A new numerical analysis for partial differential equations with noise. This project aims to design novel numerical methods, grounded in rigorous mathematical foundations, for partial differential equations with stochastic source terms, such as for instance those modelling fluid flows with random perturbations. To ensure the accuracy of numerical simulations, preserving certain quantities of importance (mass, flux) is critical. The project's goal is to develop finite volume and high-order numeri ....A new numerical analysis for partial differential equations with noise. This project aims to design novel numerical methods, grounded in rigorous mathematical foundations, for partial differential equations with stochastic source terms, such as for instance those modelling fluid flows with random perturbations. To ensure the accuracy of numerical simulations, preserving certain quantities of importance (mass, flux) is critical. The project's goal is to develop finite volume and high-order numerical methods that are applicable in real-world settings, designed to achieve this preservation of essential quantities, and mathematically proven to be robust. The expected benefits are cost-efficient and reliable numerical tools for the scientific simulation of phenomena subjected to uncontrolled influence.Read moreRead less
Interface-aware numerical methods for stochastic inverse problems. This project aims to design novel high-performance numerical tools for solving large-scale forward and inverse problems dominated by stochastic interfaces and quantifying associated uncertainties. In real-world applications such as groundwater, these tools are instrumental for assimilating big datasets into mathematical models for providing reliable predictions. By advancing and integrating high-order polytopal schemes, multileve ....Interface-aware numerical methods for stochastic inverse problems. This project aims to design novel high-performance numerical tools for solving large-scale forward and inverse problems dominated by stochastic interfaces and quantifying associated uncertainties. In real-world applications such as groundwater, these tools are instrumental for assimilating big datasets into mathematical models for providing reliable predictions. By advancing and integrating high-order polytopal schemes, multilevel methods, transport maps, and dimension reduction, this project's anticipated outcomes are highly accurate and cost-efficient numerical schemes, certified by rigorous mathematical analysis. This should provide data-centric simulation tools with enhanced reliability, for engineering and scientific applications.Read moreRead less
Towards predictive 4D computational models for the heart. This project aims to develop novel high-performance numerical algorithms for multiscale and multiphysics PDEs with dynamic interfaces, the development and analysis of a novel PDE system modelling the electromechanics of heart and torso, and the combination of these numerical techniques and models to deliver predictive tools for patient-specific simulations of the cardiac function. It involves the design and mathematical analysis of space- ....Towards predictive 4D computational models for the heart. This project aims to develop novel high-performance numerical algorithms for multiscale and multiphysics PDEs with dynamic interfaces, the development and analysis of a novel PDE system modelling the electromechanics of heart and torso, and the combination of these numerical techniques and models to deliver predictive tools for patient-specific simulations of the cardiac function. It involves the design and mathematical analysis of space-time variational discretisations on embedded meshes, 4D computational geometry algorithms for numerical integration and multilevel solvers. By combining scientific computing and machine learning, one anticipated outcome of this research is a new generation of nonlinear PDE approximations and solvers.Read moreRead less
Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in mi ....Fractional dynamic models for MRI to probe tissue microstructure. This project aims to develop new mathematical tools for mapping tissue microstructural properties via the use of space-time fractional calculus methods. In magnetic resonance imaging, mathematical models and their parameters play a key role in associating information between images and biology, with the overall aim of producing spatially resolved maps of tissue property variations. However, models which can inform on changes in microscale tissue properties are lacking. The tools developed by this project will be used to generate new magnetic resonance image based maps to convey information on tissue microstructure changes in the human brain. Additionally, the mathematical tools developed will be transferable to other applications where diffusion and transport in heterogeneous porous media play a role.Read moreRead less