Study information

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

MODULE TITLE CREDIT VALUE Data-driven Analysis and Modelling of Dynamical Systems 15 MTHM062 Dr 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 Guided Independent Study Placement / Study Abroad 33 117 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 Written Exams Practical Exams 40 60 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

• 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.