16.940: Numerical Methods for Stochastic Modeling and Inference

Offered Spring 2010, Spring 2012, Spring 2014, Fall 2015

Advanced introduction to numerical methods for treating uncertainty in computational simulation. Draws examples from a range of engineering and science applications, emphasizing systems governed by ordinary and partial differential equations. Uncertainty propagation and assessment: Monte Carlo methods, variance reduction, sensitivity analysis, adjoint methods, polynomial chaos and Karhunen-Loève expansions, and stochastic Galerkin and collocation methods. Interaction of models with observational data, from the perspective of statistical inference: Bayesian parameter estimation, statistical regularization, Markov chain Monte Carlo, sequential data assimilation and filtering, and model selection.

16.100: Aerodynamics

Offered Fall 2009, 2010, 2011; Fall 2013

Extends fluid mechanic concepts from Unified Engineering to aerodynamic performance of wings and bodies in sub/supersonic regimes. Subject generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Material may vary somewhat each year depending upon focus of design problem. Elementary usage of MATLAB and other computational tools expected.

16.90: Computational Methods in Aerospace Engineering

Offered Spring 2009, 2010, 2011

Introduction to computational techniques arising in aerospace engineering. Techniques include numerical integration of systems of ordinary differential equations; numerical discretization of partial differential equations; and probabilistic methods for quantifying the impact of variability. Specific emphasis will be given to finite volume methods in fluid mechanics, and energy and finite element methods in structural mechanics.


May 2018
Congratulations to Andrew Davis for successfully defending his PhD thesis!

February 2018
Congratulations to Xun Huan for accepting a tenure-track position at the University of Michigan!

September 2017
Congratulations to Olivier Zahm for accepting a permanent position at INRIA in Grenoble!

August 2017
Congratulations to Alessio Spantini for successfully defending his PhD thesis, "On the low-dimensional structure of Bayesian inference!"

June 2017
Congratulations to Rebecca Morrison for accepting a tenure-track position at the University of Colorado Boulder!

June 2017
Congratulations to Alex Gorodetsky for accepting a tenure-track position at the University of Michigan!

Feb 1, 2017
Congratulations to Ricardo Baptista and Ben Zhang for passing their PhD qualifying exams!

Sep 2, 2016
Congratulations to Alex Gorodetsky for successfully defending his PhD thesis!

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