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:
For
detailed information please consult the syllabus ( PDF).
The final grade is based on homework
projects.
Project
1: Ensemble
Kalman filters.
Project
2: Particle
filters.
Project
3. 4D-Var.