Current projects

Hierarchical Methods for Stochastic Partial Differential Equations

Partial Differential Equations (PDEs) are important versatile tools for modelling various phenomena, like fluid dynamics, thermodynamics, nuclear waste, etc… Stochastic Partial Differential Equations (SPDEs) generalize PDEs by introducing random parameters or forcing. One is then interested in quantifying the uncertainty of outputs of such models through the computations of various statistics. Accurate computations of such statistics can be costly as it requires fine time- and space-discretization to satisfy accuracy requirements. Several hierarchical methods were developed to address such issues and applied successfully to Stochastic Differential Equations (SDEs) and in this project we will extend these works to deal with the more complicated SPDEs.

McKean-Vlasov models, old and new.

TBC

Numerical Analysis of Consistency Models

TBC

Projects for prospective PhD students

Efficient computation of Rare-risk measures

Certain rare events have high cost, both humanitarian and financial, which make them significant events that industries and governments must plan for. Taking measures to reduce or mitigate the risks of such events is the goal of risk management which requires accurate assessment of such risks. This project’s goal is to speed up computations of accurate risk measures of rare events to ensure effective risk management. The goal will be achieved by developing novel computational methods which utilize approximation properties of the underlying stochastic models and which are based on Monte Carlo and random sampling methods which are easily parallelizable and fully exploit the increased availability of computational resources.