# MSI Friends and Alumni: Can mathematics help save energy in computing?

Professor Markus Hegland will be presenting a special lecture for MSI's Alumni, friends and colleagues. The presentation will be followed by drinks, hors-d’oeuvres and a chance to meet and chat with the speaker and other members of the MSI.

Attendance at these special lectures is by invitation only, so if you would like to attend, please register as a friend of MSI to receive your invitation.

## Abstract

In 2013, it has been estimated that the digital economy uses a tenth of the world's electricity (see Time article). Mobile phones drain their batteries quickly and often require a daily recharge. On the other side of the computing scale, the cost of running the next generation of supercomputers (typically used for weather forecast, banking and research) is estimated to overtake its purchase price within a year of usage.

There is lot of ongoing research on computer engineering focussing on energy-efficient solutions. As the major cost of computing is that of transferring data one approach is to make pathways between computational components shorter. The processors used in phones in particular have been designed with energy efficiency in mind. Supercomputing had some success by employing GPUs which are able to do certain instructions originally related to graphics applications with a low energy footprint.

Mathematics is used in the essential algorithms in computational science and engineering which underpin the development of any new technological device. Mathematics can guarantee that the simulations required throughout the development cycle produce reliable and timely results. It is thus no surprise that this kind of mathematics is an important component in the curriculum of modern science and engineering. The mathematics used here includes branches of almost all areas of (pure) mathematics. Arguably at the core are numerical analysis and approximation theory which are branches of analysis.

In this talk I will review some algorithmic approaches which (may) save energy. Traditionally, this has been done by reducing the complexity of the algorithms which initially meant a reduction of the number of multiplications used. In modern computing the number of multiplications is not really a good metric for energy any more. Today, dominating computational costs are due to data movements. This includes the costs for moving data from memory to the processors and the cost of moving data between the computational cores and between the cores and specialised processors like the

GPU. An important aspect of the computational approach is its reliability and reproducibility. Computers will produce the same accurate result every time a computation is repeated. It turns out, however, that this reliability actually does have a very high energetic footprint. The question is of course how much reliability and reproducibility do we really need. With mathematical tools we can assess how relaxing the reliability of some of the components and systems does affect the end results. Furthermore, we can develop new algorithms which are resilient to faults of the hardware.

The aim of the mathematical research is to show that we can control the accuracy and reliability of our results even if some of the hardware is less reliable. This will ultimately lead to a new way of energy saving in computing.

## About the speaker

Markus Hegland has a diploma in mathematics from the ETH in Zurich, Switzerland and worked there for 5 years in mechanical engineering. He then received a PhD with Silver Medal in mathematics from the ETH in 1988. He was one of the inaugural research fellows at the newly formed Interdisciplinary Project Center for Supercomputing for three years.

He came to ANU in 1992 on a one year stint in supercomputing after which he was supposed to continue at ETH. However, after a year his ANU contract was extended by one year and he resigned from ETH to stay at the ANU until now. Except for a short break of 7 years in computer science he has been a member of the MSI where he currently holds a professorial position. He has been awarded a Senior Hans Fischer Fellowship at the IAS of the Technical University of Munich from 2011-2013. He is still a member of the IAS Focus Group in High Performance Computing in computer science. Markus has been attracted to problems which appear to be computationally intractable due to the curse of dimensionality, ill-posedness and dependency in parallel computing.