Numbers limit how accurately digital computers model chaos

Digital computers use numbers based on flawed representations of real numbers, which may lead to inaccuracies when simulating the motion of molecules, weather systems and fluids, find UCL and Tufts University scientists. The study, published today in Advanced Theory and Simulations , shows that digital computers cannot reliably reproduce the behaviour of 'chaotic systems' which are widespread. This fundamental limitation could have implications for high performance computation (HPC) and for applications of machine learning to HPC. Professor Peter Coveney, Director of the UCL Centre for Computational Science and study co-author, said: "Our work shows that the behaviour of the chaotic dynamical systems is richer than any digital computer can capture. Chaos is more commonplace than many people may realise and even for very simple chaotic systems, numbers used by digital computers can lead to errors that are not obvious but can have a big impact. Ultimately, computers can't simulate everything." The team investigated the impact of using floating-point arithmetic - a method standardised by the IEEE and used since the 1950s to approximate real numbers on digital computers. Digital computers use only rational numbers, ones that can be expressed as fractions.