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News/Notice
- First class: Sep 13, 11-12
- Marking scheme: 5 assignments (each 15%), final project (25%)
- Important dates: First class on 09/13, Thanksgiving 10/11, Reading week 11/8-12, classes end on 12/08; Lecture dates: 09/13,15,20,22,27,29; 10/4,6,13,18,20,25,27; 11/1,3,15,17,22,24,29; 12/2,7,9
- Course Syllabus
Time
- Lectures: Monday/Wednesday 11-12, MP505
- Office hours: Monday 4:15-5:15 pm and Wednesday 2-3 pm
Lecturer
Instructor:
Qinya Liu
Office: MP 504A
Phone: 416-978-5434
Email: liuqy AT physics.utoronto.ca
Basic Topics
- What is inverse theory in physics and geophysics? When do data-consistent models even exist?
- Multivariate regression modeling of discrete models, Bayesian approaches, maximum likelihood estimation, with errors and hypothesis testing, both classical and resampling(e.g. bootstrap)
- Continuous models where spatial resolution is a meaningful concept (Backus-Gilbert theory)
- Singular Value Decomposition approach to modeling
- Answerable and unanswerable questions in modeling
- Exotic norms such as L-1, compressive sensing
- Methods for non-linear modeling and global optimization: e.g. Markov Chain Monte Carlo (MCMC), simulated annealing, genetic algorithms, etc
Reference Books
In addition to the main textbook, you may find the other following books/notes useful:
Course Schedules
| Lecture No. | Slides | Content |
Reading | HW |
| 1,2 | Introduction |
examples of inverse problems; models, forward problems; continuous/discrete inverse problems; existence, uniqueness and stability of inverse problems. | Chapter 1 | N/A |
| 3,4,5,6 | Least squares, Resampling |
under/over/even-determined problems; prediction error;
goodness of fit and chi-square statistics; model covariance and resolution; error propagation, maximum likelihood estimator, Bayesian inference |
Chapter 2 |
HW 1 (Due 10/6),
HW 2+ HW2.1 bootstrap(horm.m; Due 10/27) |
| 7,8,9,10 | Linearized inverse problem |
linearization of weakly nonlinear inverse problem, variance and resolution trade-off; ill-posed problems, regularization, SVD, pseudo-inverse, L-curve |
Chapter 3 | HW 3: Aster 2013, Page 87, section 3.6, question 2, and 4 (Due on 11/10) |
| 11,12,13,14 | Tikhonov regularization |
regularizations, cross-validation |
Chapter 4 | HW4: Aster 2013, section 4.9, Page 124, question 2 and 3: data and regularization tools (needs to be unzipped, e.g., by 7-zip) from Mathworks, due 11/24 |
| 15,16 | Iterative methods for nonlinear optimization |
Newton's method, conjugate gradient method and preconditioning |
Chapter 6 | HW 5: Page 167, 5, 6, due on Dec 8, 11:59 pm |
| 17,18,19,20 | Miscellanenous subjects |
non-negative constraints, total variation regularization; computation of data kernels; Backus and Gilbert resolution analysis |
Chapter 7, Chapter 5 | |
| 21 | Global optimization methods |
Monte Carlo methods; direct search; uniform random search; simulated annealing; metropolis algorithm; genetic algorithm |
Review Paper | Project (see below for info |
| Dec 21 | Project Paper Due |
7-8 page report on ONE of the following subjects: 1) Global optimization methods focusing on simulated annealing, genetic algorithm or other global search techniques; 2) Neighborhood Algorithms (Paper 1, Paper 2); 3) Optimization problem, compressive sensing and applications (see Tex notes section 11.1); 4) Optimization problems, machine learning, neural networks and applications (see section 11.2 of Tex notes) |
Review Paper by Sambridge & Mosegaard (2002) | Due on Dec 21, 11:59 pm |
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