CS-6404 (CRN 16857)

Inverse Modeling

Spring 2009

Quick Info

In solving the foward problem one runs a model (based on the physical laws that govern the system) to predict (observations of) reality. In solving the inverse problem one uses observations of reality to infer the properties of the model. Inverse problems are tremendously important in many fields from biology to nuclear engineering to numerical weather prediction. They are challenging because the non-uniqueness of the solution and ill-conditioning.

This class introduces different computational methods for solving invrse problems. Topics discussed in the course include:

• Statistical estimation theory
• Linear regression, least squares, least-absolute-values, and minimax criteria
• Ill-conditioning and regularization techniques
• Differential equations and adjoint modeling
• Numerical optimization
• Ensemble-based methods

The following textbooks are useful:

• A. Tarantola: "Inverse Problem Theory and Methods for Model Parameter Estimation", SIAM, 2005. ISBN 0-89871-572-5 (available on-line).
• C.R. Vogel: ``Computational Methods for Inverse Problems'', SIAM, 2002. ISBN 0-89871-550-4.
• R.C. Aster, B. Borchers, and C.H. Thurber: "Parameter Estimation and Inverse Problems", Elsevier Academic Press, 2005. ISBN 0-12-065604-3.
• J. Nocedal, S.J. Wright: "Numerical Optimization", Second Edition, Springer Series in Operations Research, 2006. ISBN-10: 0-387-30303-0.
• C. T. Kelley: "Iterative Methods for Linear and Nonlinear Equations" and "Iterative Methods for Optimization" (available on-line from SIAM)

For detailed information please consult the syllabus ( PDF).

The final grade is based on homework (65%) and on typesetting a few lecture notes assigned to you (35%).

Homework