Research Group

Possible Thesis Topics:

Both MSc and PhD theses are extensive pieces of work that take full-time commitment over several months/years. They are also deeply personal decisions by each student. Here are nevertheless some suggestions for possible research topics, which the program is particularly qualified to supervise. In the following, a list of general topics that are available for either MSc or PhD thesis is provided. The topics are organized by general research themes in my research area. It is expected to you are familiar  to numerical analysis, optimization, finite element method, functional analysis, and programming (with matlab, phyton, C++, etc.). If some of these topics interest you, then please feel free to contact me at yucelh[at] I am always looking for motivated and talented MSc and Ph.D. students interested in my research. 

  • Multi-level Monte Carlo Methods
    • See, e.g., Multilevel Monte Carlo methods by  Giles
  • Low Rank Approximations for Stochastic Partial Differential Equations
    • See, e.g., Low-rank solution of unsteady diffusion equations with stochastic coefficients by Benner, Onwunta, Stoll
  • Risk-Averse PDE-Constrained Optimization Problems
    • See, e.g., Risk–averse PDE-constrained optimization using the conditional value-at-risk by  Kouri and Surowiec,  and Optimization methods for large-scale machine learning by Bottou,  Curtis, and  Nocedal.

Current MSc/Ph.D. Students:

  • Mustafa Kütük, Ph.D. student
    • Deep Neural Network for Stochastic Partial Differential Equations
    • MSc: Departments of Electrical and Electronics Engineering, METU, 2018
    • BS: Departments of Electrical and Electronics Engineering, Dokuz Eylül University, 2014
  • Oğuz Han Altıntaş, Ph.D. student
    • Stochastic Approximation Methods for PDE-Constrained Optimization Problems Containing Uncertain Terms
    • MSc: Departments of Mechanical Engineering, METU, 2020
    • BS: Department of Aerospace Engineering, METU, 2017

Past MSc/Ph.D. Students:

     As Advisor:

  • Korkut Anapa (MSc Graduate): A Strategy Based on Statistical Modelling and Multi-Objective Optimization to Design a Dishwasher Cleaning Cycle, December 2023 (jointly supervised with Songül Bayraktar (Co-Advisor), Arçelik A.Ş.).
  • Pelin Çiloğlu (PhD Graduate): Stochastic Discontinuous Galerkin Methods for PDE-Based Models with Random Coefficients, June 2023.
  • S. Can Toraman (MSc Graduate): Stochastic Momentum Methods for Optimal Control Problems Governed by Convection-Diffusion Equations with Uncertain Coefficients, January 2022.
  • Mehmet Alp Üreten (MSc Graduate): Numerical Studies of Korteweg-de Vries Equation with Random Input Data, September 2018 (jointly supervised with Ömür Uğur (Co-Advisor),  IAM, METU).

      As Co-Advisor:

  • C. Deniz Çam (MSc Graduate): Multiple Connectivity Approach to Network Formation Games, December 2023 (jointly supervised with Esma Gaygısız, Department of Economics, METU).
  • H. Avni Yaşar (MSc Graduate): Comparison of Artificial Neural Network-Based and Adaptive Quadratic Neural Network-Based Multi-Fidelity Algorithms for Buckling Load Prediction of Stiffened Panels, April 2023 (jointly supervised with Ercan Gürses, Department of Aerospace Engineering, METU).
  • H. Burak Bayrak (MSc Graduate): Competing Labels: A Heuristic Approach to Pseudo-Labeling in Deep Semi-Supervised Learning, February 2022 (jointly supervised with Şeyda Bolelli Ertekin, Department of Computer Engineering, METU).
  • Eda Oktay (MSc Graduate): Reevaluating Spectral Partitioning for Unsymmetric Matrices, September 2020 (jointly supervised with Murat Manguoğlu, Department of Computer Engineering, METU).
  • Halil Kaya (PhD Graduate): Development of a Discrete Adjoint-Based Aerodynamic Shape optimization for Natural Laminar Flows, August 2020 (jointly supervised with İ. Hakkı Tuncer, Department of Aerospace Engineering, METU).
  • Özgür M. Arslantaş (MSc Graduate): Multigrid Methods for Optimal Control Problems Governed by Convection-Diffusion Equations, June 2015 (jointly supervised with Bülent Karasözen, IAM, METU).