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Elmongi Elbellili
A question that would not go away, a method that had to be built twice, and the hour in which all of it is defended in public.
“Continuous Time Simulation in a Discrete Event Framework using a Quantized State System Approach”
Three questions
Why this topic?
It began with something that bothered me and would not leave me alone. The field had an answer already, and I did not believe it.
What surprised you?
How often the interesting result was the one I was not looking for, and how long it took me to stop treating it as noise.
What happens after the defense?
Sleep, first. Then finding out whether what I learned survives outside the university.
In their words“At the start I thought I knew the answer. By the third year I knew I had not understood the question.”
About the thesis
Simulating complex dynamical systems is difficult when models are large, stiff, and discontinuous. Traditional numerical solvers are reliable, but they often face limitations in such settings. Quantized State System (QSS) methods offer an alternative integration paradigm: they update only variables whose values change, making them efficient in large stiff and discontinuous systems. In this thesis, I refine QSS techniques with new update formulations, improved cycle detection, and Jacobian‑based coefficient computation for better accuracy and speed. These advances are implemented in QuantizedSystemSolver.jl, an open‑source Julia package. Tests on continuous and hybrid models show that QSS methods perform robustly on large stiff systems and remain competitive across diverse discontinuous scenarios. The results highlight that solver efficiency depends on the combined effects of sparsity, stiffness, activity distribution, and event cost.
Selected work
Listed from the KU Leuven agenda.