We discuss the central importance of reproducibility in the pursuit of scientific knowledge, understanding, and prediction. Unfortunately, at this time it remains true that much computational science is not reproducible, for a number of reasons. Our current work seeks to redress some of these shortcomings through the development of a software toolkit that can provide support for verification, validation and uncertainty quantification, which is applicable and now being used in multiple different domains. In many application domains that one encounters in high performance computing contexts, one must confront both systematic and random errors; in the latter case, one commonly has to deal with chaotic dynamical systems. The question of how to sample these reliably and effectively is integral to the credibility of reported results. We have recently shown that such dynamical systems, when represented on digital computers, manifest a new pathology of the IEEE floating point numbers, which cannot be removed regardless of the level of precision used. In the case of a very simple but representative dynamical system, the generalized Bernoulli map, for which exact results are known, we find that the errors produced by floating point arithmetic can sometimes be catastrophic while, in more generic cases, the errors are of order unity. This indicates that many computational studies of chaotic systems, such as arise in turbulence and molecular dynamics, are likely to contain significant errors which hitherto are unknown to the community of practitioners. I will conclude with some suggestions for how to address this pathology.
Prof Peter V. Coveney holds a chair in Physical Chemistry, is an Honorary Professor in Computer Science at University College London (UCL), a Professor in Applied High Performance Computing at the University of Amsterdam (UvA), and Professor Adjunct at Yale University School of Medicine (USA). He is Director of the Centre for Computational Science (CCS) at UCL. Coveney is active in a broad area of interdisciplinary research including condensed matter physics and chemistry, materials science, as well as life and medical sciences in all of which high performance computing plays a major role.