SC14-006: Spectral Methods for Uncertainty Propagation

Dr. Alireza Doostan, University of Colorado

Motivated by the recent growing interest in developing predictive computational models, this short course will provide a high-level introduction to spectral methods for the propagation of uncertainty in physical systems governed by partial and ordinary differential equations. A number of core topics of this four-hour short course will include:

• Why UQ in computational mechanics?
• Elements of uncertainty characterization via random variables (essential tools from probability and statistics)
• Monte Carlo (MC) and spectral approximation of stochastic functions (standard MC, polynomial expansion techniques)
• Deterministic sampling methods (collocation approaches) for spectral approximation of stochastic functions (tensor product and sparse grids and the associated approximation properties)
• Highlights of advanced UQ techniques and research opportunities (various model reduction methods)
• Motivating examples from solid/fluid mechanics 

It is anticipated that this short course will benefit graduate students and early career researchers broadly interested in the general area of computational sciences.