Discovery Early Career Researcher Award - Grant ID: DE230100829
Funder
Australian Research Council
Funding Amount
$425,100.00
Summary
Geometric approaches to quantum many body problems. The project aims to utilise results from differential geometry and related areas to investigate the physics of interacting many-body quantum systems. This project expects to generate new knowledge in the area of mathematical physics with broad applications in quantum information, condensed matter physics and statistical mechanics. The key focus will lie on the development of variational methods for the efficient simulation of quantum evolution ....Geometric approaches to quantum many body problems. The project aims to utilise results from differential geometry and related areas to investigate the physics of interacting many-body quantum systems. This project expects to generate new knowledge in the area of mathematical physics with broad applications in quantum information, condensed matter physics and statistical mechanics. The key focus will lie on the development of variational methods for the efficient simulation of quantum evolution and the characterisation of suitable quantum state families by their correlation structures.Read moreRead less
Causal Knowledge-Empowered Adaptive Federated Learning. Federated learning tools are a promising framework for collaborative machine learning (ML) that also maintain data privacy; however, their ability to model heterogeneous data remains a key challenge. This project aims to develop a new learning scheme for coordinated training of ML models that successfully bridges variable data distributions. The framework proposed will be the first globally that can use causal knowledge to 1) handle data he ....Causal Knowledge-Empowered Adaptive Federated Learning. Federated learning tools are a promising framework for collaborative machine learning (ML) that also maintain data privacy; however, their ability to model heterogeneous data remains a key challenge. This project aims to develop a new learning scheme for coordinated training of ML models that successfully bridges variable data distributions. The framework proposed will be the first globally that can use causal knowledge to 1) handle data heterogeneity across devices and 2) address the real-world challenges when only a subset of devices have labelled data. Expected outcomes and benefits include the theoretical underpinnings and algorithms of causality-based collaborative training of ML models while better preserving the users’ data privacy.Read moreRead less
Linking wave–sea ice feedbacks to rapid ice retreat. Antarctic sea ice extent has been in sharp decline since 2016, which is stressing the fragile Southern Ocean and Antarctic environments so vital to the global climate. This project aims to investigate a crucial candidate mechanism of sea ice loss by predicting rapid ice retreat in response to large Southern Ocean waves. New theory and modelling capabilities that account for wave–ice feedbacks will underpin the predictions, leveraging on recent ....Linking wave–sea ice feedbacks to rapid ice retreat. Antarctic sea ice extent has been in sharp decline since 2016, which is stressing the fragile Southern Ocean and Antarctic environments so vital to the global climate. This project aims to investigate a crucial candidate mechanism of sea ice loss by predicting rapid ice retreat in response to large Southern Ocean waves. New theory and modelling capabilities that account for wave–ice feedbacks will underpin the predictions, leveraging on recent research breakthroughs, including novel datasets derived from satellite and field observations. The outcomes are expected to quantify sea ice retreat due to ocean waves for the first time, with potentially major implications for coupled wave–sea ice modelling in climate studies.Read moreRead less
Stochastic majorization--minimization algorithms for data science. The changing nature of acquisition and storage data has made the process of drawing inference infeasible with traditional statistical and machine learning methods. Modern data are often acquired in real time, in an incremental nature, and are often available in too large a volume to process on conventional machinery. The project proposes to study the family of stochastic majorisation-minimisation algorithms for computation of inf ....Stochastic majorization--minimization algorithms for data science. The changing nature of acquisition and storage data has made the process of drawing inference infeasible with traditional statistical and machine learning methods. Modern data are often acquired in real time, in an incremental nature, and are often available in too large a volume to process on conventional machinery. The project proposes to study the family of stochastic majorisation-minimisation algorithms for computation of inferential quantities in an incremental manner. The proposed stochastic algorithms encompass and extend upon a wide variety of current algorithmic frameworks for fitting statistical and machine learning models, and can be used to produce feasible and practical algorithms for complex models, both current and future.
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Unpacking the immune system with applied mathematics. This project aims to model immune interactions across cells and structures spanning scales of nanometres to millimetres. It expects to develop innovative mathematical insights, improve our understanding of immunology, and consolidate collaborations with top American and European laboratories and groups. Expected outcomes include cutting-edge techniques for multiscale biological modelling and improved prediction and analysis of immune dynami ....Unpacking the immune system with applied mathematics. This project aims to model immune interactions across cells and structures spanning scales of nanometres to millimetres. It expects to develop innovative mathematical insights, improve our understanding of immunology, and consolidate collaborations with top American and European laboratories and groups. Expected outcomes include cutting-edge techniques for multiscale biological modelling and improved prediction and analysis of immune dynamics. The project should provide benefits to industries where highly organised behaviours are important, for example those interested in robot swarming, optimal transportation, and epidemic management. It should also benefit Australian students and researchers with novel overseas training opportunities.Read moreRead less
ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellu ....ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. ARC Centre of Excellence for the Mathematical Analysis of Cellular Systems. The ARC Centre for the Mathematical Analysis of Cellular Systems aims to deliver the mathematics required to compute life. The Centre will deliver innovation in computational and mathematical biology and establish in silico biology alongside in vivo and in vitro biology. These models will allow us to understand the complexity of life at the cellular level and enable new ways of combining diverse and heterogenous data. This will allow us to understand the mechanisms underlying cellular behaviour, and to apply rational design engineering methods in order to control the dynamics of biological systems. Read moreRead less
How do vortices live in spatio-temporally complex flows? The project aims to understand the fundamental mechanism of vortices occurring in flows involving spatio-temporal complexity, by using the combination of dynamical systems theory and asymptotic analysis. This innovative combined mathematical analysis will be coupled with sophisticated computations to be enabled by the international interdisciplinary collaboration between the Mathematics and Engineering at Australia and Japan. The expected ....How do vortices live in spatio-temporally complex flows? The project aims to understand the fundamental mechanism of vortices occurring in flows involving spatio-temporal complexity, by using the combination of dynamical systems theory and asymptotic analysis. This innovative combined mathematical analysis will be coupled with sophisticated computations to be enabled by the international interdisciplinary collaboration between the Mathematics and Engineering at Australia and Japan. The expected outcomes are breakthroughs in the fundamental understanding of turbulence. This should lead to significant insight into better turbulent modellings used in, for example, wide range of engineering, physiological and geophysical flows.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE230100579
Funder
Australian Research Council
Funding Amount
$445,754.00
Summary
The existence and abundance of small bases of permutation groups. This project aims to study bases for permutation groups, which are the mathematical formalisation of symmetry. Bases are crucial to encoding and computing with groups in diverse areas of science. Small bases are desirable for efficiency, but can be hard to find. This project expects to combine techniques from areas of algebra and probability to determine the existence and abundance of bases. Expected outcomes of this project inclu ....The existence and abundance of small bases of permutation groups. This project aims to study bases for permutation groups, which are the mathematical formalisation of symmetry. Bases are crucial to encoding and computing with groups in diverse areas of science. Small bases are desirable for efficiency, but can be hard to find. This project expects to combine techniques from areas of algebra and probability to determine the existence and abundance of bases. Expected outcomes of this project include new methods to address enduring open problems in the study of bases, as well as novel applications of existing techniques. This should provide significant benefits, such as creating and strengthening international collaborations, and building on Australia’s reputation as a powerhouse of finite group theory.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE230100029
Funder
Australian Research Council
Funding Amount
$345,197.00
Summary
Variational Inference for Intractable and Misspecified State Space Models. State space models (SSMs) are popularly used to model economic variables such as inflation and financial volatility. Variational inference is a technique that allows for fast implementation of SSMs, but whose properties are yet to be understood. This project aims to study the properties of variational inference for SSMs used in economics.
This research will develop new variational inference techniques to improve inferent ....Variational Inference for Intractable and Misspecified State Space Models. State space models (SSMs) are popularly used to model economic variables such as inflation and financial volatility. Variational inference is a technique that allows for fast implementation of SSMs, but whose properties are yet to be understood. This project aims to study the properties of variational inference for SSMs used in economics.
This research will develop new variational inference techniques to improve inferential and predictive accuracy from SSMs. An expected implication of this project is that it will expand the ability of economic institutions to employ larger SSMs, which will allow for more accurate models for economic variables. This will provide significant social benefits by leading to better informed economic policy.
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Distributed Optimisation without Central Coordination. This project will develop the mathematical foundations for discovery and analysis of iterative methods for optimisation problems in distributed computing systems. Most methods in distributed optimisation were not designed for distributed computing, rather they were adapted for purpose post-hoc. By building on recent advances in monotone operator splitting, this project expects to develop a mathematical theory for decentralised optimisation a ....Distributed Optimisation without Central Coordination. This project will develop the mathematical foundations for discovery and analysis of iterative methods for optimisation problems in distributed computing systems. Most methods in distributed optimisation were not designed for distributed computing, rather they were adapted for purpose post-hoc. By building on recent advances in monotone operator splitting, this project expects to develop a mathematical theory for decentralised optimisation algorithms specially designed for distributed systems. The framework is expected to produce a suite of algorithms, each customised to exploit a specific network configuration. The project will provide significant benefits in distributed machine learning applications such as federated learning.Read moreRead less