**Math 577 Inference from Data and Models in Geosciences and
Engineering **

**Section 1**

**Spring 2005**

**Tu 2:30-3:45, Th 2:30-3:15 **

**Instructor:** Prof. Juan M. Restrepo

**Office:** Math 707

**Office Hours:** Th 3:30 - 4:30 in Math707. Other hours, by
appointment

**Phone: **621-4367

**E-mail: **restrepo@math.arizona.edu

**CLASS URL:
**http://www.physics.arizona.edu/~restrepo/577/577.html

Demand for scientists/engineers with skills in estimation, data assimilation, and inverse modeling is increasing. The kinds of problems in which this type of mathematics technology plays an important role come from economic and metereological forecasting, tomography in seismic and medical problems, optimization of parameters in models and in control devices.

This course is directed at making scientifically sensible deductions from the combination of observations with dynamics and kinematics represented, generically, as "models". The present course will focus on data assimilation, via Kalman, and Variational/Adjoint and their weakly nonlinear/non-Gaussian generalizations. We will also present particle methods and Monte Carlo methods that can handle the nonlinear/non-Gaussian cases. We will also cover singular value decomposition, regression, objective mapping.

The course can be considered a continuation of Prof. Richardson's course Geos/Ptys/Atmo 567, Inverse Methods in Geophysics

Book: Discrete Inverse and State Estimation Problems by Carl Wunsch

Pre-requisites: Calculus and linear algebra, basic elementary probability theory. The course will be non-rigorous and accessible to geoscience/hydrology/atmospheric science graduate students with a solid background in the above prerequisites.