ECE295, Data Assimilation and Inverse Problems, Spring 2015

Peter Gerstoft, 534-7768, gerstoft@ucsd.edu

We meet Wednesday from 5 to 6:20pm in HHS2305A

Text for first 5 classes: Parameter Estimation and Inverse Problems (2nd Edition) by Richard C. Aster, Brian Borchers and Clifford H. Thurber. here under UCSD license

Classes

1. 1 April, Intro; Linear discrete Inverse problems (Aster Ch 1 and 2) Slides
2. 8 April, SVD (Aster ch 2 and 3) Slides
3. 15 April, Regularization (ch 4) Slides
4. 22 April, Sparse methods Slides
5. 29 April, more on Sparse, no slides, we discussed this paper arXiv:1503.02339 ,
6. 6 May, Bayesian methods and Monte Carlo methods, Markov Chain Monte Carlo (ch 11) Slides
7. 13 May, Introduction to sequential Bayesian methods, Kalman Filter (KF) Slides
8. 20 May, Hidden Markov chains, Chapter 17 in Murphys "Machine Learning" (Nima Riahi)
9. 27 May, Markov Chains, Bayesian filtering, Data assimilation, Slides
10. 3 June, particle filter, review

1. 8 April: Hw 1: Download the matlab codes for the book (cd_5.3) from this website http://www.ees.nmt.edu/outside/courses/GEOP529_book.html. Run the 3 examples for chapter 2. Come to class with one question about the examples.
2. 15 April: SVD analysis: SVD homework from last year. You can also try replacing the matrix in the Shaw problem with the beamforming sensing matrix. The sensing matrix is available here .
3. 22 April, Regularization Sparse methods
4. 6 May , Monte Carlo integration
5. 13 May Sports teams
6. 20 May Kalman on ice. Use this GPS ice data.
7. 5 June: Kalman and Spectral estimation.

OLD

From 16 April all lectures will be in Spiess Hall 330

Peter Gerstoft, 534-7768, gerstoft@ucsd.edu

We meet Wednesday from 5 to 6:20pm

Text for first 5 classes: Parameter Estimation and Inverse Problems (2nd Edition) by Richard C. Aster, Brian Borchers and Clifford H. Thurber. here under UCSD license

Most engineering problems involve making inferences about the real world from noisy observations. We will address this problem for steady state as well as dynamic problems. We will focus on discrete problems. Data assimilation is a key ingredient for important applications, for example for numerical weather prediction and ocean state estimation, but it is also increasingly employed in medical and industrial applications. The methods will include inverse methods, tomography, sequential filters (Kalman and particle), and data assimilation. While the instructor's & textbook examples will be derived mostly from the physical sciences, students are encouraged to bring their own data sets for classroom discussion and in-depth analysis as part of their term papers. Problem sets and Matlab computer programming exercises form integral parts of the course.

Classes

1. 2 April, Intro; Linear discrete Inverse problems (Aster Ch 1) Slides
2. 9 April, SVD (Aster ch 2 and 3) Slides
3. 16 April, Regularization (ch 4) Slides
4. 23 April, Sparse methods (ch 7.2-7.3) Slides
5. 30 April, Bayesian methods and Monte Carlo methods (ch 11) Slides
6. 7 May, Markov Chain Monte Carlo (download from Mark Steyvers ) Slides
7. 14 May, (Caglar Yardim) Introduction to sequential Bayesian methods, Kalman Filter Slides
8. 21 May, Data assimilation, EnKF Slides
9. 28 May, EnKF, PF, Data assimilation Slides
10. 4 June, (Ganesh Gopalakrishnan) Ocean data assimilation using EnKF or 3DVar

1. Hw 1: Download the matlab codes for the book (cd_5.3) from this website http://www.ees.nmt.edu/outside/courses/GEOP529_book.html. Run the 3 examples for chapter 2. Come to class with one question about the examples. Due 9 April.
2. hw 2, 16 April, SVD ; read chapter one of Steyvers notes,
3. hw3, 23 April, Regularization
4. hw4, 30 April, Sparse problems
5. hw5, 7 May, Monte Carlo integration
6. hw6, 14 May, Metropolis algorithm (Steyvers problems 2.4.1-2.4.5); Metropolis-Hastings algorithm, (Steyvers problems 2.6.1-2.6.3).
7. hw7, 21 May, Kalman Filter
8. hw8, 28 May, Kalman Filter, EnKF
9. hw9, 4 June, evolution of tracking errors