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ACM41000

Academic Year 2024/2025

Uncertainty Quantification (ACM41000)

Subject:
Applied & Computational Maths
College:
Science
School:
Mathematics & Statistics
Level:
4 (Masters)
Credits:
5
Module Coordinator:
Dr James Herterich
Trimester:
Spring
Mode of Delivery:
On Campus
Internship Module:
No
How will I be graded?
Letter grades

Curricular information is subject to change.

This module is a synthesis of modern Applied Mathematics and Statistical Inference, and introduces students to statistical methods to determine model parameters in otherwise deterministic mathematical models. The module starts with a review of deterministic models – ordinary and partial differential equations (both linear and nonlinear). Included in this review is a topical summary of nonlinear ordinary differential equations, reaction-diffusion partial differential equations, and optimization of partial-differential equation models using an adjoint method. Students will learn how to use these equation systems to model physical systems. In doing so, various model parameters appear, which in turn need to be modelled. These parameters can be determined by reference to experimental data, which can then be used to make predictions. As such, in the second part of the module students will learn how to estimate and attain confidence limits for the parameters of the differential equations from noisy and often partially observed data.

About this Module

Learning Outcomes:

Upon completion of this module, students will

1. Be able to solve a variety of linear and nonlinear ordinary differential equation systems
2. Be able to do the same for partial differential equation models
3. Be able to apply the adjoint method to optimization problems involving parabolic partial differential equations
4. Be familiar with the application of such systems of equations in modelling physical systems
5. Understand the origin of various model parameters when such equation systems are used as mathematical models of various physical systems
6. Be able to attain statistical inference for the parameters of linear and nonlinear ordinary differential equation systems.
7. Be able to do the same for partial differential equation models.

Student Effort Hours:
Student Effort Type Hours
Lectures

36
Specified Learning Activities

40
Autonomous Student Learning

24
Total

100

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry, and problem-based learning.

Requirements, Exclusions and Recommendations
Learning Recommendations:

Modules in Probability Theory, Inferential Statistics, Regression. Further modules in Calculus of one and sevaral variables, and Linear Algebra.


Module Requisites and Incompatibles
Not applicable to this module.
 

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Quizzes/Short Exercises: MCQ in class tests Week 3, Week 6, Week 9 Alternative linear conversion grade scale 40% No
30
 No
Group Work Assignment: Group poster Week 11 Alternative linear conversion grade scale 40% No
30
 No
Exam (In-person): Final exam End of trimester
Duration:
1 hr(s)
 Alternative linear conversion grade scale 40% No
40
 No

Carry forward of passed components
No
 

Resit In Terminal Exam
Summer No
Please see Student Jargon Buster for more information about remediation types and timing. 

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Mon 12:00 - 12:50
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Thurs 14:00 - 14:50
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