ESR 5:
Ergys Çokaj

joined the THREAD project in June 2020

My name is Ergys Çokaj and I come from Albania. I have a Bachelor’s and a Master’s degree in Mathematics and Applications from the University of Camerino in Italy. In the last four years, I have worked on my PhD studies as part of the THREAD project, hosted by the Norwegian University of Science and Technology.

Reflecting on my journey with the THREAD project, I realise it has profoundly shaped my academic and professional trajectory. Beyond deepening my understanding of numerical analysis and highly flexible slender structures, THREAD has enriched me with collaborative research experiences, exposing me to diverse scientific approaches and perspectives. THREAD has provided me with advanced research training, transferable skills training and industrial workshops, which contributed to enriching my background as a scientist. The interdisciplinary nature of THREAD, with all the industrial challenges addressed, has prepared me for a possible future both in academia and industry.  A highlight of my PhD experience is the direct contact with industry during my internship at TechnipFMC, Lysaker and Kongsberg, Norway, where I worked on subsea systems, see link.

As the end of THREAD approaches, I realise that my guess from two years ago was right:  “… I think that when THREAD finishes, we will realise how much it has given to us … “, see link. I am indeed enormously grateful for being given the opportunity to grow professionally and personally with THREAD.

To know more about my career and research, check the following links: NTNU, GitHub and LinkedIn.

Ergys Çokaj, March 2024


Host Institution
Norwegian University of Science and Technology (Norway)
Supervisor
Brynjulf Owren
Description

Study implementation issues for Lie group integrators and invariant preserving integrators. Results will include: 1) Variable step size Lie group integrators with error control; 2) Invariant preserving schemes for mechanical systems evolving on Riemannian manifolds; 3) Model reduction applied to large dynamical systems on Lie groups and manifolds.

Expected Results

New software generation for Lie group integration to be used for concrete applications from THREAD. For Lie group integrators with stepwise updated local coordinates standard error control from integrators on linear spaces can be applied. There is no such direct reference to coordinate charts for composition based Lie group integrators making them more tricky to work with (order conditions for non-commutative spaces). As for integral preserving schemes the use of retractions will be essential, in particular efficient maps based on geodesics. For large dynamical systems on manifolds the methodology for reducing the dimension will follow ideas from shape analysis, collaboration with ESR4 is natural.

Secondments

planned at TechnipFMC (industrial partner), Friedrich Alexander University Erlangen-Nuremberg and Martin Luther University Halle-Wittenberg

associated with the Industrial Challenge

IC 9 Software development

Publications

PhD thesis

Ergys Çokaj (2024): Structure preserving and machine learning methods for mechanical systems. NTNU Norwegian University of Science and Technology, Department of Mathematical Sciences (IMF), see link

Articles in peer-reviewed scientific journals

  • Elena Celledoni, Ergys Çokaj, Andrea Leone, Sigrid Leyendecker, Davide Murari, Brynjulf Owren, Rodrigo Sato Martín de Almagro, Martina Stavole (2025): Neural networks for the approximation of Euler’s elastica; Computer Methods in Applied Mechanics and Engineering 435, 117584; DOI: 10.1016/j.cma.2024.117584, see also link
  • Ergys Çokaj, Halvor Gustad, Andrea Leone, Per Thomas Moe, Lasse Moldestad (2024): Supervised time series classification for anomaly detection in subsea engineering; Journal of Computational Dynamics 11, 376-408; DOI: 10.3934/jcd.2024019, see also link
  • Martin Arnold, Elena Celledoni, Ergys Çokaj, Brynjulf Owren, Denise Tumiotto (2024): B-stability of numerical integrators on Riemannian manifolds; Journal of Computational Dynamics 11, 92–107; DOI: 10.3934/jcd.2024002, see also link
  • Elena Celledoni, Ergys Çokaj, Andrea Leone, Davide Murari, Brynjulf Owren (2022): Lie group integrators for mechanical systems; International Journal of Computer Mathematics 99(1), 58–88; DOI: 10.1080/00207160.2021.1966772, see also link

Publications in conference proceedings

  • Elena Celledoni, Ergys Çokaj, Andrea Leone, Davide Murari, Brynjulf Owren (2022): Dynamics of the N-fold Pendulum in the Framework of Lie Group Integrators. In: Matthias Ehrhardt, Michael Günther (eds.): Progress in Industrial Mathematics at ECMI 2021. Mathematics in Industry, vol 39. Springer Cham, pp. 297–304; DOI: 10.1007/978-3-031-11818-0_39, see also link

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