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Erschienen in: Computing and Visualization in Science 5-6/2018

09.11.2018 | Original Article

Multilevel techniques for compression and reduction of scientific data—the univariate case

verfasst von: Mark Ainsworth, Ozan Tugluk, Ben Whitney, Scott Klasky

Erschienen in: Computing and Visualization in Science | Ausgabe 5-6/2018

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Abstract

We present a multilevel technique for the compression and reduction of univariate data and give an optimal complexity algorithm for its implementation. A hierarchical scheme offers the flexibility to produce multiple levels of partial decompression of the data so that each user can work with a reduced representation that requires minimal storage whilst achieving the required level of tolerance. The algorithm is applied to the case of turbulence modelling in which the datasets are traditionally not only extremely large but inherently non-smooth and, as such, rather resistant to compression. We decompress the data for a range of relative errors, carry out the usual analysis procedures for turbulent data, and compare the results of the analysis on the reduced datasets to the results that would be obtained on the full dataset. The results obtained demonstrate the promise of multilevel compression techniques for the reduction of data arising from large scale simulations of complex phenomena such as turbulence modelling.

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Literatur
1.
Zurück zum Zitat Ainsworth, M., Klasky, S., Whitney, B.: Compression using lossless decimation: analysis and application. SIAM J. Sci. Comput. 39(4), B732–B757 (2017)MathSciNetCrossRefMATH Ainsworth, M., Klasky, S., Whitney, B.: Compression using lossless decimation: analysis and application. SIAM J. Sci. Comput. 39(4), B732–B757 (2017)MathSciNetCrossRefMATH
2.
Zurück zum Zitat Austin, W., Ballard, G., Kolda, T. G.: Parallel tensor compression for large-scale scientific data. In: 2016 IEEE international parallel and distributed processing symposium (IPDPS), pp. 912–922, May 2016 Austin, W., Ballard, G., Kolda, T. G.: Parallel tensor compression for large-scale scientific data. In: 2016 IEEE international parallel and distributed processing symposium (IPDPS), pp. 912–922, May 2016
3.
4.
Zurück zum Zitat Bautista, G., Leonardo, A., Cappello, F.: Improving floating point compression through binary masks. In: 2013 IEEE international conference on big data, pp. 326–331, October 2013 Bautista, G., Leonardo, A., Cappello, F.: Improving floating point compression through binary masks. In: 2013 IEEE international conference on big data, pp. 326–331, October 2013
5.
Zurück zum Zitat Bornemann, F., Yserentant, H.: A basic norm equivalence for the theory of multilevel methods. Numer. Math. 64(1), 455–476 (1993)MathSciNetCrossRefMATH Bornemann, F., Yserentant, H.: A basic norm equivalence for the theory of multilevel methods. Numer. Math. 64(1), 455–476 (1993)MathSciNetCrossRefMATH
6.
Zurück zum Zitat Burtscher, M., Hari, M., Annie, Y., Farbod, H.: Real-time synthesis of compression algorithms for scientific data. In: SC ‘16: proceedings of the international conference for high performance computing, networking, storage and analysis, IEEE, pp. 264–275, November 2016 Burtscher, M., Hari, M., Annie, Y., Farbod, H.: Real-time synthesis of compression algorithms for scientific data. In: SC ‘16: proceedings of the international conference for high performance computing, networking, storage and analysis, IEEE, pp. 264–275, November 2016
7.
Zurück zum Zitat Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley Series in Telecommunications, 1st edn. Wiley, New York (1991)CrossRefMATH Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley Series in Telecommunications, 1st edn. Wiley, New York (1991)CrossRefMATH
9.
Zurück zum Zitat Daubechies, I.: The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inf. Theory 36(5), 961–1005 (1990)MathSciNetCrossRefMATH Daubechies, I.: The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inf. Theory 36(5), 961–1005 (1990)MathSciNetCrossRefMATH
10.
Zurück zum Zitat Di, S., Cappello, F.: Fast error-bounded lossy HPC data compression with SZ. In: 2016 IEEE 30th international parallel and distributed processing symposium, IEEE, Chicago, IL, USA, pp. 730–739, May 2016 Di, S., Cappello, F.: Fast error-bounded lossy HPC data compression with SZ. In: 2016 IEEE 30th international parallel and distributed processing symposium, IEEE, Chicago, IL, USA, pp. 730–739, May 2016
11.
Zurück zum Zitat Donoho, D.L., Vetterli, M., DeVore, R.A., Daubechies, I.: Data compression and harmonic analysis. IEEE Trans. Inf. Theory 44(6), 2435–2476 (1998)MathSciNetCrossRefMATH Donoho, D.L., Vetterli, M., DeVore, R.A., Daubechies, I.: Data compression and harmonic analysis. IEEE Trans. Inf. Theory 44(6), 2435–2476 (1998)MathSciNetCrossRefMATH
12.
Zurück zum Zitat Edmunds, D.E., Triebel, H.: Function Spaces, Entropy Numbers, Differential Operators, 1st edn. Cambridge University Press, Cambridge (1996)CrossRefMATH Edmunds, D.E., Triebel, H.: Function Spaces, Entropy Numbers, Differential Operators, 1st edn. Cambridge University Press, Cambridge (1996)CrossRefMATH
13.
Zurück zum Zitat Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)MATH Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)MATH
14.
Zurück zum Zitat Grgic, S., Kers, K., Grgic, M.: Image compression using wavelets. In: Proceedings of the IEEE international symposium on industrial electronics, 1999. ISIE ‘99, vol. 1, pp. 99–104 (1999) Grgic, S., Kers, K., Grgic, M.: Image compression using wavelets. In: Proceedings of the IEEE international symposium on industrial electronics, 1999. ISIE ‘99, vol. 1, pp. 99–104 (1999)
15.
Zurück zum Zitat Griebel, M., Oswald, P.: Stable splittings of Hilbert spaces of functions of infinitely many variables. J. Complex. 41, 126–151 (2017)MathSciNetCrossRefMATH Griebel, M., Oswald, P.: Stable splittings of Hilbert spaces of functions of infinitely many variables. J. Complex. 41, 126–151 (2017)MathSciNetCrossRefMATH
16.
Zurück zum Zitat Ibarria, L., Lindstrom, P., Rossignac, J., Szymczak, A.: Out-of-core compression and decompression of large n-dimensional scalar fields. Comput. Graph. Forum 22(3), 343–348 (2003)CrossRef Ibarria, L., Lindstrom, P., Rossignac, J., Szymczak, A.: Out-of-core compression and decompression of large n-dimensional scalar fields. Comput. Graph. Forum 22(3), 343–348 (2003)CrossRef
17.
Zurück zum Zitat Johns Hopkins Turbulence Databases. Forced isotropic turbulence dataset description, October 2017. Last update: 10/19/2017 5:55:14 PM. Accessed 01 Feb 2018 Johns Hopkins Turbulence Databases. Forced isotropic turbulence dataset description, October 2017. Last update: 10/19/2017 5:55:14 PM. Accessed 01 Feb 2018
18.
Zurück zum Zitat Kolmogorov, A.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds’ numbers. Akademiia Nauk SSSR Doklady 30, 301–305 (1941)MathSciNet Kolmogorov, A.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds’ numbers. Akademiia Nauk SSSR Doklady 30, 301–305 (1941)MathSciNet
19.
Zurück zum Zitat Lakshminarasimhan, S., Shah, N., Ethier, S., Klasky, S., Latham, R., Ross, R., Samatova, N. F.: Compressing the incompressible with ISABELA: in-situ reduction of spatio-temporal data. In: Emmanuel J., Raymond N., Jean R. (eds) Euro-Par 2011: Parallel Processing Workshops, Lecture Notes in Computer Science, Bordeaux, France, Springer, Berlin, Heidelberg, vol. 6852, pp. 366–379, August 2011 Lakshminarasimhan, S., Shah, N., Ethier, S., Klasky, S., Latham, R., Ross, R., Samatova, N. F.: Compressing the incompressible with ISABELA: in-situ reduction of spatio-temporal data. In: Emmanuel J., Raymond N., Jean R. (eds) Euro-Par 2011: Parallel Processing Workshops, Lecture Notes in Computer Science, Bordeaux, France, Springer, Berlin, Heidelberg, vol. 6852, pp. 366–379, August 2011
20.
Zurück zum Zitat Li, Y., Perlman, E., Wan, M., Yang, Y., Meneveau, C., Burns, R., Chen, S., Szalay, A., Eyink, G.: A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. J. Turbul. 9, N31 (2008)CrossRefMATH Li, Y., Perlman, E., Wan, M., Yang, Y., Meneveau, C., Burns, R., Chen, S., Szalay, A., Eyink, G.: A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. J. Turbul. 9, N31 (2008)CrossRefMATH
21.
Zurück zum Zitat Lindstrom, P.: Fixed-rate compressed floating-point arrays. IEEE Trans. Vis. Comput. Graph. 20(12), 2674–2683 (2014)CrossRef Lindstrom, P.: Fixed-rate compressed floating-point arrays. IEEE Trans. Vis. Comput. Graph. 20(12), 2674–2683 (2014)CrossRef
22.
Zurück zum Zitat Lindstrom, P., Isenburg, M.: Fast and efficient compression of floating-point data. IEEE Trans. Vis. Comput. Graph. 12(5), 1245–1250 (2006)CrossRef Lindstrom, P., Isenburg, M.: Fast and efficient compression of floating-point data. IEEE Trans. Vis. Comput. Graph. 12(5), 1245–1250 (2006)CrossRef
23.
Zurück zum Zitat Marcellin, M. W., Gormish, M. J., Bilgin, A., Boliek, M. P.: An overview of JPEG-2000. In: Proceedings DCC 2000. Data compression conference, pp. 523–541 (2000) Marcellin, M. W., Gormish, M. J., Bilgin, A., Boliek, M. P.: An overview of JPEG-2000. In: Proceedings DCC 2000. Data compression conference, pp. 523–541 (2000)
24.
Zurück zum Zitat Oswald, P.: Multilevel Finite Element Approximation. Theory and Applications. Teubner Skripten zur Numerik. B. G. Teubner, Stuttgart (1994)CrossRefMATH Oswald, P.: Multilevel Finite Element Approximation. Theory and Applications. Teubner Skripten zur Numerik. B. G. Teubner, Stuttgart (1994)CrossRefMATH
25.
Zurück zum Zitat Perlman, E., Burns, R., Li, Y., Meneveau, C.: Data exploration of turbulence simulations using a database cluster. In: Proceedings of the 2007 ACM/IEEE conference on supercomputing, ACM, Reno, NV, USA, vol. 23, November 2007 Perlman, E., Burns, R., Li, Y., Meneveau, C.: Data exploration of turbulence simulations using a database cluster. In: Proceedings of the 2007 ACM/IEEE conference on supercomputing, ACM, Reno, NV, USA, vol. 23, November 2007
26.
Zurück zum Zitat Salomon, D.: Data Compression: The Complete Reference, 4th edn. Springer, London (2007)MATH Salomon, D.: Data Compression: The Complete Reference, 4th edn. Springer, London (2007)MATH
27.
Zurück zum Zitat Schendel, E. R., Jin, Y., Shah, N., Chen, J., Chang, C. S., Ku, S.-H., Ethier, S., Klasky, S., Latham, R., Ross, R., Samatova, N. F.: ISOBAR preconditioner for effective and high-throughput lossless data compression. In: 2012 IEEE 28th international conference on data engineering, pp. 138–149, April 2012 Schendel, E. R., Jin, Y., Shah, N., Chen, J., Chang, C. S., Ku, S.-H., Ethier, S., Klasky, S., Latham, R., Ross, R., Samatova, N. F.: ISOBAR preconditioner for effective and high-throughput lossless data compression. In: 2012 IEEE 28th international conference on data engineering, pp. 138–149, April 2012
28.
Zurück zum Zitat Schneider, K., Farge, M., Pellegrino, G., Rogers, M.M.: Coherent vertex simulation of three-dimensional turbulent mixing layers using orthogonal wavelets. J. Fluid Mech. 534, 39–66 (2005)MathSciNetCrossRefMATH Schneider, K., Farge, M., Pellegrino, G., Rogers, M.M.: Coherent vertex simulation of three-dimensional turbulent mixing layers using orthogonal wavelets. J. Fluid Mech. 534, 39–66 (2005)MathSciNetCrossRefMATH
29.
Zurück zum Zitat Shah, N., Schendel, E. R., Lakshminarasimhan, S., Pendse, S. V., Rogers, T., Samatova, N. F.: Improving I/O throughput with PRIMACY: preconditioning ID-mapper for compressing incompressibility. In: 2012 IEEE international conference on cluster computing, pp. 209–219, September 2012 Shah, N., Schendel, E. R., Lakshminarasimhan, S., Pendse, S. V., Rogers, T., Samatova, N. F.: Improving I/O throughput with PRIMACY: preconditioning ID-mapper for compressing incompressibility. In: 2012 IEEE international conference on cluster computing, pp. 209–219, September 2012
30.
Zurück zum Zitat Strengert, M., Magallón, M., Weiskopf, D., Guthe, S., Ertl, T.: Hierarchical visualization and compression of large volume datasets using GPU clusters. EGPGV, pp. 41–48 (2004) Strengert, M., Magallón, M., Weiskopf, D., Guthe, S., Ertl, T.: Hierarchical visualization and compression of large volume datasets using GPU clusters. EGPGV, pp. 41–48 (2004)
31.
Zurück zum Zitat Wallace, G. K.: The JPEG still picture compression standard. IEEE Trans. Consum. Electron. 38(1), xviii–xxxiv (1992) Wallace, G. K.: The JPEG still picture compression standard. IEEE Trans. Consum. Electron. 38(1), xviii–xxxiv (1992)
Metadaten
Titel
Multilevel techniques for compression and reduction of scientific data—the univariate case
verfasst von
Mark Ainsworth
Ozan Tugluk
Ben Whitney
Scott Klasky
Publikationsdatum
09.11.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Computing and Visualization in Science / Ausgabe 5-6/2018
Print ISSN: 1432-9360
Elektronische ISSN: 1433-0369
DOI
https://doi.org/10.1007/s00791-018-00303-9

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