Novel nonlinear functional analysis methods for singular and impulsive boundary value problems. This project aims to develop innovative functional analysis theories and methods to study various complex nonlinear boundary value problems, with particular focus on singular and impulsive problems. The outcomes of this project aims to enhance Australia’s capability of tackling complex nonlinear science and engineering problems using sophisticated mathematical methods. This project aims to also provid ....Novel nonlinear functional analysis methods for singular and impulsive boundary value problems. This project aims to develop innovative functional analysis theories and methods to study various complex nonlinear boundary value problems, with particular focus on singular and impulsive problems. The outcomes of this project aims to enhance Australia’s capability of tackling complex nonlinear science and engineering problems using sophisticated mathematical methods. This project aims to also provide engineers and scientists with a theoretical base and simulation technique for the study and optimal control of impulsive systems and processes involving nonlinear singularity.Read moreRead less
Liberating the Dimension - Frontier Technologies for Very High Dimensional Problems. Real world problems tend to involve an enormous number of variables (the dimension) - hundreds, thousands, millions, or even infinite. Very high dimensional problems arise in finance, statistics, physics and many other application areas. For example, in option pricing, maximum likelihood estimation in health statistics, and porous flow through a random medium. In this project, the theory of very high dimensional ....Liberating the Dimension - Frontier Technologies for Very High Dimensional Problems. Real world problems tend to involve an enormous number of variables (the dimension) - hundreds, thousands, millions, or even infinite. Very high dimensional problems arise in finance, statistics, physics and many other application areas. For example, in option pricing, maximum likelihood estimation in health statistics, and porous flow through a random medium. In this project, the theory of very high dimensional computation will be developed in step with applications, with the applications being chosen to help in shaping the theory. The project involves interdisciplinary collaborations and aims to develop frontier technologies for tackling realistic high dimensional problems.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