Monge-Ampere equations and applications. The Monge-Ampere equation is a premier fully nonlinear partial differential equation with significant applications in geometry, physics and applied science. Building upon breakthroughs made by the proposers in previous grant research, this project aims to resolve challenging problems involving Monge-Ampere type equations and applications. The project goal is to establish new regularity theory and classify singularity profile for solutions to Monge-Ampere ....Monge-Ampere equations and applications. The Monge-Ampere equation is a premier fully nonlinear partial differential equation with significant applications in geometry, physics and applied science. Building upon breakthroughs made by the proposers in previous grant research, this project aims to resolve challenging problems involving Monge-Ampere type equations and applications. The project goal is to establish new regularity theory and classify singularity profile for solutions to Monge-Ampere type equation arising in applied sciences, by introducing new ideas and developing innovative cutting-edge techniques. Expected outcomes include resolution of outstanding open problems and continuing enhancement of Australian leadership and expertise in a major area of mathematics.
Read moreRead less
Design of Real-time Optimisation Methods with Guaranteed Performance. The project aim is the development of a framework for the advancement of optimisation algorithms operating in real-time applications. This project expects to generate new knowledge in the area of systems theory and optimisation, and its application to time-varying problems. Expected outcomes of this project should lead to a new theoretical and practical framework that aims to ameliorate the shortcomings of the existing approac ....Design of Real-time Optimisation Methods with Guaranteed Performance. The project aim is the development of a framework for the advancement of optimisation algorithms operating in real-time applications. This project expects to generate new knowledge in the area of systems theory and optimisation, and its application to time-varying problems. Expected outcomes of this project should lead to a new theoretical and practical framework that aims to ameliorate the shortcomings of the existing approaches that struggle to rapidly respond to new information. This should provide significant benefits. Specifically, this project aims to facilitate a technological leap that generates smaller, faster, and more powerful embedded systems such as broadband services, mobile phones, medical imagining, radar and avionics.Read moreRead less
Digitally networked dynamical systems: Performance and robustness analysis. The project aim is to advance mathematical and computational tools for analyzing collections of dynamical systems that interact with each other by the digital exchange of information. The significance of this aim stems from the emergence and growing complexity and scale of such cyber-physical networks in diverse domains, including agriculture, manufacturing, transport, and infrastructure management. The expected outcomes ....Digitally networked dynamical systems: Performance and robustness analysis. The project aim is to advance mathematical and computational tools for analyzing collections of dynamical systems that interact with each other by the digital exchange of information. The significance of this aim stems from the emergence and growing complexity and scale of such cyber-physical networks in diverse domains, including agriculture, manufacturing, transport, and infrastructure management. The expected outcomes will broaden the scope for exploring achievable performance in the design and deployment of systems that leverage networked interaction for operational gains. Beyond the technical advances, benefits will include sustaining Australia's strong reputation in systems engineering research and researcher training in this area.Read moreRead less
Uncertainty in the social cost of carbon dioxide: control theoretic methods. This project aims to redevelop the most commonly used social cost of carbon dioxide (SC-CO2) modeling framework using the best available scientific data and state-of-the-art uncertainty quantification techniques, providing government and industry decision-makers with a robust tool to tackle a carbon-constrained future. This project will deliver improved, robust estimates of the SC-CO2, a proxy for a price on carbon emis ....Uncertainty in the social cost of carbon dioxide: control theoretic methods. This project aims to redevelop the most commonly used social cost of carbon dioxide (SC-CO2) modeling framework using the best available scientific data and state-of-the-art uncertainty quantification techniques, providing government and industry decision-makers with a robust tool to tackle a carbon-constrained future. This project will deliver improved, robust estimates of the SC-CO2, a proxy for a price on carbon emissions that is used by governments, businesses, and financial bodies. This will enable Australia to play a leading and proactive role in the international pursuit of significant and sustained reductions in greenhouse gas emissions.Read moreRead less
Safe, Plug and Play, Multi Agent Dynamic Systems. From driverless cars, to networks of nano satellites, and complex biological networks, the modern world has many examples of multi agent dynamic systems that need careful coordination and control to perform correctly. In many cases, these systems are built up using designs based on intuition, computer simulations and empirical testing. However, there is a clear need to advance the fundamental understandings of such systems: (i) Verifiable overall ....Safe, Plug and Play, Multi Agent Dynamic Systems. From driverless cars, to networks of nano satellites, and complex biological networks, the modern world has many examples of multi agent dynamic systems that need careful coordination and control to perform correctly. In many cases, these systems are built up using designs based on intuition, computer simulations and empirical testing. However, there is a clear need to advance the fundamental understandings of such systems: (i) Verifiable overall dynamic system properties need to be derived to give assurance of performance in situations not previously envisaged; (ii) It is also critical to understand stable system behaviours not just with fixed configurations, but with agile configurations such as splitting, merging, and morphingRead moreRead less
Discovery Early Career Researcher Award - Grant ID: DE230100954
Funder
Australian Research Council
Funding Amount
$354,968.00
Summary
Partial Differential Equations, geometric aspects and applications. The study of Partial Differential Equations (PDEs) is a classical and prolific field of research having a fundamental role in the development of mathematical analysis and motivated by important applications in natural and applied sciences.
This project aims to obtain substantial progress in the field of PDEs. The area of mathematical research covered is extremely broad, at the confluence of analysis and geometry, and with many a ....Partial Differential Equations, geometric aspects and applications. The study of Partial Differential Equations (PDEs) is a classical and prolific field of research having a fundamental role in the development of mathematical analysis and motivated by important applications in natural and applied sciences.
This project aims to obtain substantial progress in the field of PDEs. The area of mathematical research covered is extremely broad, at the confluence of analysis and geometry, and with many applications to other areas of mathematics and natural and applied sciences. The results that will be obtained will produce a significant amount of new knowledge in this extremely difficult, but rapidly growing, field, by exploiting international scientific collaborations and interdisciplinary methods.Read moreRead less
Robust Data-Driven Control for Safety-Critical Systems. This project aims to develop new approaches to controlling robotic and cyber-physical systems in safety-critical applications. This project expects to generate new knowledge in how to harness the power of machine learning for robot control, while guaranteeing safety and stability at all times. The outcomes of this project will be new algorithms and a deeper understanding of the interplay of data, learning, and models, as well as experimenta ....Robust Data-Driven Control for Safety-Critical Systems. This project aims to develop new approaches to controlling robotic and cyber-physical systems in safety-critical applications. This project expects to generate new knowledge in how to harness the power of machine learning for robot control, while guaranteeing safety and stability at all times. The outcomes of this project will be new algorithms and a deeper understanding of the interplay of data, learning, and models, as well as experimental validation on a surgical robot and a bipedal walking robot. This project will provide significant benefits by dramatically increasing the range of applications in which the power of machine learning can be safely applied to advance the capabilities and uptake of robotics.Read moreRead less
Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concr ....Non-local equations at work. This project aims to study non-local fractional equations. These problems arise naturally in many fields of pure and applied mathematics. This project will consider symmetry and rigidity results; problems from atom dislocation theory; nonlocal minimal surfaces; symbolic dynamics for nonlocal equations; and free boundary problems. This project aims to obtain substantial progress in this field, both from the point of view of the mathematical theory and in view of concrete applications. This project should contribute to the development of the mathematical theory and give insight for concrete applications in physics and biology.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
Innovations in sparse optimisation: big data nonsmooth optimisation. This project aims to produce innovative optimisation methods capable of solving a wide range of practical problems that are currently too complex to be solved. Optimisation involving huge data sets is ubiquitous. Sparse optimisation has emerged as a challenging frontier of modern optimisation because it effectively computes an optimal solution with desired low complexity structure so that a resulting solution can be efficiently ....Innovations in sparse optimisation: big data nonsmooth optimisation. This project aims to produce innovative optimisation methods capable of solving a wide range of practical problems that are currently too complex to be solved. Optimisation involving huge data sets is ubiquitous. Sparse optimisation has emerged as a challenging frontier of modern optimisation because it effectively computes an optimal solution with desired low complexity structure so that a resulting solution can be efficiently stored, implemented and utilised, and is robust to the data inexactness. This project aims at developing innovative mathematical techniques and efficient numerical schemes for solving sparse optimisation problems. The intended outcomes will have significant impact on many areas of science, medicine and engineering, where sparse optimisation is used, including cancer radiotherapy optimal planning.Read moreRead less