David Bailey stated that science is built upon the foundations of theory and experiment validated and improved through open and transparent communication. Numerical round-off error and numerical differences though are greatly magnified as computational simulations are scaled up to run on highly parallel systems.
The problem of numerical reliability is that many applications routinely use either 32-bit or 64-bit IEEE arithmetic.
The 2012 discovery of the Higgs boson in the ATLAS experiment at the Large Hadron Collider in Geneva relied crucially on the ability to track charged particles with an exquisite precision and high reliability, David Bailey explained
The software involved 5 millions line of C++ and python code, developed by roughly 2000 physicists and engineers over 15 years.
Recently, in an attempt to speed up the calculation, one has employed expert numerical analysts to re-examine every algorithm employed in the computation to ensure that only the most stable known schemes are being used, as the speaker outlined.
Of the 2010 University of California at Berkeley graduation class, 870 students were in a discipline likely to require technical computing. Fewer than 2% of Berkeley graduates who will do technical computing have had rigorous training in numerical analysis. David Bailey thought this might become problematic for future HPC development.
Plans are being unfolded to enhance reproducibility with high-precision arithmetic. The computation takes only 3.47 seconds when the summation is changed to double-double, the result is identical to the double-double result.
There has been considerable resistance in the scientific computing community to the notion that more than 64-bit arithmetic is not only useful, but may even be essential in some scientific computing.
David Bailey expanded on the CORVETTE project and the Precimonious tool. The aim is to develop software facilities to find and ameliorate numerical anomalies in large-scale computations. This involves facilities to test the level of numerical accuracy rewired for an application; facilities to delimit the portions of code that are inaccurate; facilities to search the space of possible code modifications; and facilities to repair numerical difficulties including usage of high precision arithmetic.
David Bailey said that applications where high precision is useful or essential are planetary orbit calculations but also supernova simulations. Researchers at Lawrence Berkeley National Laboratory have used quad-double arithmetic to solve for non-local thermodynamic equilibrium.
In climate modelling, computational results are altered even if minor changes are made to the code or the system. Numerical variation is a major nuisance for code maintenance, David Bailey explained. By using double-double arithmetic in two key inner loops, most of this numerical variation disappeared.
The most practical solution to difficulties is to judiciously employ higher-precision arithmetic, combined with some smart tools to identify sensitivities and make the requisite code modifications, David Bailey stated.
Fortunately, such computations are now feasible using modern HPC technology, he concluded.