# 2021/22 Taught Postgraduate Module Catalogue

## SOEE5116M Computational Inverse Theory

### 15 creditsClass Size: 40

Module manager: Dr Phil Livermore
Email: P.W.Livermore@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2021/22

### Pre-requisite qualifications

Course entrance pre-requisite

This module is not approved as an Elective

### Module summary

In this module, students will learn both the techniques and theory of inverse theory but also how to use the Linux operating system and Python for scientific programming. Inverse theory practicals will be undertaken in Python, underlining the links between these two subjects.

### Objectives

To provide training in the use of Linux and Python code to perform basic data processing and visualisation. To design and find the solution to inverse problems, including model formulation and parametrisation, over- and under-constrained problems, linear and non-linear solution methods. To provide an understanding of how to quantify the uncertainty in a solution, based on data uncertainty and model setup.

Learning outcomes
After completing this module, students will be able to
1. Formulate inverse problems
2. Explain the difficulties inherent in inverse problems
3. Solve linear inverse problems using least-squares
4. Linearise and solve non-linear inverse problems
5. Describe and implement methods for regularization of ill-posed problems
6. Formulate inverse problems in terms of probability distributions
7. Solve inverse problems using Markov chain Monte Carlo algorithms
8. Describe and implement some machine learning algorithms.
9. Use computer coding algorithms to plot data, perform basic data processing including conditional logic and loops, and solve inverse problems.

### Syllabus

Computing: overview of computers and the Linux operating system. Programming in Python: the user interface, syntax, variables, matrices, plotting, script design, conditional statements, loops, input/output, functions.

Inverse theory: formulation of inverse problems, linear least-squares, best linear unbiased estimator (BLUE), propagation of errors, maximum likelihood solutions, linearisation of non-linear problems, Monte Carlo error propagation, ill-posed problems, resolution matrix, regularization, cross validation, Bayesian inference, Markov chain Monte Carlo algorithms, neighbourhood algorithms, machine learning.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 11 1.00 11.00 Practical 8 3.00 24.00 Practical 11 2.00 22.00 Private study hours 93.00 Total Contact hours 57.00 Total hours (100hr per 10 credits) 150.00

### Private study

Completion of practicals and assessments, computer exercises, literature search, reading text books, and revision for examination.

### Opportunities for Formative Feedback

Continuous monitoring during practicals with immediate formative assessment and feedback. Weekly short answer questions in inverse theory will build towards a cumulative answer to a mock exam; formative feedback will be given on answers. A formative computing assignment will give opportunity for feedback before the summative computing assignment.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment In-Class Assessed Unseen Exam 20.00 Total percentage (Assessment Coursework) 20.00

Re-sit is by examination only (see below)

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 80.00 Total percentage (Assessment Exams) 80.00

A student who fails this Module may be offered a resit. The re-sit for this module will be a single unseen examination, of duration 2 hours, covering all Module Learning Outcomes. It will not necessarily be of the same format as the original examination. If the re-sit is granted as a new first attempt, the original examination mark will be discarded, and replaced by the re-sit examination mark even if it is lower. It will then be aggregated with the first-attempt coursework to provide a new Module mark. If the re-sit is a second and final attempt, the re-sit mark provides a new alternative mark for the whole Module and will be capped at 50%.