MA3A9 Data-Driven Mathematical Modelling

Introductory description

This module bridges the gap between traditional mechanistic modeling (physics-based) and modern data science, using data to describe processes, predict behavior, and identify complex system dynamics.

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

In this module we focus mainly on time series data produced from a possible unknown dynamical system. The data establish the ground truth, and we like to apply methods that can differentiate between, or reconstruct a dynamical system which is partly or fully unknown.

Introduction: Different Levels Of Unknowns In Mathematical Modelling

Parameter Estimation

Model Selection, Akaike’s Information Criterion

Singular Value Decomposition (DMD)

Koopman Operator Theory

Sparse Identification of Nonlinear Dynamics (SINDy)

Background: Neural Networks and Deep Learning (as needed in this module)

General Physics-Informed Machine Learning

Physics-Informed Neural Networks (PINNs), Neural-Network ODEs (NN-ODEs) and PDEs (NN-PDEs).

Learning outcomes

By the end of the module, students should be able to:

• Understanding the level of uncertainty in dynamic mathematical modelling
• Understanding the core reconstruction methods of dynamical systems from time series data
• Practical knowledge to implement the methods introduced in the module

Indicative reading list

Reading lists can be found in Talis

Subject specific skills

Using module specific code

Transferable skills

Complex modelling and problem solving using data analysis