Mathematical Methods for Data Driven Modelling

Content

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Description

Time: Thursdays 9.00 - 11.00 

Location for Maxwell Institute students: Bayes Centre (room 5.46)

Module Leader: Debasish Das (Strathclyde University)

Module Summary

This module introduces the mathematical and computational foundations of modern data-driven modelling for dynamical systems. It develops the linear algebra and numerical methods underlying matrix factorisations, least-squares problems, regularisation, low-rank approximation, principal component analysis and proper orthogonal decomposition, before introducing dynamic mode decomposition and projection-based reduced-order modelling. The module then considers approaches for learning nonlinear reduced dynamics directly from data, including sparse regression methods. The final part develops gradient-based optimisation and adjoint methods for parameter estimation, inverse problems and dynamical systems. Throughout, emphasis is placed on the mathematical structure and numerical implementation of the methods, with examples drawn from differential equations, fluid mechanics and other areas of applied mathematics.

Assessment

Assessment will be through an individual computational project. Students will choose from a list of projects that will be made available after the first few weeks of the module. They will apply mathematical and numerical methods from the module to a data-driven modelling problem, analyse the resulting model and critically assess its accuracy and limitations. The submission will consist of a written report (minimum length 8 pages and maximum length 10 pages) together with reproducible computational code, and will assess both understanding of the underlying mathematics and the ability to implement and interpret the methods in practice.