Welcome to the Uncertainty Quantification Group, in the Institute of Applied Mathematics at METU.

Uncertainty quantification (UQ) is a modern inter-disciplinary science that cuts across traditional research groups and combines statistics, numerical analysis and computational applied mathematics. When we attempt to simulate complex real-world phenomena, e.g., fluid dynamics, climate science, chemically reacting systems, oil field research, the price of stock pricing, using mathematical and computer models, there is almost always uncertainty in our predictions.  The objective is usually that of propagating quantitative information on the data through a computation to the solution. Our research focuses on advancing fundamental computational methodology for UQ  in complex physical systems.

The aim of this research group is to answer the following core questions?

  • How to quantify confidence in computational predictions?
  • How to build or refine models of complex physical processes from indirect and limited observations?
  • What information is needed to drive inference, design, and control?
  • How to calibrate and validate our computational models?

In classical setting we solve partial differential equations (PDEs)  for a given sets of input data such as material properties, domain geometries, boundary  and intial conditions, forcing terms. However, in real-life applications, it is not possible to obtain all this information due to the limited information. If the inputs to the systems under consideration are uncertain, we require mathematical techniques that propagate this uncertainty to the output quantities of interest and methods for computing probabilities of events rather than specific solutions. Our current research includes investigating the numerical solution of partial differential equations (PDEs) with random input data, especially convection dominated problems, for a range of linear and non-linear flow problems.

Team Members:



Lecture Series:  

  • Low-Rank Approximatian: In this lecture series,  we discuss theoretical foundations of low-rank approximation and applications in engineering, scientific computing, data analysis, ... where low-rank approximation plays a central role. We will follow the lecture notes of Danie Kressner.
    • February  17, 2020 (15:30-16:30) : Hamdullah Yücel 
    • February  20, 2020 (16:00-17:00) : Pelin Çiloğlu
    • March 02, 2020 (15:30-16:30): M. Alp Üreten
    • March 05, 2020 (15:00-16:00): Eda Oktay

Group Meetings: Since February 06, 2019, we regularly come together on Thursdays, 14:00 to discuss the revelant topics in the scope of UC Research Group on  in S212.  Each  person give a talk related to his/her research interests. If you are interested, please feel free to join the meetings.

  • March 05, 2020: M. Alp Üreten, "Multilevel Monte Carlo Analysis for Optimal Control of Elliptic PDEs with Random Coefficients"
  • February 20, 2020: Eda Oktay, " Iterative Solvers for the Stochastic Finite Element Method"
  • February 13, 2020: Pelin Çiloğlu, "A Low-Rank Solver for the Navier-Stokes Equations with Uncertain Viscosity"
  • February 06, 2020: Mustafa Kütük, "An Energy Approach to the Solution of Partial Differential Equation via Machine/Deep Learning"
  • December 20, 2019: M. Alp Üreten, "Defect-Deferred Correction Methods for Time Dependent Problems  "
  • December 06, 2019: Pelin Çiloğlu, "Low-Rank Solution of Unsteady Diffusion Equations with Stochastic Coefficients"
  • November 29, 2019: Saliha Yıldırım,   "Numerical Techniques for Advective Cahn-Hilliard Equations"
  • November 22, 2019: Gizem Yıldız,  "Numerical Techniques for Advective Allen-Cahn Equations"
  • November 15, 2019: Sıtkı Can Toraman,  "Kernel Principal Component Analysis for Stochastic Input Model Generation "
  • November 08, 2019: Mustafa Kütük,  "DEEPXDE: A Deep Learning Library for Solving Differential Equations"
  • November 01, 2019: Eda Oktay,  "Solvers and Precondtioners based on Gauss-Seidel and Jacobi Algorithms for Non-symmetric Stochastic Galerkin System of Equations"
  • October 25, 2019: Pelin Çiloğlu, "Optimal Control of Elliptic PDEs with Random Coefficients"
  • October 18, 2019: M. Alp Üreten,  "Monte Carlo and Multilevel Monte Carlo Methods "
  • August 02, 2019: Mustafa Kütük, "Simulator Free Solution of High dimensional Stochastic Elliptic Partial Differential Equations using Deep Neural Networks"
  • July   19, 2019: Mustafa Kütük, "Deep Learning: An Introduction for Applied Mathematicians: Part II"
  • June  28, 2019: Pelin Çiloğlu, "Ensemble Time-Stepping Algorithm for the Convection-Diffusion Equation with Random Diffusivity"
  • June  21, 2019: Mustafa Kütük, "Deep Learning: An Introduction for Applied Mathematicians: Part I"
  • June  14, 2019: M. Alp Üreten, "Further Analysis of Multilevel Monte Carlo Methods for Elliptic PDEs with Random Coefficients"
  • May    30, 2019: Pelin Çiloğlu, "A Domain Decomposition Model Reduction Method for Linear Convection Diffusion Equations with Random Coefficients"
  • May    30, 2019: Eda Oktay, " Graph Partitioning Techniques"
  • May    10, 2019: Ertuğrul Umut Yıldırım, "Numerical Analysis of Stochastic Advection-Diffusion Equation via Karhunen-Loeve Expansion"
  • May    10, 2019: İsa Eren Yıldırım, "First-Arrival Traveltime Tomography based on the Adjoint-State Method"
  • May    03, 2019: M. Alp Üreten, "Finite Element Methods with MATLAB"
  • April   12, 2019: Bülent Karasözen "Quantification of Uncertainty"
  • April   05, 2019: Hamdullah Yücel, "PDE-constrained optimization"  
  • March 22, 2019: Mustafa Kütük, "Target Detection Algorithms"
  • March 15, 2019: M. Alp Üreten,  "Implementation of Multilevel Monte Carlo Methods" 
  • March 08, 2019: Pelin Çiloğlu,    "Preconditioning"
  • March 01, 2019: M. Alp Üreten,  "Introduction to Multilevel Monte Carlo Methods"

Prospective Students:

If you are interested in uncertainty quantification or for any other comments or questions, please feel free to contact me at yucelh[at]metu.edu.tr. We are always looking for motivated and talented  research members.  

Last Updated:
17/03/2020 - 00:38