MAthematics for Competitive ADvantage (MACAD)

This project addresses the major challenges of performance and energy efficiency in modern large-scale computing systems. As the industry shifts towards accelerator technology in order to continue delivering the performance gains needed in massive data processing applications, focusing on optimised algorithmic behaviour inside these applications is becoming increasingly important. This project will deliver new analysis and modelling techniques for the numerical properties of applications. This will allow us to harness the flexibility of accelerator technology through specialised number formats and algorithm discretisation steps that are tailored to the unique requirements of the application.

The efficiency of the proposed approach will be demonstrated in two application areas with high academic and industrial impact:

Monte Carlo hybrid methods for linear algebra, are stochastic methods which have linear complexity proportional to the size of the matrix. Algorithmically these methods enable high levels of parallelism: Markov chains generation can be done independently to provide efficient computation with minimal communication using pipelining. The Monte Carlo matrix inverse can be calculated and used as a preconditioner with GMRES, BICGSTAB or any other efficient iterative method thus delivering a highly efficient hybrid method.
Machine Learning became an almost ubiquitous technology underpinning multiple economic sectors. Besides Machine Learning applications are notorious for their numerical flexibility, where many core matrix operations can be performed in reduced (half) or mixed precision. This makes it an ideal candidate for optimisation with Maxeler hardware and software. This project will explore and optimise key linear algebra operations at the heart of multiple Machine Learning applications: matrix inversion for Kahlman filters, Conjugate Gradient Method for training neural networks and diagonalisation of large dense matrices for principal components analysis.
The new optimisation techniques deployed have the potential to deliver a 10x improvement in terms of processing speed and energy efficiency over implementations in traditional numeric formats. In addition, we expect to have a generalised methodology of mapping these type of problems efficiently on dataflow type architectures.