A machine-learning checkpoint/restart algorithm for particle-in-cell simulations.

With ever-increasing computing power and memory capacity, particle check-pointing for fault recovery of particle-in-cell simulations is stressing I/O subsystems, and becoming prohibitive. Given that future exascale computers are expected to be significantly more vulnerable to hard faults than current HPC systems, the availability of a fast and accurate recovery strategy is absolutely essential. In this study, we consider compression of the particle distribution function (PDF) by unsupervised machine-learning techniques.\footnote{G. Chen and L. Chac\'on, ``A machine-learning checkpoint/restart algorithm for particle-in-cell simulations'', in preparation} Specifically, we approximate the PDF with a Gaussian mixture.\footnote{Geoffrey McLachlan and David Peel. Finite Mixture Models. John Wiley \& Sons, 2004.} The Gaussian mixture is found by employing maximum likelihood principle with an information criterion, the minimum-message-length principle, for determining an optimal density estimation of the PDF.$^2$ Restart is conducted by moment-matching sampling of the Gaussian mixture, which strictly conserves charge/mass, momentum, and energy. We demonstrate the effectiveness of the method with various electrostatic and electromagnetic particle-in-cell simulations in 1D and 2D.