Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelec ....Optimisation of piezoelectric metamaterials: Towards robotic stress sensors. This project aims to design new piezoelectric material microstructures that can enhance the measurement of complex local stress states within robotic limbs. The project expects to generate new knowledge of the achievable properties of multi-poled piezoelectric materials and develop computational tools for the analysis and structural optimisation of such materials. The designed microstructures may revolutionise piezoelectric sensor technology. Expected outcomes include manufactured proof-of-concept sensors that enable measurement of local stress fields. This should provide significant benefits, such as improved future robot capability and reliability, and research training for next-generation Australian computational mathematicians. Read moreRead less
New mathematics for multi-extremal optimization and diffusion tensor imaging. This project aims to establish numerically certifiable mathematical theory and methods for semi-algebraic optimisation problems. Numerically certifiable optimisation principles and techniques are vital for the practical use of optimisation technologies because they can be readily implemented by common computer models and algorithms. Yet no such methodologies exist for multi-extremal, semi-algebraic optimisation problem ....New mathematics for multi-extremal optimization and diffusion tensor imaging. This project aims to establish numerically certifiable mathematical theory and methods for semi-algebraic optimisation problems. Numerically certifiable optimisation principles and techniques are vital for the practical use of optimisation technologies because they can be readily implemented by common computer models and algorithms. Yet no such methodologies exist for multi-extremal, semi-algebraic optimisation problems which are common in modern science and medicine. The expected outcomes of this project include enhanced optimisation methods for diffusion tensor imaging, an emerging technology in brain sciences.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
Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, i ....Decomposition and Duality: New Approaches to Integer and Stochastic Integer Programming. Because of their rich modelling capabilities, integer programs are widely used in industry for decision making and planning. However their solution algorithms do not have the maturity of their cousins in convex optimisation, where the theory of strong duality is ubiquitous. Efficient methods for convex optimisation under uncertainty do not apply to the integer case, which is highly non-convex. Furthermore, integer models usually assume the data is known with certainty, which is often not the case in the real world. This project will develop new theory and algorithms to enhance the analysis of integer models, including those that incorporating uncertainty, while also enabling the use of parallel computing paradigms. Read moreRead less
Decentralisation and robustness for practical control of complex systems. This project aims to develop the theory and tools to address the control of complex interconnected systems. There is currently an enormous disconnect in decentralised control between the celebrated theoretical advances and the concepts that are used for implementation, or even for computation. The project expects to isolate the key reasons for this disconnect and develop ways to address the control of complex interconnecte ....Decentralisation and robustness for practical control of complex systems. This project aims to develop the theory and tools to address the control of complex interconnected systems. There is currently an enormous disconnect in decentralised control between the celebrated theoretical advances and the concepts that are used for implementation, or even for computation. The project expects to isolate the key reasons for this disconnect and develop ways to address the control of complex interconnected systems. The expected outcome is a tool which can observe information from only a small portion of a network but which may ultimately effect a large portion of the network. This includes smart building management, multi-vehicle systems and convoys, irrigation networks, large array telescopes, and the power distribution grid.Read moreRead less
Fuzzy modelling and design of complex networked systems. This project aims to develop analysis and synthesis approaches for non-linear networked control systems, including modelling, stability analysis and design problems. The non-linear effects and analysis of networked control systems have received considerable attention because of the universal existence of nonlinearities in practice. Network-based non-linear systems are widely used but face problems from non-linearities and networks. This pr ....Fuzzy modelling and design of complex networked systems. This project aims to develop analysis and synthesis approaches for non-linear networked control systems, including modelling, stability analysis and design problems. The non-linear effects and analysis of networked control systems have received considerable attention because of the universal existence of nonlinearities in practice. Network-based non-linear systems are widely used but face problems from non-linearities and networks. This project will establish a software-based nonlinear networked control system platform to test the presented algorithms and strengthen the scenarios in applications. This project is expected to increase Australian excellence in cyber-security and advanced manufacturing.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
Saving energy on trains - demonstration, evaluation, integration. Reducing energy use from rail transport will significantly contribute to cutting carbon dioxide emissions. This project will develop a toolkit to facilitate the introduction of in-cab technologies that help train drivers save energy and stay on time. The toolkit will make it easier to demonstrate, evaluate and integrate the system in a range of railways.
Discovery Early Career Researcher Award - Grant ID: DE120100049
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
New integer programming based theory, formulations and decomposition techniques with applications to integrated problems. Optimisation problems permeate science and industry. By developing new techniques to solve larger and harder problems than is currently possible, more complex questions can be answered, and more accurate solutions obtained. Industries can use such tools to make better financial, resource management, operational, and/or strategic planning decisions.
Discovery Early Career Researcher Award - Grant ID: DE200101791
Funder
Australian Research Council
Funding Amount
$427,082.00
Summary
Mathematically optimal R&D for coral reef conservation. This project aims to develop mathematical methodologies for optimising Research & Development (R&D) of technologies that will secure complex and uncertain ecosystems into the future. Current conventional management approaches will not prevent the degradation of threatened ecosystems like the Great Barrier Reef, so new technologies are needed. The biggest challenge in choosing these technologies is the long delay between development and depl ....Mathematically optimal R&D for coral reef conservation. This project aims to develop mathematical methodologies for optimising Research & Development (R&D) of technologies that will secure complex and uncertain ecosystems into the future. Current conventional management approaches will not prevent the degradation of threatened ecosystems like the Great Barrier Reef, so new technologies are needed. The biggest challenge in choosing these technologies is the long delay between development and deployment, in which time ecosystem function may collapse and complex, dynamic ecological and social systems will change. The mathematical methods and theory developed will inform a Great Barrier Reef case study, and will be ready for rapid application to other ecosystems as the urgent need arises.Read moreRead less