PDE-driven Digital Twins
Project Description
There are many definitions for digital twins but here we define a digital twin as a computational model of a physical (natural, engineered, social or hybrid) system combined with algorithms for assimilating observed data into the model and for controlling the physical system so that there is bidirectional interaction updated in real time. Some applications include: flood forecasting with river control, vertical farming, renewable energy devices, traffic pollution control in cities, etc.
This topic is for PhD researchers who are interested in numerical discretisations for PDEs and their embedding inside algorithms that couple them with data.
Existing background work
The lead supervisor is an expert in data assimilation (having written a textbook with Sebastian Reich) and also in finite element discretisations of PDEs.
Main objectives of the project
In this project topic we will focus on the algorithmic challenges arising when the computational model involves the numerical solution of PDEs. In this case, to realise the full potential uses of digital twins, we need to develop new mathematics and algorithms to address the challenge to computational resources that otherwise exists. This includes: multiscale and multifidelity modelling, reduced order modelling, empirical surrogates (including generative models) and hybrid empirical/mechanistic models, data assimilation and control algorithms, all of which may need to be federated into a fully functional digital twin.
Projects in this topic will focus in one or more of this algorithmic areas, developed in the context of finite element methods for partial differential equations, with the application area open depending on the interests and capabilities of the PhD researcher.
Details of Software/Data Deliverables
The project will deliver software for the chosen algorithms, so that they can be evaluated and extended. The software will take the form of a general purpose tool that can be applied to a range of models implemented using the Firedrake framework.
