Transforming Australian bio-based industries through multiscale modelling. Agricultural and forestry biomass can be converted into feedstocks for production of biofuels and biomaterials via synthetic biology. A key challenge is the complex biomass microstructure renders it highly resistant to conversion, and pretreatment is crucial for enhancing process efficiency. Micro-CT imaging will enable particle characterisation and identification of changes in the fibre composition during pretreatment. T ....Transforming Australian bio-based industries through multiscale modelling. Agricultural and forestry biomass can be converted into feedstocks for production of biofuels and biomaterials via synthetic biology. A key challenge is the complex biomass microstructure renders it highly resistant to conversion, and pretreatment is crucial for enhancing process efficiency. Micro-CT imaging will enable particle characterisation and identification of changes in the fibre composition during pretreatment. This information will be used to create a virtual biomass particle model for an in silico investigation to inform optimal process design. The framework will transform the way biomass is processed, contributing to the growth of the Australian bio-manufacturing industry by making it more productive, profitable and sustainable.Read moreRead less
Approximation theory of structured neural networks . Mathematical theory for deep learning has been desired due to the power applications of deep neural networks to deal with big data in various practical domains. The main difficulty lies in the structures and architectures imposed to networks designed for specific learning tasks. Neither the classical approximation theory nor the recent one for depths of ReLU neural networks can be applied due to the structures imposed for processing large dime ....Approximation theory of structured neural networks . Mathematical theory for deep learning has been desired due to the power applications of deep neural networks to deal with big data in various practical domains. The main difficulty lies in the structures and architectures imposed to networks designed for specific learning tasks. Neither the classical approximation theory nor the recent one for depths of ReLU neural networks can be applied due to the structures imposed for processing large dimensional data such as natural images of tens of thousands of dimensions. This project aims at an approximation theory for structured neural networks. We plan to establish mathematical theories for deconvolution with deep convolutional neural networks, operator learning, and spectral graph networks. Read moreRead less
Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods f ....Development of a novel best approximation theory with applications . The aim of this project is to develop an innovative best approximation theory for complex fractional boundary value problems with discontinuities and with no compactness, and then apply the theory to study two classes of complex partial differential equation boundary value problems with industrial applications. The work will lead to the development of a new theory and a suite of innovative analytical and computational methods for solving a wide range of nonlinear problems with singularities and non-local properties. The expected outcomes of the project will significantly advance our methods for the modelling and control of many industrial systems and processes.
Read moreRead less
High Dimensional Approximation, Learning, and Uncertainty. This project aims to develop next-generation computational methods for complex problems in science and engineering that have many uncertain parameters, using advanced high-dimensional strategies and deep learning to enhance computational speed. The significance of the project is that these methods will help address important applications that at present are not feasible or at the edge of feasibility. The expected outcomes are powerful me ....High Dimensional Approximation, Learning, and Uncertainty. This project aims to develop next-generation computational methods for complex problems in science and engineering that have many uncertain parameters, using advanced high-dimensional strategies and deep learning to enhance computational speed. The significance of the project is that these methods will help address important applications that at present are not feasible or at the edge of feasibility. The expected outcomes are powerful methods that will be mathematically rigorous and suitable for a wide variety of applications. The benefits are that the project will boost Australia’s position as a leader in innovation, and contribute to future developments over a wide area, from aerospace engineering to personalised computational oncology.Read moreRead less
Creating Hybrid Exponential Asymptotics for use with Computational Data. Asymptotic analysis is a vital tool for studying small influences with critical effects. This project aims to create an innovative fully-automated asymptotic framework for studying phenomena which are invisible to classical approximation methods, using new ideas from asymptotics and numerical complex analysis. The outcome will be the first framework that can be used on data from numerical simulations or real-life measuremen ....Creating Hybrid Exponential Asymptotics for use with Computational Data. Asymptotic analysis is a vital tool for studying small influences with critical effects. This project aims to create an innovative fully-automated asymptotic framework for studying phenomena which are invisible to classical approximation methods, using new ideas from asymptotics and numerical complex analysis. The outcome will be the first framework that can be used on data from numerical simulations or real-life measurements, and which can be applied automatically without hands-on expert input. It will be used to design submerged structures and efficient vessels with minimal energy loss from surface waves. Expected benefits include making powerful methods accessible to scientists, and new paths for energy-efficient industrial design.Read moreRead less