Related papers: Data-driven uncertainty quantification for constra…

Nowadays, with the unprecedented penetration of renewable distributed energy resources (DERs), the necessity of an efficient energy forecasting model is more demanding than before. Generally, forecasting models are trained using observed…

We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected…

Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…

Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…

This paper introduces a new approach to generating sample paths of unknown Markovian stochastic differential equations (SDEs) using diffusion models, a class of generative AI methods commonly employed in image and video applications. Unlike…

This paper presents a new robust data-driven predictive control scheme for unknown linear time-invariant systems by using input-state-output or input-output data based on whether the state is measurable. To remove the need for the…

Offshore wind power (OWP) exhibits significant fluctuations under typhoon conditions, posing substantial challenges to the secure operation of power systems. Accurate forecasting of OWP is therefore essential. However, the inherent scarcity…

This paper studies the behavior of a strategic aggregator offering regulation capacity on behalf of a group of distributed energy resources (DERs, e.g. plug-in electric vehicles) in a power market. Our objective is to maximize the…

The integration of the global Photovoltaic (PV) market with real time data-loggers has enabled large scale PV data analytical pipelines for power forecasting and long-term reliability assessment of PV fleets. Nevertheless, the performance…

Parameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary nonlinear drift, and nonlinear diffusion is accomplished in combination with a non-parametric clustering methodology. Such a model-based…

For short-term solar irradiance forecasting, the traditional point forecasting methods are rendered less useful due to the non-stationary characteristic of solar power. The amount of operating reserves required to maintain reliable…

We study optimization for data-driven decision-making when we have observations of the uncertain parameters within the optimization model together with concurrent observations of covariates. Given a new covariate observation, the goal is to…

A large variety of sophisticated metaheuristic methods have been proposed for photovoltaic parameter extraction. Our aim is not to develop another metaheuristic method but to investigate two practically important yet rarely studied issues:…

In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and…

Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…

Long-horizon spatiotemporal prediction remains a challenging problem due to cumulative errors, noise amplification, and the lack of physical consistency in existing models. While diffusion models provide a probabilistic framework for…

Accurate estimation of solar irradiance is essential for reliable modelling of solar photovoltaic (PV) power production. In Ireland's highly variable maritime climate, where ground-based measurement stations are sparsely distributed,…

Sampling from Diffusion Models can alternatively be seen as solving differential equations, where there is a challenge in balancing speed and image visual quality. ODE-based samplers offer rapid sampling time but reach a performance limit,…

Rare events arising in nonlinear atmospheric dynamics remain hard to predict and attribute. We address the problem of forecasting rare events in a prototypical example, Sudden Stratospheric Warmings (SSWs). Approximately once every other…

We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. Given observations of the system state over time, we formulate the forecasting problem as sampling from the conditional distribution of…