the swing equations (specifically, the mechanical wind power) as random processes, which turns these equations into stochastic differential equations. We solve these equations for the mean and variance of the power grid system using the Monte Carlo simulations method. We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate both observed and unobserved states, including the mean behavior and associated uncertainty. For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR, with both forecasts being significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is much more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.
The output of solar power generation is significantly dependent on the available solar radiation. Thus, with the proliferation of PV generation in the modern power grid, forecasting of solar irradiance is vital for proper operation of the grid. To achieve an improved accuracy in prediction performance, this paper discusses a Bayesian treatment of probabilistic forecasting. The approach is demonstrated using publicly available data obtained from the Florida Automated Weather Network (FAWN). The algorithm is developed in Python and the results are compared with point forecasts, other probabilist…
University of Kaiserslautern（凯泽斯劳滕大学）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心（DFKI））
Time series forecasting is one of the challenging problems for humankind. Traditional forecasting methods using mean regression models have severe shortcomings in reflecting real-world fluctuations. While new probabilistic methods rush to rescue, they fight with technical difficulties like quantile crossing or selecting a prior distribution. To meld the different strengths of these fields while avoiding their weaknesses as well as to push the boundary of the state-of-the-art, we introduce ForGAN - one step ahead probabilistic forecasting with generative adversarial networks. ForGAN utilizes th…
We discuss an approach to probabilistic forecasting based on two chained machine-learning steps: a dimensional reduction step that learns a reduction map of predictor information to a low-dimensional space in a manner designed to preserve information about forecast quantities; and a density estimation step that uses the probabilistic machine learning technique of normalizing flows to compute the joint probability density of reduced predictors and forecast quantities. This joint density is then renormalized to produce the conditional forecast distribution. In this method, probabilistic calibrat…
Some real-world decision-making problems require making probabilistic forecasts over multiple steps at once. However, methods for probabilistic forecasting may fail to capture correlations in the underlying time-series that exist over long time horizons as errors accumulate. One such application is with resource scheduling under uncertainty in a grid environment, which requires forecasting electricity demand that is inherently noisy, but often cyclic. In this paper, we introduce the conditional approximate normalizing flow (CANF) to make probabilistic multi-step time-series forecasts when corr…
Forecasting imbalance prices is essential for strategic participation in the short-term energy markets. A novel two-step probabilistic approach is proposed, with a particular focus on the Belgian case. The first step consists of computing the net regulation volume state transition probabilities. It is modeled as a matrix computed using historical data. This matrix is then used to infer the imbalance prices since the net regulation volume can be related to the level of reserves activated and the corresponding marginal prices for each activation level are published by the Belgian Transmission Sy…
We propose a probabilistic mortality forecasting model that can be applied to derive forecasts for populations with regular and irregular mortality developments. Our model (1) uses rates of mortality improvement to model dynamic age patterns of mortality change and it can (2) optionally complement the mortality trend of a country of interest with that of at least one reference country. Retrospective mortality forecasts for British and Danish women from 1991 to 2011 suggest that our model can generate smaller forecast errors than other widely accepted approaches like, for instance, the Lee-Cart…
Weather forecasting is mostly based on the outputs of deterministic numerical weather forecasting models. Multiple runs of these models with different initial conditions result in forecast ensembles which is are used for estimating the distribution of future atmospheric variables. However, these ensembles are usually under-dispersive and uncalibrated, so post-processing is required. In the present work Bayesian Model Averaging (BMA) is applied for calibrating ensembles of temperature forecasts produced by the operational Limited Area Model Ensemble Prediction System of the Hungarian Meteorolog…
Prediction of various weather quantities is mostly based on deterministic numerical weather forecasting models. Multiple runs of these models with different initial conditions result ensembles of forecasts which are applied for estimating the distribution of future weather quantities. However, the ensembles are usually under-dispersive and uncalibrated, so post-processing is required. In the present work Bayesian Model Averaging (BMA) is applied for calibrating ensembles of wind speed forecasts produced by the operational Limited Area Model Ensemble Prediction System of the Hungarian Meteorolo…
GEIRI North America（北美电力科学研究院）；State Grid Jiangsu Electric Power Company Ltd.（国网江苏省电力有限公司）
Short-term load forecasting is a critical element of power systems energy management systems. In recent years, probabilistic load forecasting (PLF) has gained increased attention for its ability to provide uncertainty information that helps to improve the reliability and economics of system operation performances. This paper proposes a two-stage probabilistic load forecasting framework by integrating point forecast as a key probabilistic forecasting feature into PLF. In the first stage, all related features are utilized to train a point forecast model and also obtain the feature importance. In…
AI Institute（人工智能研究院）；Shanghai Jiao Tong University（上海交通大学）
Probabilistic time series forecasting involves estimating the distribution of future based on its history, which is essential for risk management in downstream decision-making. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks and the dependency is modeled by recurrent neural nets. We take the automatic relevance determination (ARD) view and devise a network to exploit the exogenous variables in addition to time series. In particular, our ARD network can incorporate the uncertai…
Probabilistic, hierarchically coherent forecasting is a key problem in many practical forecasting applications -- the goal is to obtain coherent probabilistic predictions for a large number of time series arranged in a pre-specified tree hierarchy. In this paper, we present an end-to-end deep probabilistic model for hierarchical forecasting that is motivated by a classical top-down strategy. It jointly learns the distribution of the root time series, and the (dirichlet) proportions according to which each parent time-series is split among its children at any point in time. The resulting foreca…
Stanford University（斯坦福大学）；Open Climate Fix（开放气候修复）；National Center for Atmospheric Research（美国国家大气研究中心）
Advancing probabilistic solar forecasting methods is essential to supporting the integration of solar energy into the electricity grid. In this work, we develop a variety of state-of-the-art probabilistic models for forecasting solar irradiance. We investigate the use of post-hoc calibration techniques for ensuring well-calibrated probabilistic predictions. We train and evaluate the models using public data from seven stations in the SURFRAD network, and demonstrate that the best model, NGBoost, achieves higher performance at an intra-hourly resolution than the best benchmark solar irradiance …
Probabilistic forecasting, i.e. estimating the probability distribution of a time series' future given its past, is a key enabler for optimizing business processes. In retail businesses, for example, forecasting demand is crucial for having the right inventory available at the right time at the right place. In this paper we propose DeepAR, a methodology for producing accurate probabilistic forecasts, based on training an auto regressive recurrent network model on a large number of related time series. We demonstrate how by applying deep learning techniques to forecasting, one can overcome many…
Technical University of Munich（慕尼黑工业大学）；Institute for Advanced Study, Technical University of Munich（慕尼黑工业大学高等研究院）；University of Cambridge（剑桥大学）
We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their predictions do not violate physical laws. This is achieved by introducing an additional loss function during the training of the ESNs, which penalizes non-physical predictions without the need of any additional training data. This approach is demonstrated on a chaotic Lorenz system, where the physics-informed ESNs improve the predictability horizon by about two Lyapun…
ProGen: Revisiting Probabilistic Spatial-Temporal Time Series Forecasting from a Continuous Generative Perspective Using Stochastic Differential Equations
Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
Point forecasting of univariate time series is a challenging problem with extensive work having been conducted. However, nonparametric probabilistic forecasting of time series, such as in the form of quantiles or prediction intervals is an even more challenging problem. In an effort to expand the possible forecasting paradigms we devise and explore an extrapolation-based approach that has not been applied before for probabilistic forecasting. We present a novel quantile Fourier neural network is for nonparametric probabilistic forecasting of univariate time series. Multi-step predictions are p…
Weather-Informed Probabilistic Forecasting and Scenario Generation in Power Systems
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology（工业与系统工程系，佐治亚理工学院）；AI Institute for Advances in Optimization（优化前沿人工智能研究所）
Toronto Metropolitan University（多伦多都会大学）；University of Toronto（多伦多大学）
Despite the high performance of neural network-based time series forecasting methods, the inherent challenge in explaining their predictions has limited their applicability in certain application areas. Due to the difficulty in identifying causal relationships between the input and output of such black-box methods, they rarely have been adopted in domains such as legal and medical fields in which the reliability and interpretability of the results can be essential. In this paper, we propose \model, a novel deep learning-based probabilistic time series forecasting architecture that is intrinsic…
Department of Computer Science, ETH Zürich（苏黎世联邦理工学院计算机科学系）；Department of Computer Science, ETH Zürich, Switzerland（苏黎世联邦理工学院计算机科学系）
We develop an effective generation of adversarial attacks on neural models that output a sequence of probability distributions rather than a sequence of single values. This setting includes the recently proposed deep probabilistic autoregressive forecasting models that estimate the probability distribution of a time series given its past and achieve state-of-the-art results in a diverse set of application domains. The key technical challenge we address is effectively differentiating through the Monte-Carlo estimation of statistics of the joint distribution of the output sequence. Additionally,…
We introduce a new category of multivariate conditional generative models and demonstrate its performance and versatility in probabilistic time series forecasting and simulation. Specifically, the output of quantile regression networks is expanded from a set of fixed quantiles to the whole Quantile Function by a univariate mapping from a latent uniform distribution to the target distribution. Then the multivariate case is solved by learning such quantile functions for each dimension's marginal distribution, followed by estimating a conditional Copula to associate these latent uniform random va…
Spatio-temporal forecasting has numerous applications in analyzing wireless, traffic, and financial networks. Many classical statistical models often fall short in handling the complexity and high non-linearity present in time-series data. Recent advances in deep learning allow for better modelling of spatial and temporal dependencies. While most of these models focus on obtaining accurate point forecasts, they do not characterize the prediction uncertainty. In this work, we consider the time-series data as a random realization from a nonlinear state-space model and target Bayesian inference o…
Parametric quantile regressions are a useful tool for creating probabilistic energy forecasts. Nonetheless, since classical quantile regressions are trained using a non-differentiable cost function, their creation using complex data mining techniques (e.g., artificial neural networks) may be complicated. This article presents a method that uses a new nearest neighbors quantile filter to obtain quantile regressions independently of the utilized data mining technique and without the non-differentiable cost function. Thereafter, a validation of the presented method using the dataset of the Global…
We present a methodology for probabilistic load forecasting that is based on lasso (least absolute shrinkage and selection operator) estimation. The model considered can be regarded as a bivariate time-varying threshold autoregressive(AR) process for the hourly electric load and temperature. The joint modeling approach incorporates the temperature effects directly, and reflects daily, weekly, and annual seasonal patterns and public holiday effects. We provide two empirical studies, one based on the probabilistic load forecasting track of the Global Energy Forecasting Competition 2014 (GEFCom20…
Bigo Inc.（Bigo公司）；Beihang University（北京航空航天大学）；IBM China CIC（IBM中国创新中心）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
We present a probabilistic forecasting framework based on convolutional neural network for multiple related time series forecasting. The framework can be applied to estimate probability density under both parametric and non-parametric settings. More specifically, stacked residual blocks based on dilated causal convolutional nets are constructed to capture the temporal dependencies of the series. Combined with representation learning, our approach is able to learn complex patterns such as seasonality, holiday effects within and across series, and to leverage those patterns for more accurate for…
Sharif University of Technology（谢里夫理工大学）；Institute of Science and Technology Austria (IST Austria)（奥地利科学技术研究所（IST Austria））
We introduce a spatio-temporal convolutional neural network model for trajectory forecasting from visual sources. Applied in an auto-regressive way it provides an explicit probability distribution over continuations of a given initial trajectory segment. We discuss it in relation to (more complicated) existing work and report on experiments on two standard datasets for trajectory forecasting: MNISTseq and Stanford Drones, achieving results on-par with or better than previous methods.
Probabilistic Forecasting with Generative Networks via Scoring Rule Minimization
University of Oxford（牛津大学）；Southern University of Science and Technology（南方科技大学）；University of Warwick（华威大学）；European Centre for Medium-Range Weather Forecasts（欧洲中期天气预报中心）
Probabilistic forecasting consists in predicting a distribution of possible future outcomes. In this paper, we address this problem for non-stationary time series, which is very challenging yet crucially important. We introduce the STRIPE model for representing structured diversity based on shape and time features, ensuring both probable predictions while being sharp and accurate. STRIPE is agnostic to the forecasting model, and we equip it with a diversification mechanism relying on determinantal point processes (DPP). We introduce two DPP kernels for modeling diverse trajectories in terms of…
Benchmarking Physics-Informed Time-Series Models for Operational Global Station Weather Forecasting
Department of Computer Science and Engineering, Hong Kong University of Science and Technology, Hong Kong SAR China（香港科技大学计算机科学与工程系）；Department of Computer Science and Engineering, Southern University of Science and Technology, Shenzhen, China（南方科技大学计算机科学与工程系）；School of Computer and Information Sciences, University of Newcastle, Newcastle, Australia（新castle大学计算机与信息科学学院）；Hangzhou Innovation Institute of Beihang University, Hangzhou, China（北京航空航天大学杭州创新研究院）；Shanghai Artificial Intelligence Laboratory, Shanghai, China（上海人工智能实验室）
Artificial Intelligence Department Universidad Nacional de Educación a Distancia — UNED（西班牙马德里开放大学（UNED）人工智能系）
High concentration episodes for NO$_2$ are increasingly dealt with by authorities through traffic restrictions which are activated when air quality deteriorates beyond certain thresholds. Foreseeing the probability that pollutant concentrations reach those thresholds becomes thus a necessity. Probabilistic forecasting is a family of techniques that allow for the prediction of the expected distribution function instead of a single value. In the case of NO$_2$, it allows for the calculation of future chances of exceeding thresholds and to detect pollution peaks. We thoroughly compared 10 state o…
Middle-term horizon (months to a year) power consumption prediction is a main challenge in the energy sector, in particular when probabilistic forecasting is considered. We propose a new modelling approach that incorporates trend, seasonality and weather conditions, as explicative variables in a shallow Neural Network with an autoregressive feature. We obtain excellent results for density forecast on the one-year test set applying it to the daily power consumption in New England U.S.A.. The quality of the achieved power consumption probabilistic forecasting has been verified, on the one hand, …
University of Patras（帕特雷大学）；Roma Tre University（罗马第三大学）；National Technical University of Athens（雅典国立技术大学）
Machine and statistical learning algorithms can be reliably automated and applied at scale. Therefore, they can constitute a considerable asset for designing practical forecasting systems, such as those related to urban water demand. Quantile regression algorithms are statistical and machine learning algorithms that can provide probabilistic forecasts in a straightforward way, and have not been applied so far for urban water demand forecasting. In this work, we aim to fill this gap by automating and extensively comparing several quantile-regression-based practical systems for probabilistic one…
We present a simple quantile regression-based forecasting method that was applied in a probabilistic load forecasting framework of the Global Energy Forecasting Competition 2017 (GEFCom2017). The hourly load data is log transformed and split into a long-term trend component and a remainder term. The key forecasting element is the quantile regression approach for the remainder term that takes into account weekly and annual seasonalities such as their interactions. Temperature information is only used to stabilize the forecast of the long-term trend component. Public holidays information is igno…
Time-series is ubiquitous across applications, such as transportation, finance and healthcare. Time-series is often influenced by external factors, especially in the form of asynchronous events, making forecasting difficult. However, existing models are mainly designated for either synchronous time-series or asynchronous event sequence, and can hardly provide a synthetic way to capture the relation between them. We propose Variational Synergetic Multi-Horizon Network (VSMHN), a novel deep conditional generative model. To learn complex correlations across heterogeneous sequences, a tailored enc…
Budapest University of Technology and Economics（布达佩斯技术与经济大学）
Energy price forecasting is a relevant yet hard task in the field of multi-step time series forecasting. In this paper we compare a well-known and established method, ARMA with exogenous variables with a relatively new technique Gradient Boosting Regression. The method was tested on data from Global Energy Forecasting Competition 2014 with a year long rolling window forecast. The results from the experiment reveal that a multi-model approach is significantly better performing in terms of error metrics. Gradient Boosting can deal with seasonality and auto-correlation out-of-the box and achieve …
Florida Atlantic University（佛罗里达大西洋大学）；Harbor Branch Oceanographic Institute, Florida Atlantic University（佛罗里达大西洋大学海港分校海洋学研究所）
According to the National Academies, a weekly forecast of velocity, vertical structure, and duration of the Loop Current (LC) and its eddies is critical for understanding the oceanography and ecosystem, and for mitigating outcomes of anthropogenic and natural disasters in the Gulf of Mexico (GoM). However, this forecast is a challenging problem since the LC behaviour is dominated by long-range spatial connections across multiple timescales. In this paper, we extend spatiotemporal predictive learning, showing its effectiveness beyond video prediction, to a 4D model, i.e., a novel Physics-inform…
The problem of probabilistic forecasting and online simulation of real-time electricity market with stochastic generation and demand is considered. By exploiting the parametric structure of the direct current optimal power flow, a new technique based on online dictionary learning (ODL) is proposed. The ODL approach incorporates real-time measurements and historical traces to produce forecasts of joint and marginal probability distributions of future locational marginal prices, power flows, and dispatch levels, conditional on the system state at the time of forecasting. Compared with standard M…
The reliable estimation of forecast uncertainties is crucial for risk-sensitive optimal decision making. In this paper, we propose implicit generative ensemble post-processing, a novel framework for multivariate probabilistic electricity price forecasting. We use a likelihood-free implicit generative model based on an ensemble of point forecasting models to generate multivariate electricity price scenarios with a coherent dependency structure as a representation of the joint predictive distribution. Our ensemble post-processing method outperforms well-established model combination benchmarks. …
The exponential growth of renewable energy capacity has brought much uncertainty to electricity prices and to electricity generation. To address this challenge, the energy exchanges have been developing further trading possibilities, especially the intraday and balancing markets. For an energy trader participating in both markets, the forecasting of imbalance prices is of particular interest. Therefore, in this manuscript we conduct a very short-term probabilistic forecasting of imbalance prices, contributing to the scarce literature in this novel subject. The forecasting is performed 30 minut…
