# ACM41000 Uncertainty Quantification

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.

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Curricular information is subject to change

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 Open Book Exam Component Scale Must Pass Component % of Final Grade
Assignment: Individual assignments Varies over the Trimester n/a Standard conversion grade scale 40% No

100

Carry forward of passed components
No

Resit In Terminal Exam
Summer Yes - 2 Hour