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Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential…

We consider the numerical approximation of stochastic partial differential equations (SPDEs) based models for a quasi-periodic climate pattern in the tropical Pacific Ocean known as El Ni\~no phenomenon. We show that for these models the…

We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…

Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…

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…

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…

Accurate short-term wind speed forecasting is needed for the rapid development and efficient operation of wind energy resources. This is, however, a very challenging problem. Although on the large scale, the wind speed is related to…

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,…

Electricity networks are vulnerable to weather damage, with severe events often leading to faults and power outages. Timely forecasts of fault occurrences, ranging from nowcasts to several days ahead, can enhance preparedness, support…

Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…

The transition from conventional methods of energy production to renewable energy production necessitates better prediction models of the upcoming supply of renewable energy. In wind power production, error in forecasting production is…

Weather forecasting remains a crucial yet challenging domain, where recently developed models based on deep learning (DL) have approached the performance of traditional numerical weather prediction (NWP) models. However, these DL models,…

We study a smart grid with wind power and battery storage. Traditionally, day-ahead planning aims to balance demand and wind power, yet actual wind conditions often deviate from forecasts. Short-term flexibility in storage and generation…

Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…

Effective multivariate time series forecasting often benefits from accurately modeling complex inter-variable dependencies. However, existing attention- or graph-based methods face three key issues: (a) strong temporal self-dependencies are…

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…

Wind power forecasting has drawn increasing attention among researchers as the consumption of renewable energy grows. In this paper, we develop a deep learning approach based on encoder-decoder structure. Our model forecasts wind power…

The paper presents a spatio-temporal wind speed forecasting algorithm using Deep Learning (DL)and in particular, Recurrent Neural Networks(RNNs). Motivated by recent advances in renewable energy integration and smart grids, we apply our…

In many scientific fields, the generation and evolution of data are governed by partial differential equations (PDEs) which are typically informed by established physical laws at the macroscopic level to describe general and predictable…

Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE…