# CS-6404 (CRN 91132)

# Computational data
assimilation: Inverse problems with differential equations

# Spring 2022

## 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 computational methods
for solving inverse problems constrained by differential equations. Topics
discussed in the course include:

- Review of probability theory,
estimation theory, Bayesian methods
- The Kalman filter and smoother
- Ensemble Kalman filters and
smoothers
- Particle filters and smoothers
- Variational methods: 3D-Var,
4D-Var, adjoint model construction, numerical optimization.

For
detailed information please consult the syllabus ( PDF).

The final grade is based on homework
projects.

## Homework

Project
1: Ensemble
Kalman filters.

Project
2: Particle
filters.

Project
3. 4D-Var.

sandu@cs.vt.edu
(Adrian Sandu)

http://www.cs.vt.edu/~asandu/Courses/CS6404/CS6404.html