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. If some of these topics interest you, then please feel free to contact me at yucelh[at]metu.edu.tr. I am always looking for motivated and talented MSc and Ph.D. students interested in my research.

  • Multi-level Monte Carlo Methods
    • Qualifications: implementation of finite element method in Matlab, knowledge of basic probability, 
    • See, e.g., Multilevel Monte Carlo methods by  Giles
  • Low Rank Approximations for Stochastic Partial Differential Equations
    • Qualifications:  implementation of finite element method in Matlab, knowledge of basic probability, numerical techniques for linear systems
    • See, e.g., Low-rank solution of unsteady diffusion equations with stochastic coefficients by Benner, Onwunta, Stoll
  • Deep Neural Network for Partial Differential Equations
    • Qualifications: programming expertise in python, numeric of PDEs
    • See, e.g., Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations by Raissi, Perdikaris, Karniadakis

Current MSc/Ph.D. Students:

  • Pelin Çiloğlu, Ph.D. student
    • Stochastic discontinuous Galerkin methods for optimal control problems with random coefficients
    • BS: Department of Mathematics, METU, 2015
  • 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
    • A numerical investigation of stochastic optimal control problems containing uncertain terms
    • MSc: Departments of Mechanical Engineering, METU, 2020
    • BS: Departments of Aerospace Engineering, METU, 2017
  • Korkut Anapa, MSc student
    • Sponsored by Arçelik A. Ş.
    • BS: Departments of Mechanical Engineering, METU, 1999

Past MSc/Ph.D. Students:

  • 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 (Advisor), Department of Computer Engineering, METU).
  • S. Can Toraman (MSc Graduate): Stochastic Momentum Methods for Optimal Control Problems Governed by Convection-Diffusion Equations with Uncertain Coefficients, January 2022.
  • Eda Oktay (MSc Graduate):  Reevaluating Spectral Partitioning for Unsymmetric Matrices, September 2020 (jointly supervised with Murat Manguoğlu (Advisor), 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 (Advisor), Department of Aerospace Engineering, METU).
  • 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).
  • Özgür M. Arslantaş (MSc Graduate): Multigrid Methods for Optimal Control Problems Governed by Convection-Diffusion Equations, 2015 (jointly supervised with Bülent Karasözen (Advisor), IAM, METU).

News:

Group Meetings: 

We regularly come together  to discuss the relevant topics in the scope of my research group.  Each  person give a talk related to his/her research interests. If you are interested to join the meetings, please feel free to contact me at yucelh[at]metu.edu.tr.