Related papers: Data-driven uncertainty quantification for constra…
We develop a data-driven methodology based on parametric It\^{o}'s Stochastic Differential Equations (SDEs) to capture the real asymmetric dynamics of forecast errors. Our SDE framework features time-derivative tracking of the forecast,…
Probabilistic forecasts of renewable energy production provide users with valuable information about the uncertainty associated with the expected generation. Current state-of-the-art forecasts for solar irradiance have focused on producing…
The stochastic differential equation (SDE)-based random process models of volatile renewable energy sources (RESs) jointly capture the evolving probability distribution and temporal correlation in continuous time. It has enabled recent…
In this paper, a stochastic model with regime switching is developed for solar photo-voltaic (PV) power in order to provide short-term probabilistic forecasts. The proposed model for solar PV power is physics inspired and explicitly…
Spatio-temporal problems exist in many areas of knowledge and disciplines ranging from biology to engineering and physics. However, solution strategies based on classical statistical techniques often fall short due to the large number of…
We present a novel framework for spatiotemporal photovoltaic (PV) power forecasting and use it to evaluate the reliability, sharpness, and overall performance of seven intraday PV power nowcasting models. The model suite includes…
The rapid growth of weather-dependent renewable generation increases price volatility and imbalance penalty risk in power markets, creating the need for advanced quantitative trading strategies. We develop a data-driven continuous-time…
As renewable distributed energy resources (DERs) penetrate the power grid at an accelerating speed, it is essential for operators to have accurate solar photovoltaic (PV) energy forecasting for efficient operations and planning. Generally,…
Accurate and reliable prediction of Photovoltaic (PV) power output is critical to electricity grid stability and power dispatching capabilities. However, Photovoltaic (PV) power generation is highly volatile and unstable due to different…
This paper presents and evaluates the performance of an optimal scheduling algorithm that selects the on/off combinations and timing of a finite set of dynamic electric loads on the basis of short term predictions of the power delivery from…
This work presents a robust framework for quantifying solar irradiance variability and forecastability through the Stochastic Coefficient of Variation (sCV) and the Forecastability (F). Traditional metrics, such as the standard deviation,…
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
We introduce and test methods for the calibration of the diffusion term in Stochastic Partial Differential Equations (SPDEs) describing fluids. We take two approaches, one uses ideas from the singular value decomposition and the Biot-Savart…
We propose a novel problem formulation of continuous-time information propagation on heterogenous networks based on jump stochastic differential equations (SDE). The structure of the network and activation rates between nodes are naturally…
Surface solar irradiance (SSI) plays a crucial role in tackling climate change - as an abundant, non-fossil energy source, exploited primarily via photovoltaic (PV) energy production. With the growing contribution of SSI to total energy…
Accurate forecasting of spatiotemporal data remains challenging due to complex spatial dependencies and temporal dynamics. The inherent uncertainty and variability in such data often render deterministic models insufficient, prompting a…
We present a stochastic constrained output-feedback data-driven predictive control scheme for linear time-invariant systems subject to bounded additive disturbances. The approach uses data-driven predictors based on an extension of Willems'…