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Goals of the course: This course is an introduction to model calibration and the optimization technology used for model calibration. We will cover the following topics
- Review of probability concepts: random variables, probability distribution, law of large numbers, multivariate distribution, covariance matrix, Bayesian inference, examples
- Review of linear least squares: theory, computational methods, implementation, examples
- Kalman filtering: derivation, implementation, examples
- Computing gradients and Jacobians: sensitivities, adjoints, automatic differentiation
- Nonlinear least squares: theory, computational methods, implementation, examples
- Monte Carlo methods: pseudo random numbers, Monte Carlo integration, variance reduction, implementation, examples
- Optimization without derivatives: Nelder-Meade, implicit filtering
- Ensemble Kalman filtering: theory, computational methods, implementation, examples
- Examples
Grade: will be determined by the completion of a individual project (to be discussed with the instructors) to be presented in class.
Notes: the instructors will make their notes available
Office hours: TBA
Contact info:
- Pierre Gremaud, Dept. of Math, NCSU, Raleigh, NC 27695-8205, phone: 919-515-3085, fax: 919-515-1636, email: gremaud@ncsu.edu
- Tim Kelley, Dept. of Math, NCSU, Raleigh, NC 27695-8205, phone: 919-515-7163, fax: 919-515-1636, email: tim_kelley@ncsu.edu