Saifeddine Ben Naamia successfully defended his MSc thesis

 In a remarkable display of academic excellence, On June 9, 2023, Saifeddine Ben Naamia successfully defended his Msc. thesis entitled " Data   driven UQ for wind and solar production using SDE models with generalized diffusion coefficient and stochastic optimization

 Committee Chairperson:   

 Prof. Raúl Tempone, AMCS, KAUST

 Committee Members:

  Prof. Ajay Jasra, AMCS, KAUST

  Prof. Mohamed-Slim Alouini, AMCS, KAUST

 Abstract:

 In the first part of the thesis, we focus on the development of a generalized Itoˆ stochastic differential equation (SDE) model to assess the uncertainty of de- terministic forecasts when data are naturally constrained. By incorporating a time-dependent upper bound, we extend the Itoˆ Stochastic Differential Equation (SDE) framework to enable the path-wise evaluation of short-term forecast er- rors. This upper bound restricts the range of normalized observable historical data and forecasts, enhancing the accuracy of the evaluation process. In our study, we present a novel generalized SDE model that is nonlinear and time- inhomogeneous. To enhance the calibration accuracy, this model incorporates a diffusion term with two additional parameters that surpass the limitations of previous approaches, resulting in an improved quality of calibration, and is driven by both the forecast and an upper bound constraint. We use an iterative multi-stage optimization procedure to approximate the likelihood function and calibrate the SDE model parameters using stochastic optimization. We maxi- mize the likelihood using adaptive momentum and learning rates and improve the time of convergence by a factor of 90 to 100. We also introduce an adaptive time-stepping method to ensure that the numerical approximation of the process does not violate the natural bounds imposed by the physical and mathematical constraints of the modeled problem.

In the second part of the thesis, we focus on SDE modeling of electricity spot prices by implementing a mean-reverting jump-diffusion SDE with a constant diffusion term and a Poisson jump part. We develop a two-step iterative method to identify jumps present in the data and use maximum likelihood estimation to calibrate the model parameters. We also present a dataset of electricity spot prices and their forecast for Germany spanning from 2016 to 2018 to identify areas where the model may require further refinement to capture the underlying characteristics of electricity spot prices more comprehensively.

Biography:

Saifeddine Ben Naamia is a Ms/PhD Student at the Stochastic Numerics Research Group (STOCHNUM), guided by Professor Raul F. Tempone, at King Abdullah University of Science and Technology (KAUST). His research encompasses diverse fields, including Stochastic Differential Equations, Optimization, Data-driven modeling, Uncertainty quantification, and Stochastic Optimal Control. Saifeddine pursued a Master of Science in Applied Mathematics and Computational Sciences at KAUST, where he currently continues his studies. Prior to that, he earned a National Engineering Diploma in Multidisciplinary Engineering from École Polytechnique de Tunisie, Tunisia, and an Undergraduate Degree in Mathematics and Physics from the Preparatory Institute for Engineering Studies of Sfax, Tunisia. Throughout his early career, Saifeddine gained valuable experiences in different international research institutions. He was a Visiting Project Student at KAUST and a Visiting Student at RWTH Aachen University, Germany. Additionally, he worked as a Research Intern at Université Paris Dauphine-PSL, France.