## Uncertainty Quantification Group

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 and statistical inference 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:**

- Pelin Çiloğlu
- Mustafa Kütük
- Eda Oktay
- M. Alp Üreten
- Hamdullah Yücel

**Projects:**

- Numerical Studies for Petrol and Gas Reservoir Problems (TUBITAK 1001: 119F022, August 01 2019 - August 01 2021)
- Numerical Studies of Korteweg-de Vries Equation with Random Input Data (Proje No: YÖP-705-2018-2820, May 29 2018 - May 29 2019)

**News:**

**March 26, 2019:**P. Çiloğlu, H. Yücel, "Discontinuous Galerkin Methods for Convection--Diffusion Equations with Random Coefficients", Submitted.**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 on Fridays, 10:30 to discuss the revelant topics in the scope of UC Research Group on** in S213**. Each person give a talk related to his/her research interests.

**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.