相关论文: Data-driven uncertainty quantification for constra…
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…
Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…
We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
The simulation of stochastic wind loads is necessary for many applications in wind engineering. The proper orthogonal decomposition (POD)-based spectral representation method is a popular approach used for this purpose due to its…
Progressively applying Gaussian noise transforms complex data distributions to approximately Gaussian. Reversing this dynamic defines a generative model. When the forward noising process is given by a Stochastic Differential Equation (SDE),…
We report a data-parsimonious machine learning model for short-term forecasting of solar irradiance. The model inputs include sky camera images that are reduced to scalar features to meet data transmission constraints. The output irradiance…
In this paper, we study the following time-dependent stochastic differential equation (SDE) in ${\bf R}^d$: $$ d X_{t}= \sigma_t(X_{t-}) d Z_t + b_t(X_{t})d t, \quad X_{0}=x\in {\bf R}^d, $$ where $Z$ is a $d$-dimensioanl nondegenerate…
We propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents…
In this paper, we propose Stoch-IDENT, a novel framework for identifying stochastic partial differential equations (SPDEs) from observational data. Our method can handle linear and nonlinear high-order SPDEs driven by time-dependent Wiener…
Power systems engineers are actively developing larger power plants out of photovoltaics imposing some major challenges which include its intermittent power generation and its poor dispatchability. The issue is that PV is a variable…
Owing to the growing concern of global warming and over-dependence on fossil fuels, there has been a huge interest in last years in the deployment of Photovoltaic (PV) systems for generating electricity. The output power of a PV array…
Solar energy is one of the most promising renewable energy resources. Forecasting photovoltaic power generation is an important way to increase photovoltaic penetration. However, the difficulty in qualifying the uncertainty of PV power…
From an operational and planning perspective, it is important to quantify the impact of increasing penetration of photovoltaics on the distribution system. Most existing impact assessment studies are scenario-based where derived results are…
In this paper, we propose a novel conditional diffusion-based framework for multivariable time-series solar power forecasting. The proposed method reformulates temporal PV data as structured two-dimensional representations (images) using a…
In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects set-ups. We also allow the functional part associated with the drift…
In this paper, a short-term load forecasting approach based network reconfiguration is proposed in a parallel manner. Specifically, a support vector regression (SVR) based short-term load forecasting approach is designed to provide an…
Due to the stochastic nature of photovoltaic (PV) power generation, there is high demand for forecasting PV output to better integrate PV generation into power grids. Systematic knowledge regarding the factors influencing forecast accuracy…
We study a coupled system of controlled stochastic differential equations (SDEs) driven by a Brownian motion and a compensated Poisson random measure, consisting of a forward SDE in the unknown process $X(t)$ and a \emph{predictive…
Renewable resources are strongly dependent on local and large-scale weather situations. Skillful subseasonal to seasonal (S2S) forecasts -- beyond two weeks and up to two months -- can offer significant socioeconomic advantages to the…
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…