Discovery Early Career Researcher Award - Grant ID: DE120101707
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Regularisation methods for solving nonlinear ill-posed inverse problems. Nonlinear inverse problems arise in numerous applications and their stable resolutions require regularisation methods. This project will develop various efficient solvers by using optimisation tools and Newton type procedures and consider their convergence properties. The methods will be applied to practical problems including the tomography techniques.
Sparse grid approximations and fitting using generalised combination techniques. Sparse grid techniques provide an effective tool to deal with the
computational curse of dimensionality which is a constant challenge in
modelling complex data. The proposed research is aimed at the
development and analysis of algorithms for data fitting with sparse
grids using variants of the combination technique. The outcome of the
research is a theory which will provide insights in the applicability,
limit ....Sparse grid approximations and fitting using generalised combination techniques. Sparse grid techniques provide an effective tool to deal with the
computational curse of dimensionality which is a constant challenge in
modelling complex data. The proposed research is aimed at the
development and analysis of algorithms for data fitting with sparse
grids using variants of the combination technique. The outcome of the
research is a theory which will provide insights in the applicability,
limitations and the convergence properties of the proposed
algorithms. The outcomes will be widely applicable in modelling of
large scale and complex data as is encountered in areas of
bioinformatics, physics and experimental studies of complex systems.
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Physics of Risk: new tools to survey the Australian market and beyond. The lives of most Australians depend on the dynamics of financial markets that affects investments, savings, business, employment, growth, wealth and -ultimately- the daily functioning of our society. Understanding, monitoring and managing the dynamics of financial markets is of crucial importance to policy-makers, financial institutions and businesses that are increasingly faced with managing risk, planning strategies and ta ....Physics of Risk: new tools to survey the Australian market and beyond. The lives of most Australians depend on the dynamics of financial markets that affects investments, savings, business, employment, growth, wealth and -ultimately- the daily functioning of our society. Understanding, monitoring and managing the dynamics of financial markets is of crucial importance to policy-makers, financial institutions and businesses that are increasingly faced with managing risk, planning strategies and taking decisions in an increasingly complex market-place. The project is also of importance to the continued evolution of physics in this country contributing to the emergence of a strong new area of statistical physics concerned with the ?real world? in a manner hitherto unknown.Read moreRead less
Existence and Stability of a Model for Three-Dimensional Toroidal Plasma Equilibria. There is great physical interest in modelling strongly non-axisymmetric toroidal plasmas, but fundamental existence problems have made rigorous numerical analysis so far impossible. We seek to overcome this by investigating a class of idealized, but physically motivated, magnetohydrodynamic equilibria with stepped pressure profiles for which existence in the neighbourhood of axisymmetry has been proven. We will ....Existence and Stability of a Model for Three-Dimensional Toroidal Plasma Equilibria. There is great physical interest in modelling strongly non-axisymmetric toroidal plasmas, but fundamental existence problems have made rigorous numerical analysis so far impossible. We seek to overcome this by investigating a class of idealized, but physically motivated, magnetohydrodynamic equilibria with stepped pressure profiles for which existence in the neighbourhood of axisymmetry has been proven. We will (i) develop numerical techniques to extend these piece-wise Beltrami states far away from axisymmetry (ii) develop practical tests to determine when existence breaks down (iii) analyze the frequency spectrum of small oscillations about such equilibria (iv) extend the model to two-fluid MHD.Read moreRead less
Use of Interval Arithmetic and GRID Computing in Computational Molecular Science: Bounding Errors and Locating Global Minima. Catastrophic failure of the Ariane 5 rocket in 1996 and the inability of Patriot missile systems to reach their targets during the 1991 Gulf war were both attributed to numerical computing errors. Less dramatic, but in a similar vein, this project aims to study the numerical stability of contemporary computational molecular science applications. The focus will be on linea ....Use of Interval Arithmetic and GRID Computing in Computational Molecular Science: Bounding Errors and Locating Global Minima. Catastrophic failure of the Ariane 5 rocket in 1996 and the inability of Patriot missile systems to reach their targets during the 1991 Gulf war were both attributed to numerical computing errors. Less dramatic, but in a similar vein, this project aims to study the numerical stability of contemporary computational molecular science applications. The focus will be on linear scaling electronic structure codes, methods that are critical to the study of nano- and bio-materials, and are therefore of great importance to our economic future and medical well being. The project will build expertise within Australia in the area of interval arithmetic, an area that is currently poorly represented.Read moreRead less
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0453911
Funder
Australian Research Council
Funding Amount
$391,529.00
Summary
Microwave Antenna Testing Facility for Far-Field and Spherical Near-Field Measurements. The proposed facility is for testing broad-beam microwave antennas (1 GHz - 18 GHz), designed and developed by collaborators for several research and commercial projects. These antennas are important in telecommunications, defence and biomedical applications. While facilitating timely pattern measurements of antenna prototypes, it will open new opportunities in antenna experimentation. This facility will enha ....Microwave Antenna Testing Facility for Far-Field and Spherical Near-Field Measurements. The proposed facility is for testing broad-beam microwave antennas (1 GHz - 18 GHz), designed and developed by collaborators for several research and commercial projects. These antennas are important in telecommunications, defence and biomedical applications. While facilitating timely pattern measurements of antenna prototypes, it will open new opportunities in antenna experimentation. This facility will enhance collaborators' highly acclaimed theoretical research by providing experimental results for theory validation. Near-field patterns available from the facility will advance our knowledge on complicated antennas. This will generate researchers skilled in state-of-the art antenna measurements, and will help develop competitive Australian industries in this frontier technology.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
NUMERICAL MODELS OF PLATE TECTONICS, MANTLE CONVECTION AND SLAB DYNAMICS WITH EVOLVING FAULTS. We plan to develop a method for simulating large-scale
geological structures with a much improved treatment
of tectonic faults in 3D.
Current computer models have sharp geological faults at plate
boundaries represented by broad, blurred zones. New techniques
for modeling cracks in engineering structures will be scaled up to
the whole Earth.
This will help us to understand how the Earth's p ....NUMERICAL MODELS OF PLATE TECTONICS, MANTLE CONVECTION AND SLAB DYNAMICS WITH EVOLVING FAULTS. We plan to develop a method for simulating large-scale
geological structures with a much improved treatment
of tectonic faults in 3D.
Current computer models have sharp geological faults at plate
boundaries represented by broad, blurred zones. New techniques
for modeling cracks in engineering structures will be scaled up to
the whole Earth.
This will help us to understand how the Earth's plates move and
interact now and in the past and how the structure of the continents
arose.
Not only is this intrinsically interesting, it
will also be of immediate practical benefit to geological modelers.Read moreRead less
Black Hole Accretion: The Effects of Magnetic Fields and Radiation. This project represents a significant contribution by Australian researchers to one of Science's Big Questions: How do Black Holes channel gravitational energy into radiation at many different energies and into high speed outflows. It offers Australian Astronomy an opportunity to expand its endeavours into the rapidly growing and high profile areas of high-energy and computational astrophysics, injecting new expertise into the i ....Black Hole Accretion: The Effects of Magnetic Fields and Radiation. This project represents a significant contribution by Australian researchers to one of Science's Big Questions: How do Black Holes channel gravitational energy into radiation at many different energies and into high speed outflows. It offers Australian Astronomy an opportunity to expand its endeavours into the rapidly growing and high profile areas of high-energy and computational astrophysics, injecting new expertise into the interpretation of multi-wavelength data on accreting black holes. We will train a new cohort of internationally competitive students and early career researchers, equipping them with the advanced computational and modelling skills that are in increasingly higher demand in many technology-based industries.Read moreRead less
The link between the deep Earth and its dynamic surface. Modelling the two-way interaction of plate tectonics with the actions of erosion and sedimentation gives a fundamentally new view of the dynamics of our planet and the importance of the surface on the deep interior. It will improve our understanding of the formation of sedimentary basins, their evolution and their preservation over geological time.