Multiscale modelling of systems with complex microscale detail. In modern science and engineering many complex systems are described by distinctly different microscale physical models within different regions of space. This project is to develop systematic mathematical and computational methods for the compact and accurate macroscale modelling and computation of such systems for application in industrial research and development. Our sparse simulations, justified with mathematical analysis, use ....Multiscale modelling of systems with complex microscale detail. In modern science and engineering many complex systems are described by distinctly different microscale physical models within different regions of space. This project is to develop systematic mathematical and computational methods for the compact and accurate macroscale modelling and computation of such systems for application in industrial research and development. Our sparse simulations, justified with mathematical analysis, use small bursts of particle/agent simulations, PDEs, or difference equations, to efficiently evaluate macroscale system-level behaviour. The objective is to accurately interface between disparate microscale models and establish provable predictions on how the microscale parameter spaces resolve at the macroscale.Read moreRead less
Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to devel ....Regularisation methods of inverse problems: theory and computation. This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to develop purely data-driven rules to choose the regularisation parameter and show how they work in theory, and in practice. It will also develop convex framework, acceleration strategies as well as preconditioning and splitting ideas to design efficient regularisation solvers.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL210100110
Funder
Australian Research Council
Funding Amount
$3,021,288.00
Summary
New Approaches to Understand How Form and Function Shape Complex Systems. As biology and medicine transform into quantitative sciences, existing mathematical methods are often inadequate to explain the data they generate. This project aims to unlock the potential of such biomedical data through the development of new mathematical approaches that combine concepts from pure and applied mathematics, statistics and data science, and then to investigate their ability to generate mechanistic insight i ....New Approaches to Understand How Form and Function Shape Complex Systems. As biology and medicine transform into quantitative sciences, existing mathematical methods are often inadequate to explain the data they generate. This project aims to unlock the potential of such biomedical data through the development of new mathematical approaches that combine concepts from pure and applied mathematics, statistics and data science, and then to investigate their ability to generate mechanistic insight into fundamental biomedical processes. In this way, the project expects to affect a paradigm shift in mathematical biology while strengthening Australia’s reputation as a world-leader in mathematical biology. An outcome from this project could be new mathematical models that guide decision making in the clinic.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
Discovery Early Career Researcher Award - Grant ID: DE200100063
Funder
Australian Research Council
Funding Amount
$394,398.00
Summary
Nonmonotone Algorithms in Operator Splitting, Optimisation and Data Science. This project aims to develop the mathematical foundations for the analysis and development of optimisation algorithms used in data science. Despite their now ubiquitous use, machine learning software packages routinely rely on a number of algorithms from mathematical optimisation which are not properly understood. By moving beyond the traditional realms of Fejér monotone algorithms, this project expects to develop the m ....Nonmonotone Algorithms in Operator Splitting, Optimisation and Data Science. This project aims to develop the mathematical foundations for the analysis and development of optimisation algorithms used in data science. Despite their now ubiquitous use, machine learning software packages routinely rely on a number of algorithms from mathematical optimisation which are not properly understood. By moving beyond the traditional realms of Fejér monotone algorithms, this project expects to develop the mathematical theory required to rigorously justify the use of such algorithms and thereby ensure the integrity of the decision tools they produce. This mathematical framework is also expected to produce new algorithms for optimisation which benefit consumers of data science such as the health-care and cybersecurity sectors.Read moreRead less
Integrating rifts and swell in the mathematics of ice shelf disintegration. Antarctic ice-shelf disintegrations have the alarming potential to cause rapid sea level rise, through accelerated discharge of the Antarctic Ice Sheet and initiating runaway Ice Sheet destabilisations. The project aims to develop a mathematical model of swell-induced ice-shelf vibrations in a coupled ocean–shelf 3D framework, focusing on interactions between vibrations and the rift networks that characterise outer shelf ....Integrating rifts and swell in the mathematics of ice shelf disintegration. Antarctic ice-shelf disintegrations have the alarming potential to cause rapid sea level rise, through accelerated discharge of the Antarctic Ice Sheet and initiating runaway Ice Sheet destabilisations. The project aims to develop a mathematical model of swell-induced ice-shelf vibrations in a coupled ocean–shelf 3D framework, focusing on interactions between vibrations and the rift networks that characterise outer shelf margins before disintegration. Accurate, efficient solutions will be developed by fusing powerful approximation theories, and validated by numerical solutions. The model will be combined with state-of-the-art data to predict trends in Antarctica’s remaining ice shelves and indicate potential future disintegrations.Read moreRead less
Modeling, Mathematical Analysis, and Computation of Multiscale Systems. This project develops and implements a systematic approach, both analytic and computational, to extract compact, accurate, system level models of complex physical and engineering systems. Our wide ranging methodology is to construct computationally efficient "wrappers" around fine scale, microscopic, detailed descriptions of dynamical systems (particle or molecular simulation, or PDE or lattice equations). Comprehensively a ....Modeling, Mathematical Analysis, and Computation of Multiscale Systems. This project develops and implements a systematic approach, both analytic and computational, to extract compact, accurate, system level models of complex physical and engineering systems. Our wide ranging methodology is to construct computationally efficient "wrappers" around fine scale, microscopic, detailed descriptions of dynamical systems (particle or molecular simulation, or PDE or lattice equations). Comprehensively accounting for multiscale interactions between subgrid processes among macroscale variations ensures stability and accuracy. Based on dynamical systems theory and analysis, our approach will empower systematic analysis and understanding for optimal macroscopic simulation for forthcoming exascale computing. Read moreRead less
Mathematics the key to modern glass and polymer fibre technology. This project aims to develop fully coupled flow and energy models to determine the preform structure and fibre-drawing parameters needed to fabricate a desired microstructured optical fibre by stretching of the preform to a fibre. It will focus on polymer to develop a non-Newtonian flow model, which can handle the subset of Newtonian glass fibre drawing. It will develop fast, powerful three-dimensional predictive tools to solve th ....Mathematics the key to modern glass and polymer fibre technology. This project aims to develop fully coupled flow and energy models to determine the preform structure and fibre-drawing parameters needed to fabricate a desired microstructured optical fibre by stretching of the preform to a fibre. It will focus on polymer to develop a non-Newtonian flow model, which can handle the subset of Newtonian glass fibre drawing. It will develop fast, powerful three-dimensional predictive tools to solve the models and experimentally validate solutions. This work will direct future design of microstructured optical fibres to empower next-generation optical-fibre technologies. Expected outcomes are fibre designs for telecommunications, medicine, biotechnology, sensing and imaging.Read moreRead less