ACSE 7: Inversion and Optimization¶
Module Lead: Mr. Stephan Kramer
Staff: Mr. Stephan Kramer; Prof. Matthew Piggott;
Course Description¶
The main aim of this module is to introduce the methods that can be used to extract useful information from incomplete, inconsistent and inaccurate physical datasets using practical computational resources.
The following topics will be covered:
Forward and inverse problems
Incomplete, inconsistent and inadequate data
Linear & non-linear problems
Square linear systems
Over-determined problems – least squares
Under-determined problems – minimum norm
Mixed-determined systems – generalised inverse
Regularisation, constraints and penalties
Linearised non-linear problems
Gradient descent, conjugate gradient, higher-order methods
Practical solutions for large systems
Global inversion methods
Full-waveform inversion
Linear filters
Reading List¶
Numerical Optimzation, Jorge Nocedal and Stephen J. Wright
Iterative Methods for Linear and Nonlinear Equations, C. T. Kelley
Iterative Methods for Optimization C. T. Kelley