Uncertainty Quantification

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 idea of uncertainty quantification (UQ), i.e. quantifying the effects of uncertainty on the result of a computation, has attracted much interest in the last few years. 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?

Therefore, we run regular study groups every Thursday from 15:40 to 17:30  at S212 (If not specified before). In the study groups, we  follow the book titled “An Introduction to Computational Stochastic PDEs” by G. J. Lord, C. E. Powell and T. Shardlow. See the webpage of the book.

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.

The schedule of meeting is as follows:

Date Speaker Topics
November 16 Emre Akdogan Probability spaces and random variables
November 20 Abdulwahab Animoku Correlation and independence
Examples of Rd-valued random variables
Hilbert space-valued random variables
Convergence of random variables
November 30 Özenç Murat Mert Sums of random variables
Estimating the mean and variance of a random variable
Approximating multivariate Gaussian random variables
Random number generation(all section)
December 07 Rahym Salamov Introduction and Brownian motion
December 07 Eda Oktay Gaussian processes and the covariance function
Brownian Bridge, Fraction Brownian motion
December 14 Hamdullah Yücel White and coloured noise
Karhunen–Loève expansion
Regularity of stochastic processes
December 28 Pelin Çiloğlu Finite Element Method in 1D, Matlab Codes
January 4 Etkin Hasgül Stochastic  ODE, Ito Integral,
Numerical Methods for Ito Integral
Stratonovich Integral
January 11 Cansu Evcin Finite Element Method in 1D with Mixed BC, Matlab Codes
January 18 Alp Üreten Elliptic PDEs with Random Data