Stochastic Differential Equations for Quantifying Forecast Uncertainty and Application to Renewable Power Forecast Data


Project Description

The student will work on building stochastic forecast models. We propose to model wind and

solar power forecast errors using parametric stochastic differential equations (SDEs). This

approach has been applied in various works: (Elkantassi et al., 2017 and Møller et al., 2016)

for wind power and (Badosa et al., 2018) for solar power. These SDEs will describe the evolution

over time of wind and solar power forecast errors. By inferring the parameters of our SDEs,

we can construct several possible forecast scenarios that are crucial to the decision-making

process. To compute the SDEs' parameters, we will use historical power production and an available deterministic forecast provided by official sources. We will also introduce an adaptive stepping method to simulate the paths of our SDE. We apply our approach on data from Uruguay as the country has been a global leader in the renewable energy transition.

The outcome of this project will be a general framework for uncertainty quantification and scenario

generation. In particular, this framework will be useful to:

  • provide novel different parametric model forms for renewable power using probabilistic forecasts based on stochastic differential equations.
  • develop computationally efficient and mathematically rigorous methods for estimating the SDE model parameters.
  • quantify the uncertainty of the given physic based renewable power numerical forecasts.
  • compare systematically power numerical forecasts in terms of the available data.
Program - Applied Mathematics and Computer Science
Division - Computer, Electrical and Mathematical Sciences and Engineering
Field of Study - Stochastic Differential Equations; Computational Statistics, Numerical Analysis, Stochastic Optimal Control, energy system modeling and optimization; data-driven modeling; machine learning, non-convex optimization, uncertainty quantification.

About the

Raul F. Tempone

Professor, Applied Mathematics and Computational Science

Raul F. Tempone
Raul Tempone's research interests are in the mathematical foundation of computational science and engineering. More specifically, he has focused on a posteriori error approximation and related adaptive algorithms for numerical solutions of various differential equations, including ordinary differential equations, partial differential equations, and stochastic differential equations.

He is also interested in the development and analysis of efficient numerical methods for optimal control, uncertainty quantification and bayesian model calibration, validation and optimal experimental design. The areas of application he considers include, among others, engineering, chemistry, biology, physics as well as social science and computational finance.

Desired Project Deliverables

As the main project deliverable, we expect  a scientific report (eventually a research manuscript) including detailed description and analysis of the proposed methodology developed within the course of the internship and providing all numerical experiments to showcase the versatility of the proposed framework. 


The working environment  the student will use should include a GIT repository shared with the project collaborators in which he includes all project-related materials such as progress reports codes, figures, and important references from the literature to facilitate the supervision  task and communicate ideas more effectively.


We will meet weekly during the period of the project. The student is asked to work within a team that includes myself, an Associate Professor at Universidad De La Republica (Uruguay) and an Associate Professor at Paris 13 University.




Education in applied mathematics education and possibly experience in the field stochastic numerics. Experience with code development and software engineering skills, such as Matlab and/or Python.