RANDOMNESS: A RESOURCE FOR REAL-TIME ANALYTICS

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.

1. Academic and Research:

The utilisation of randomness as a computational resource for large-scale problem is a topic that resonates with many scientific areas of current inquisition, transcending the disciplines that are conventionally associated with engineering and physical sciences. We trust that our work will be appealing and influential to many colleagues in engineering, applied mathematics and statistics, working on electromagnetics, acoustics, optics, mechanics as well as biology and finance. Our plans to reach this diverse community involve conference presentations and journal publications with multi-disciplinary audiences. To boost the dissemination of our work and receive the appropriate feedback we have planned a short-term secondment at the lab of Prof Drineas at Purdue, a pioneer of randomised linear algebra as well as monthly interactions with the Alan Turing Institute colleagues. Through the project a PDRA will be trained in a topic that combines mathematical modelling, computational engineering and big data analytics, a exciting and promising sets of skills in today's job market.
The project will also help advance the PI's knowledge in randomisation algorithms.

2. Industry and business:

The randomised FEM and data fitting methods will find beneficiaries within the software industry, particular the providers of technical computing like Comsol, Mathworks, Kitware and many others that are active in numerical simulation of engineering and physical systems. Our planned short-term secondment at Kitware, a worldwide leader in FEM-based simulation, high performance and parallel computing and visualisation, is aimed at facilitating this impact. Manufacturing and multiphase flow metrology companies in pharmaceutical and chemical industries will be helped in achieving better process monitoring analytics at an improved temporal resolution. Due to restrictions for real-time monitoring most of these companies use oversimplified models for measuring and characterising the flow of chemicals within production lines, so our technology will allow them to improve the information content on their diagnostics without sacrificing real-time process diagnostics.

Oil/gas and geophysical exploration companies will also benefit from this research as their imaging and data processing centres deal with massive amounts of survey data and models of extremely high dimension. This research's results could mean reducing their data processing time by significant amounts. We mention indicatively, that by current standards, even with the use of supercomputers, modelling and inversion computations take up to several days of continuous processing. Clinical system manufacturers who develop imaging scanners and cancer therapy equipment can take advantage of our technology to develop real-time imaging of cancer therapy making the treatment more effective. Currently computational constraints prevent imaging and therapy to operate simultaneously.

3. Society at large:

As computational science underpins many engineering aspects, it is natural to anticipate that once sufficiently developed will find its way in healthcare sector to improve data processing times and patient scanning throughput. Existing high-end scanners such as PET, MRI and X-ray CT have significant computational power on board, but still take a significant amount of time to process offline the data before they yield an image. Also, homeland security is of paramount importance in safeguarding the safety of the citizens as they go about their normal business. Scanning for security threads in public places such as airports, train stations as indeed at the front line of the war, relies on remote sensing and data processing that need to take place in real-time to be effective.We trust that our research will pave the way for more efficient and informative security analytics for protecting people.