Almost 18 months ago, Bill Harrod (my boss) and I discussed what more needed to be done in mathematics for the era of extreme-scale computing. We had already started a modest program named “RX-Solvers” to look at fault-tolerant algorithms. As the three ASCR Exascale Co-Design Centers (exmatex.org, cesar.mcs.anl.gov, and exactcodesign.org) work to influence future computer architectures and consider the tradeoffs, more computational scientists have begun to realize that it may be impossible to “port” codes to the future computers: algorithms and the machines have been ill-suited for each other for a long time now; a new execution model may be required; and new algorithms for the new systems would need to be designed, implemented, and analyzed. Thus the Exascale Mathematics Working Group (EMWG) was born. You can learn more about the EMWG – and read the report here.
A lot of work has gone into organizing the huge volume of materials the EMWG has processed into a coherent report. As stated in the Summary, this report is a “synthesis of the perspectives” of over seventy members of the applied mathematics community on research gaps, approaches, and directions “into an integrated outlook on the applied mathematics research necessary to achieve scientific breakthroughs using exascale systems.” Section 3 briefly lays out the hardware challenges that open up new avenues in mathematics research. My fellow mathematicians will find Section 4 creatively organized, comprehensive but with sufficient depth, touching on a wide variety of topics relevant to solving worthy problems on a computer – and always bringing out what’s important! Section 5, in particular Section 5.3, talks about the dependencies on efforts outside of mathematics: in the era of extreme-scale computing, no one person can do it alone, and mutually-beneficial collaboration is the key to success. And, of course, do not miss Section 6: Common Themes, Findings, and Recommendations.
Members of the Working Group put aside personal agendas to help me visualize the immense opportunities the paradigm shift in hardware architectures may bring to mathematics. They made time for the Working Group meetings in spite of competing priorities from a flurry of exascale-related activities — for example, in the midst of writing this report, a good chunk of the Working Group was pulled away to work on yet another exascale-related report requested by the Acting Director of Office of Science. That they were able to stick to it for more than 12 months is a testament to their professionalism and love of mathematics. You can find the details of EMWG’s process in the Introduction of its report.
I invite the SIAM community to visit the Exascale Mathematics homepage and let me know what you think! I hope to see you all in July at the Annual Meeting in Chicago!