# NUMERICAL SIMULATIONS & MACHINE LEARNING - 2025/6

Module code: ENG3209

## Module Overview

The FHEQ Level 6 treatment of numerical methods builds on the material taught at FHEQ Level 5. It is presented in two linked sections: Numerical Simulations and Machine Learning. The Numerical Simulations section discusses typical methods used in engineering simulations to obtain numerical solutions to real-world problems described by ordinary and partial differential equations. Students apply their programming skills acquired at FHEQ Level 5 to use numerical methods for the solution of engineering problems. The Machine Learning section introduces concepts from artificial intelligence relevant for engineers. It provides an overview and discussion of machine-learning techniques, and students apply these techniques to solve data-driven engineering problems. A laboratory session is used to explore the concepts of uncertainty, verification and validation for computer simulations.

### Module provider

Mechanical Engineering Sciences

MARXEN Olaf (Mech Eng Sci)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 86

Lecture Hours: 14

Tutorial Hours: 14

Laboratory Hours: 4

Guided Learning: 12

Captured Content: 20

Semester 2

N/A

## Module content

Indicative content includes:

Numerical simulations:

• Overview of numerical solution of engineering problems, workflow for simulation methods and numerical modelling.

• Stability and accuracy of integration methods for ordinary differential equations; Implementation of methods for the integration of ordinary differential equations.

• Finite difference methods: derivation based on Taylor-series expansion; finite difference approximation for the first and second derivatives and their accuracy; the concept of modified wave number, von Neumann and Fourier analysis.

• Partial differential equations: order, linearity and classification (elliptic, parabolic and hyperbolic equations).

• Analysis of numerical schemes: consistency, stability and convergence; Lax' equivalence theorem.

• Methods and combined analysis of spatio-temporal discretization for partial differential equations; amplitude and phase errors including numerical dispersion and diffusion; the convection-based CFL number and corresponding diffusion number.

• Verification and validation of simulations for physical modelling.

Machine Learning:

• Introduction to machine learning for engineering; machine-learning workflow and model selection;

• Supervised and unsupervised learning;

• Clustering and classification;

• Regression;

• Deep-learning methods and artificial neural networks;

• Application of data-driven modelling to engineering problems.

## Assessment pattern

Assessment type Unit of assessment Weighting
Attendance only Laboratory Demonstration(s) Pass/Fail
Coursework Programming and Analysis Assignment 80
Practical based assessment Laboratory Session 20

## Alternative Assessment

Laboratory Demonstration(s): written answers or on-line quiz for an experiment and the associated numerical method used to simulate it, including the analysis implementation or adaptation and running of a computer code to validate simulation results. Laboratory Session: assignment that may include written answers, on-line quiz and/or computer coding for an engineering problem of similar complexity as in the associated Laboratory Session.

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate command of a variety of numerical methods and machine-learning techniques as well as the ability to select appropriate methods, and then use these methods and techniques to obtain numerical solutions to engineering problems, including the analysis of errors.

The laboratory demonstrations serves to let the students assess their ability to create numerical model(s) for one or more simple engineering problem(s), perform and/or observe (virtual or in person) the associated laboratory experiment(s) and compare results, including an analysis of results and discussion of errors as well as uncertainties (verification and validation).

The coursework assignment tests the students ability to analyze, select and implement one or more numerical simulation methods and machine-learning techniques, including suitable combination(s) of techniques, for one or more engineering problems.

The practical based assessment tests the students ability to create numerical model(s) for complex engineering problem(s), perform and/or observe (virtual or in person) the associated laboratory experiment(s) and compare results, including an analysis of results and discussion of errors as well as uncertainties (verification and validation).

Thus, the summative assessment for this module consists of: laboratory demonstrations [Learning outcome 2], coursework assignment [Learning outcome 1], and Practical based assessment [Learning outcome 2,3].

Formative assessment: Feedback given Students will perform online quizzes for formative assessment.

Feedback:

Formative feedback is given throughout the semester during Q&A sessions as part of lectures by staff. Formative feedback is also given throughout the semester in IT-Lab based tutorials by staff and/or PG assistants, and through example demonstrations and computer codes posted on the VLE and through quiz outcomes on the VLE. In the laboratory session, students have a face-to face discussion with the demonstrator. Electronic feedback is given on the coursework assignment.

## Module aims

• Provide students with the knowledge and experience of analysis and selection of numerical and machine-learning methods for complex engineering problems .
• Equip students with the knowledge and experience of implementation and application of appropriate computer-based programming methods to solve ordinary and partial differential equations governing complex engineering problems.
• Provide training in all steps to simulate complex engineering problems using numerical and machine-learning methods, to critically assess the validity of solutions and to quantify errors of computer simulations for complex engineering problems.

## Learning outcomes

 Ref Attributes Developed 001 Analyze and implement computer-based numerical methods and/or machine-learning techniques to solve engineering problem(s); KC C1,C2 002 Produce and assess results of computer-based and (real-world) experimental methods for a simple engineering problem, including verification and validation; CPT C3,C12 003 Develop, select and implement a suitable approach for the computer simulation of a complex engineering problem, then perform simulations and critically analyze results as well as communicate corresponding findings; KCPT C1,C2,C3,C17

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to introduce numerical simulation techniques and machine learning through theory with worked examples carried out by the students. This is delivered through synchronous lectures, captured content and tutorial classes with the students conducting a coursework assignment as well as one or more laboratory sessions.

The learning and teaching methods include:

• synchronous lectures, including question and answer session;

• captured content;

• guided learning (such as electronic/online learning and multi-media resources);

• IT-lab based tutorials, were practical programming skills are developed through several formative exercises.

• one or more laboratory sessions in small groups; the lab session(s) may feature supervisor-led discussions and group work to conduct an experiment, and may also require preparatory work.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: ENG3209

## Other information

The School of Mechanical Engineering Sciences is committed to developing graduates with strengths in Employability, Digital Capabilities, Global and Cultural Capabilities, Sustainability, and Resourcefulness and Resilience. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

Digital capabilities: The students will use appropriate technology to complete authentic assignments including the numerical simulation of real-work experiment(s). Students will further develop data handling and programming skills specifically using advanced numerical methods in Matlab and/or Python. They will also be able to use specialist software (Matlab and/or Python) to solve engineering problems.

Employability: Transferrable skills including communication and report writing will be improved through module activities - all skills which will help them become employment ready.

Resourcefulness and resilience: Through participation in one or more group laboratory session(s), students will actively engage in group working which will emphasise the importance of team cohesion, respect, empathy and build trust with other learners. This will provide opportunities to positively respond to team setbacks i.e. if an experiment does not go to plan, they can discuss together as a team how they could have improved the results and this will reinforce the message that engineering tasks often “fail” in the first instance and this is not seen as a failure, it is just part of the journey to improve design or to solve a problem.

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Automotive Engineering (Dual degree with HIT) BEng (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mechanical Engineering BEng (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mechanical Engineering MEng 2 Optional A weighted aggregate mark of 40% is required to pass the module
Automotive Engineering MEng 2 Optional A weighted aggregate mark of 40% is required to pass the module
Automotive Engineering BEng (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Aerospace Engineering BEng (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Aerospace Engineering MEng 2 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2025/6 academic year.