Uncertainty quantification for random moving boundary problems

Moving boundary problems form an important class of mathematical models describing various processes with evolving interfaces from physics, engineering, biology, and chemistry. In real world applications such processes are affected by a variety of uncertainties which require modelling via random moving boundary problems. Being able to efficiently quantify such uncertainties is crucial for the mentioned applications. The objectives of this PhD project include (i) to construct, justify, analyse and test efficient algorithms for the Bayesian inverse problem within the moving boundary setting; (ii) use the algorithms for quantifying uncertainties in one of the main manufacturing processes for producing advanced composites - resin transfer moulding (RTM); and (iii) apply the algorithm to real data from composite laboratory experiments. The project will also involve questions related to design of experiments, e.g. optimal spatial positions and frequency for data collection under a restriction of the total number of data collection points.
To have more information about the topic, see the recent paper https://doi.org/10.1088/1361-6420/aad1cc