A.M." Ito

H. "Ohtani

K Hagita

T. Kato

T. Saitoh

T. Takeda

National Institute for Fusion Science (NIFS-Repository)

The peta-scale computers, e.g., Titan, Sequoia andK computer, have started operation, and ultra-huge-scale simulations can be performed. Though many scien-tiﬁc discoveries are expected, there are big urgent issues,that are, data input and output (data I/O), transmis-sion, saving, and analysis including visualization for theenormous volumes of data. These problems are a majorbottleneck in the huge-scale simulation in many ﬁelds.In order to resolve the problems of data size, severaldata compression schemes were proposed. We propose inthis paper that a compression of simulation data from alarge-scale particle simulation holds favorable prospectsfor scientiﬁc visualization of particle systems1,2).Our concepts deal with the data of particle orbitsobtained by simulation directly and have following fea-tures: (i) By the control over the compression scheme,the diﬀerence between the simulation variables and thereconstructed values from the compressed data becomessmaller than an allowed constant for the visualization.(ii) The particles in the simulation are regarded as inde-pendent particles and the time-series data for each par-ticle is compressed with independent time-step for theparticle. (iii) A particle trajectory is approximated bya polynomial function based on the characteristic mo-tion of the particle. In other words, the parameters ofeach polynomial are stored in place of the original data.It is reconstructed as a continuous curve by the inter-polation from the values of the function for intermedi-ate values of the sample data. In short, the continuouscurve which is established by a small number of parame-ters of the interpolation function approximates the origi-nal particle trajectory and the amount of necessary datacan be reduced. We name this concept “TOKI (Time-Order Kinetic Irreversible compression)” originated fromirreversible compression of time-ordered data sequences,such as a particle trajectory, for visualization.In this paper, we encode the simulation data as apost process to examine whether our concepts of datacompression and the encoder work well or not. Thatis, we encode the data which has been already obtainedby simulation. Moreover, we use a cubic function as aninterpolation polynomial for the encoder test.We ﬁrst apply our compression scheme to theplasma particle simulation. The simulation code is athree-dimensional electromagnetic particle-in-cell simu-lation. The boundary conditions are periodic. The datafor compression is a part of full simulation data, andthe number of particles in the encoder test is 800. Theobtained data was calculated during 10,000 time steps.Figure 1 shows the comparison between the simula-tion data and the decoded data reconstructed from theencoded data by the decoder for one electron in x di-rection, and the error between the simulation and thedecoded data. It is found that the decoded data repro-duces the high-frequency motion of the particle, and thatthe error between the simulation data and the decodeddata is less than the allowed error value (=0.1). The er-ror by the encoder can be controlled due to the allowederror value. Compression rate is deﬁned as the ratio ofthe encoded data to the raw data. The rate is 5.7% inthis case. We apply this concept to the galaxy forma-tion simulation result, and get 32.2% compression rate.These rates are good for practical application.We proposed the data compression method “TOKI”of particle trajectory data produced by simulation. Itwas possible to realize a good reproducibility from en-coded data and to control an error between the decodedvalues and simulation data. The next stage is that weinstall this encoder into the simulation code and encodesimultaneously the data with performing simulation.This work was supported by National Institutes ofNatural Sciences (NINS) Program for Cross-DisciplinaryStudy. 0 2 4 6 8 0  2000  4000  6000  8000  10000xDecoded dataRaw data 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0  2000  4000  6000  8000  10000errorstepxyzFig. 1. Reproducibility and error between the simulationand the decoded data. (top) Time evolution of the parti-cle x coordinates is shown. Red line indicates the decodeddata, and green plus symbol shows the simulation data. (bot-tom)Errors (diﬀerence) between the simulation and decodeddata are shown. Plus, cross and square symbols are the errorsfor x, y and z coordinates, respectively.1) Ohtani, H. et al: Conference on ComputationalPhysics 20122) Ohtani, H. et al: J. Physics: Conference Series, ac-cepted.435§32. Irreversible Data Compression Concepts in Time-order of Particle Trajectory for Visualization of Huge Particle SystemOhtani, H., Hagita, K. (Natl. Defense Academy of Japan), Ito, A.M., Kato, T. (Hiroshima Univ.),  Saitoh, T. (Tokyo Inst. of Tech.), Takeda, T. (NAOJ)

Irreversible Data Compression Concepts in Time-order of Particle Trajectory for Visualization of Huge Particle System

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