The scope:
Modern engineering relies on data and models to broaden our understanding of complex systems, devices and processes, through predictive and diagnostic analytics. Examples of this include fluid dynamic simulations for energy conversion, electromagnetic models in geophysical and environmental monitoring, mechanics in design of resilient infrastructures, acoustic and X-ray models for non-destructive testing and optical models in biomedical imaging. Traditionally, numerical computing has been at the forefront of engineering, however its embedding within the engineering process is still hindered by the complexity associated with realistic data models. Currently, process analytics, operate either off-line, on high performance computing infrastructure for accurate simulations and sophisticated data processing algorithms, or in real-time
based on oversimplified problem specifications that yield some crude imperative information.
The challenge:
To empower data centric engineering in manufacturing and quality assurance processes with real-time, accurate modelling and data processing we take on the challenge of real-time, large-scale computing, by replacing the conventional way we perform algebraic computations with a more efficient randomised scheme. In the context of basic solution of linear equations for example, this approach randomly selects a small fraction of the elements in the matrices and the vectors involved, radically reducing the computational effort and time. What's more impressive than this, is that when optimally sampled, this computational efficiency is also complemented by a very small solution error, and thus by investigating ways that we can compute these optimal sampling distributions we can achieve massive computational savings, ultimately providing the productive sectors of the economy with an affordable solution for real-time modelling and data processing, without compromising the quality and accuracy of the sought information.
Main objectives:
The main objective of this project is to develop a new form of the popular finite element method by incorporating algorithms for randomised linear algebra. Through theory, analysis and computation we seek to prove a concept of randomised finite element method for simulating diffusion processes and solving the associated inverse data-fitting problems by investigating how the respective optimal sampling distributions can be computed and sampled in an efficient way.
Why does it matter?
The success of this project will make a measurable contribution on making accurate, high-dimensional computing portable and affordable to the broad engineering and manufacturing sector, allowing for real-time process monitoring and control even where high performance computing infrastructure is not available.
What difference will it achieve?
Our novel framework of data analytics aims to provide prompt and accurate insights into complex and dynamic data and models. In a manufacturing process this will lead to a rise in productivity, monitoring quality of services and products, as well as reduction of operational costs and waste. We also foresee that these advances will find application in the broader engineering sector as well as having an impact health informatics to enable simultaneous imaging and therapy for cancer patients and national security in being able to detect and screen in real time against threads.
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