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:

• September 12-14, 2022:  Pelin Çiloğlu attends Summer School-Uncertainty, Adaptivity, and Machine Learning in Augsburg.
• July 18-29, 2022: Mustafa Kütük attends CIMPA Summer School 2022, which focuses on Mathematical Methods in Data Analysis in Tirana.
• April 14, 2022: Pelin Çiloğlu gives a research talk, titled “Stochastic Discontinuous Galerkin Methods for Robust Deterministic Control of Convection Diffusion Equations with Uncertain Coefficients” in the SIAM Conference on Uncertainty Quantification (UQ22) (Virtual).
• April 05, 2022: Pelin Çiloğlu gives a research talk, titled “Solving Optimal Control Problems Containing Uncertain Coefficients with Stochastic Discontinuous Galerkin Methods” in the 17th Copper Mountain Conference On Iterative Methods (Virtual).
• March 21-25, 2022:  Pelin Çiloğlu attends  the annual SFB Spring School 2022 organized by SFB 1294-Data Assimilation in Postdam.
• January 06, 2022: S. Can Toraman successfully defends his Master thesis, titled “Stochastic Momentum Methods for Optimal Control Problems Governed by Convection-Diffusion Equations with Uncertain Coefficients”.
• November 19, 2021: S. Can Toraman and Hamdullah Yücel, “Stochastic momentum methods for optimal control problems containing uncertain inputs”, Submitted 2021.
• October 09,  2021: Pelin Çiloğlu and Hamdullah Yücel, “Stochastic discontinuous Galerkin methods with low-rank solvers for convection diffusion equations”, Accepted for Applied Numerical Mathematics.
• September 06, 2021: Pelin Çiloğlu and Hamdullah Yücel, “Stochastic discontinuous Galerkin methods for robust deterministic control of convection diffusion equations with uncertain coefficients”, Submitted 2021.
• September 07, 2021: Pelin Çiloğlu gives a research talk, titled “Stochastic Discontinuous Galerkin Methods with Low-Rank Solvers for Convection Diffusion Equations” in the Chemnitz FE Symposium 2021.
• September 10, 2019: Mustafa Kütük gives a research talk, titled “Hyperspectral Target Detection by using Superpixels and Signature Based Methods” in BEYOND 2019: Computational Science and Engineering Conference.
• September 10, 2019: Pelin Çiloğlu gives a research talk, titled “Discontinuous Galerkin Methods for Convection Diffusion Equations with Random Coefficients” in BEYOND 2019: Computational Science and Engineering Conference.
• October 21, 2018: Pelin Çiloğlu gives a research talk, titled “Discontinuous Galerkin Methods for Unsteady Convection Diffusion Equation with Random Coefficients” in BEYOND: Workshop on Computational Science and Engineering.
• September 24, 2018: Pelin Çiloğlu gives a research talk, titled “Unsteady Convection Diffusion Equation with Random Input Data” in the Chemnitz FE Symposium 2018.
• September 03, 2018: M. Alp Üreten successfully defends his Master thesis, titled “Numerical Studies of Korteweg-de Vries Equation with Random Input Data”.

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.