Study information

Data-driven Analysis and Modelling of Dynamical Systems - 2024 entry

MODULE TITLEData-driven Analysis and Modelling of Dynamical Systems CREDIT VALUE15
MODULE CODEMTHM062 MODULE CONVENERDr Frank Kwasniok (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11
Number of Students Taking Module (anticipated) 50
DESCRIPTION - summary of the module content

On this module, the students will be introduced to the topical area of data-driven modelling of dynamical systems. In contrast to the direct or forward approach, where a given model is integrated in time, the data-driven or inverse approach builds models from time series data and then uses them to gain insight into or predict the underlying system. We will cover identification/reconstruction of ordinary, partial and stochastic differential equations, extraction of generic time series models as well as pattern-based techniques for spatio-temporal modelling. You will make use of the computer package MATLAB to numerically implement the methods in computer lab classes. The background and skills you will obtain in this module will be useful in various areas inside and outside of academia.

Pre-requisite modules: MTH2003 Differential Equations (or equivalent), MTH2011 Linear Algebra (or equivalent)

 

AIMS - intentions of the module

Data-driven modelling is playing an increasing role in many areas such as weather and climate science, fluid dynamics and biological/medical applications. This module introduces basic techniques for analysing, modelling and predicting dynamical systems based on time series data. Using MATLAB and other relevant software, you will develop practical skills in the use of computers in data-driven modelling.

 

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge

1. understand and apply mathematical techniques for identification/reconstruction of various dynamical systems as well as model-free prediction from time series data;
2. demonstrate expertise in the use of MATLAB widely used both inside and outside the academic community and be able to use it to model challenging data-driven mathematical problems.

Discipline Specific Skills and Knowledge

3. tackle a wide range of data-driven mathematical problems using modern computational methods
4. model realistic situations and also understand the principles underlying the techniques and when they are applicable.

Personal and Key Transferable / Employment Skills and Knowledge

5. show enhanced modelling, problem-solving and computing skills;
6. demonstrate the ability to use the sophisticated computer package MATLAB.

 

SYLLABUS PLAN - summary of the structure and academic content of the module
  • Curve fitting: interpolation with polynomials and splines, least-squares regression
  • Numerical integration of ordinary and partial differential equations
  • Reconstruction of ordinary and partial differential equations from time series data: least-squares parameter estimation
  • Numerical integration of stochastic differential equations: the Euler-Maruyama scheme
  • Reconstruction of stochastic differential equations from time series data: maximum likelihood methods
  • Linear time series modelling and prediction: autoregressive and vector-autoregressive models
  • Nonlinear time series modelling and prediction: analogue prediction, local polynomial modelling, time-delay embedding
  • Advanced matrix algebra: singular value decomposition and variants
  • Pattern-based techniques: principal component analysis (PCA), canonical correlation analysis (CCA), dynamic mode decomposition (DMD)

 

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 33 Guided Independent Study 117 Placement / Study Abroad 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 22 Lectures
Scheduled learning and teaching activities 11 Computer lab classes
Guided independent study 117 Lecture and assessment preparation, wider reading

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
N/a      
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 40 Written Exams 60 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed notes 60 2 hours  All Written/verbal on request

Coursework 1

 20 8-12 hours All Written comments on script

Coursework 2

 20 8-12 hours All Written comments on script
         
         

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
Written exam – closed notes Written exam – closed notes All Referral/deferral period

Coursework 1

Coursework 1

 All Referral/deferral period

Coursework 2

 Coursework 2 All Referral/deferral period

 

RE-ASSESSMENT NOTES

Referrals:

Reassessment will be by a written exam worth 100% of the module mark only. The mark will be capped at the pass mark.

Deferrals:

Reassessment will be by coursework and/or written exam in the deferred element only. The mark will be uncapped.

 

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Basic reading:

  • Kharab A., Guenther R.B. (2012): An Introduction to Numerical Methods: a MATLAB Approach, Chapman & Hall.
  • Hamilton J.D. (2012): Time Series Analysis, Levant Books.
  • Kantz H., Schreiber T. (2004): Nonlinear Time Series Analysis, Cambridge University Press.
  • Kutz J.N. (2013): Data-Driven Modeling & Scientific Computation, Oxford University Press.

Reading list for this module:

There are currently no reading list entries found for this module.

CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES MTH2011, MTH2003
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 7 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Monday 11th March 2024 LAST REVISION DATE Tuesday 19th March 2024
KEY WORDS SEARCH Data-driven modelling; time series analysis; differential equations; system reconstruction; prediction; MATLAB

Please note that all modules are subject to change, please get in touch if you have any questions about this module.