CS-6404: Inverse Modeling 
Instructor: Adrian Sandu, Computer Science

An inverse problem is the task (often encountered in science and
engineering) where the model state, or values of some model parameter(s),
must be obtained from the observed data. Applications include  ocean and
atmospheric sciences (find the most likely state given local observations
of wind fields, currents, temperatures, etc.), geophysical prospecting
(given a signal and an unknown obstacle, what does the obstacle look
like?), industrial applications (find the fluid flows from only the
boundary measurements), medical diagnosis (find out something about the
inside of a body from measurements only taken on the outside), etc.

In this class we discuss computational approaches for solving
inverse problems. The problem formulation will be developed based on
a description of uncertainties. Difficulties like ill-conditioning or
non-unique solutions will be highlighted, and regularization techniques
will be discussed to alleviate these difficulties. Computational tools
discussed include both variational and Monte Carlo approaches. Variational
techniques will include an in-depth discussion of numerical optimization
methods and adjoint modeling. Monte Carlo approaches include ensemble
Kalman and particle filters.