Introduction to Uncertainty Quantification

General information

  • Instructor: Mohammad Motamed

  • Description: The behavior of many physical systems can be mathematically modeled by deterministic ordinary or partial differential equations (ODEs or PDEs). These models however differ from reality for two main reasons: 1) an intrinsic variability of the physical system (aleatoric uncertainty); and/or 2) our inability to accurately characterize all parameters of the mathematical model (epistemic uncertainty). Uncertainty is therefore a fundamental feature of physical systems and needs to be taken into account when studying complex systems. Examples appear in climate modeling, the description of flows in porous media, behavior of living tissues, combustion problems, deformation of composite materials, earthquake motions, etc. In order to understand the uncertainties inherent in the model, and often represented in a probabilistic setting, we need a process called “uncertainty quantification” (UQ).

    In this course we consider different types of ODEs/PDEs with stochastic input parameters (coefficients, forcing terms, initial/boundary conditions, etc.) and study various numerical techniques for solving both forward and inverse problems.

  • Background:

    • Required: Students should be comfortable with undergraduate mathematics and statistics, particularly calculus, linear algebra, differential equations, and basic probability. Experience writing and debugging computer programs is also required.
    • Recommended: Experience with mathematical/statistical computing, for example in Matlab or R, is preferred. Past exposure to numerical analysis and computation is a plus.

Homework assignments