Numerical Algorithms for High-Performance Computational Science: Highlights of the Meeting

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Word cloud from abstracts.

The Royal Society discussion meeting Numerical Algorithms for High-Performance Computational Science, which I organized with Jack Dongarra and Laura Grigori, was held in London, April 8-9, 2019. The meeting had 16 invited speakers and 23 contributed posters, with a poster blitz preceding the lively poster session.

The meeting brought together around 150 people who develop and implement numerical algorithms and software libraries—numerical analysts, computer scientists, and high-performance computing researchers—with those who use them in some of today’s most challenging applications. The aim was to discuss the challenges brought about by evolving computer architectures and the characteristics and requirements of applications, both to produce greater awareness of algorithms that are currently available or under development and to steer research on future algorithms.

Several key themes emerged across multiple talks, all in the context of today’s high performance computing landscape in which processor clock speeds have stagnated (with the end of Moore’s law) and exascale machine are just two or three years away.

  • An important way of accelerating computations is through the use of low precision floating-point arithmetic—in particular by exploiting a hierarchy of precisions.
  • We must exploit low rank matrix structure where it exists, for example in hierarchical (H-matrix) form, combining it with randomized approximations.
  • Minimizing data movement (communication) is crucial, because of its increasing costs relative to the costs of floating-point arithmetic.
  • Co-design (the collaborative and concurrent development of hardware, software, and numerical algorithms, with knowledge of applications) is increasingly important for numerical computing.

Applications treated included deep learning, climate modeling, computational biology, and the Square Kilometre Array (SKA) radio telescope project. We learned that the latter project needs faster FFTs in order to deal with the petabytes of data it will generate each year.

Papers from the meeting will be published in a future issue of Philosophical Transactions of the Royal Society A.

Here are the talks (in order of presentation), with links to the slides.

For a brief summary of the talks see George Constantinides’s insightful thoughts on the meeting.

Here are some photos from the meeting.

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