Module leader: Yulia Timofeeva (Computer Science)
This is a core module for the Mathematics for Real-World Systems II CDT. The aim is to introduce students to cutting-edge topics in mathematical modelling that cover the application areas of the CDT: biomedical science, epidemiology, socio-technical systems, and industrial processes and optimization. The topics covered will be used as examples to illustrate fundamental modelling approaches, in particular multiscale modelling and hybrid modelling, which bridges the divide between a-priori and data-driven methods.
The module consists of sets of lecture series by various staff related to the CDT. The module will provide practical examples of the two research themes of the MathSys II CDT: (1) Multiscale Modelling and (2) Hybrid Modelling. These will be demonstrated using practical examples taken from the application areas of the CDT: quantitative biomedical research, mathematical epidemiology, socio-technical systems and advanced modelling and optimisation of industrial processes. Students will learn how to relate and apply the skills learned in the first-term core modules and understand how the various theoretical methodologies can be used to solve real-world problems. The concepts utilised will include: symmetries and constraints, phase transitions, stochastic and deterministic modelling, data-driven modelling, agent-based modelling, course graining, non-linearities and bifurcations and probability.