Research Group

Possible Thesis Topics:

Both MSc and PhD theses are extensive pieces of work that take full-time commitment over several months/years. Choosing a thesis topic is a deeply personal decision for each student. However, here are some suggested research topics that the program is particularly well-equipped to supervise. Below is a list of general topics available for either MSc or PhD theses, organized by the main research themes in my area of expertise. It is expected that you are familiar with numerical analysis, optimization, the finite element method, functional analysis, and programming (using MATLAB, Python, etc.). Please feel free to contact me at yucelh[at]metu.edu.tr if any of the following topics are of interest to you. I am always on the lookout for motivated and talented MSc and PhD students interested in my research

  • Shape Optimization 
    • See, e.g., A level set-based structural optimization code using FEniCS by  Laurain, and Shape optimization using a level set based mesh evolution method: an overview and tutorial by Dapognya and Feppon.
  • 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.
  • Physics-Informed Neural Network
    • See, e.g., DeepXDE: A deep learning library for solving differential equations by Lu, Meng, Mao, and Karniadakis.

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:

  • Muhammed Çakır (PhD Graduate): Constitutive Modeling and Experimental Identification of Material Parameters of Viscoelastic Materials by Variable Order Non-Integer Derivatives, March 2025 (jointly supervised with Ergin Tönük, Department of Mechanical Engineering, METU).
  • 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).