Error-Controlled Lossy Compression Optimized for High Compression - - PowerPoint PPT Presentation
Error-Controlled Lossy Compression Optimized for High Compression Ratios of Scientific Datasets Xin Liang(University of California, Riverside) Sheng Di (Argonne National Laboratory) Dingwen Tao (University of Alabama) Sihuan Li (University of
Xin Liang(University of California, Riverside) Sheng Di (Argonne National Laboratory) Dingwen Tao (University of Alabama) Sihuan Li (University of California, Riverside) Shaomeng Li (National Center for Atmospheric Research) Hanqi Guo (Argonne National Laboratory) Zizhong Chen (University of California, Riverside) Franck Cappello (Argonne National Laboratory & UIUC)
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u Introduction
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Large amount of scientific data
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Limitations of lossless compression
u Related Works and Limitations u Proposed Predictors
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Mean-integrated Lorenzo predictor
Ø
Regression predictor
u Adaptive Predictor Selection u Evaluation u Conclusion
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u Extremely large amount of data are produced by scientific
simulations and instruments
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CESM (Climate Simulation)
² 2.5 PB raw data produced ² 170 TB post-processed data Ø
HACC (Cosmology Simulation)
² 20 PB data: a single 1-trillion-particle simulation ² Mira at ANL: 26 PB file system storage ² 20 PB / 26 PB ~ 80%
Two partial visualizations of HACC simulation data: coarse grain on full volume or full resolution on small sub-volumes
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u APS-U: next-generation APS (Advanced
Ø 15 PB data for storage Ø 35 TB post-processed floating-point data Ø 100 GB/s bandwidth between APS and Mira Ø 15 PB / 100 GB/s ~ 105 seconds (42 hours)
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u I/O improvement is less than the other parts u From 1960 ~ 2014
Ø Supercomputer speed increased by 11 orders of
magnitude
Ø I/O capacity increased 6 orders of magnitude Ø Internal drive access rate increased by 3~4 orders
Ø We are producing more data than we can store!
Parallel I/O introductory tutorial, online
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u Existing lossless compressors work not efficiently on large-scale scientific data
(compression ratio up to 2)
Table 1: Compression ratios for lossless compressors on large-scale simulations Compression ratio = Original data size / Compressed data size
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u Lossy compression is then proposed to trade the accuracy for compression ratio u Error-bounded lossy compression, in addition, provides user with means to control the error
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u Common compression modes for error-bounded lossy compressors Ø Point-wise absolute error bound ² ² SZ, ZFP, TTHRESH etc. Ø Point-wise relative error bound ² ² ISABELA, FPZIP, SZ etc.
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u Common metrics for accessing error-bounded lossy compressors
Ø Compression Ratio (cratio) ² cratio = ()*+,-./00/1 023/ *+,-./00/1 023/ Ø Compression/Decompression Rate/Speed (crate/drate) ² 45678 = ()*+,-./00/1 023/ *+,-./002+) 92,/
:5678 =
()*+,-./00/1 023/ 1/*+,-./002+) 92,/ Ø RMSE (root of mean squared error) & PSNR (peak signal-to-noise ratio) ² ;<=> = ? @ ∑2B? @
8CD0 E FGH5 = 20 KLM?N
OPQRSOPTU VWXY Ø Rate-distortion
Tao etal, Z-checker: A framework for assessing lossy compression of scientific data, IJHPCA
bitrate = G\]8L^ :6769_-/ ∗ 8 4567\L
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u Existing state-of-the-art error-bounded lossy compressors Ø ISABELA (NCSU) ² Sorting preconditioner ² B-Spline interpolation Ø FPZIP (LLNL) ² Lorenzo prediction with truncation on fixed-point residuals ² Entropy encoding Ø ZFP (LLNL) ² Block-wise exponent align and customized orthogonal block transform ² Block-wise embedded encoding Ø SZ-1.4 (ANL) ² Multi-layer prediction with linear-scaling quantization ² Huffman encoding followed by lossless compression
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u SZ has 4 key stages, among which prediction and quantization are the most important two.
3D Lorenzo predictor
input prediction encoding (lossless)
quantization
x y z
Current data point
f111
(L)
'
f000
'
f100
'
f110
'
f011
'
f001
'
f010
'
f101
SZ multi-layer predictor, default 1 (Lorenzo predictor)
Tao etal., Significantly Improving Lossy Compression for Scientific Data Sets Based on Multidimensional Prediction and Error- Controlled Quantization, IPDPS17.
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input prediction encoding (lossless)
quantization
Uniform quantization with linear scaling in SZ-1.4
Tao etal., Significantly Improving Lossy Compression for Scientific Data Sets Based on Multidimensional Prediction and Error-Controlled Quantization, IPDPS17.
First-phase Predicted Value Real Value Error Bound 2*Error Bound 2*Error Bound
… …
Uniform Quan>za>on Code +1
+2 Second-phase Predicted Value Second-phase Predicted Value Second-phase Predicted Value Second-phase Predicted Value 2*Error Bound 2*Error Bound
Predicted Value Real Value Error Bound
SZ-1.1 à SZ-1.4
(i) Expand the quantization interval from the predicted value (made by previous prediction model) by linear scaling of the error bound (ii) Encode the real value using the quantization interval number (quantization code)
Quantization with one interval in SZ-1.1
Tao etal., Significantly Improving Lossy Compression for Scientific Data Sets Based on Multidimensional Prediction and Error-Controlled Quantization, IPDPS17.
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u Has to use decompressed data for prediction Ø Low prediction accuracy for large error bound ² Predict using inaccurate decompressed data ² The higher dimensional data, the larger the error ² Lead to unexpected artifacts
SZ 1.4 decompressed (cr 111:1) Origin data
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u Has to use decompressed data for prediction Ø Low prediction accuracy for large error bound ² Predict using inaccurate decompressed data ² The higher dimensional data, the larger the error ² Lead to unexpected artifacts Ø Hard to parallelize ² Frequent data dependency between points Ø Prone to error ² One error may propagate to all data
SZ multi-layer predictor, default 1 (Lorenzo predictor)
Tao etal., Significantly Improving Lossy Compression for Scientific Data Sets Based on Multidimensional Prediction and Error-Controlled Quantization, IPDPS17.
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u Use mean to approximate data in the densest interval Ø Advantages ² Predict without decompressed data ² Reduced artifacts ² Work well when data has obvious background Ø Limitations ² Only cover data in the interval ² Degraded performance for more uniform data
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u Adaptive selection – select Lorenzo or M-Lorenzo according to maximum data density in the
densest interval
² Sample dataset: Hurricane, 13 data fields
20 30 40 50 60 70 80 90 100 110 1 2 3 4 5 6 PSNR Bit Rate M-Lorenzo Lorenzo 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4 5 6 Percent of Mean-Integrated Lorenzo Bit Rate
Overall rate distortion on Hurricane Percent of M-Lorenzo
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u Divide data into individual blocks and predict data point in a block by the coefficients from the
linear regression model
Ø Compute Regression Coefficients Ø Predict the data by regression coefficients ² 3D case: !"#"$ = &' ∗ ) + &+ ∗ , + &- ∗ . + &/
2D Regression
Di etal., SZ turtorial, SC18
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u Does not need to use decompressed data for prediction Ø Prediction accuracy will hold for different error bounds ² Predict using the stored coefficients ² Less visible artifacts even when error bound is large
SZ 1.4 decompressed (cr 111:1) OurSol decompressed (cr 117:1) Origin data
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u Does not need to use decompressed data for prediction Ø Prediction accuracy will hold for different error bounds ² Predict using the stored coefficients ² Less visible artifact even when error bound is large Ø Highly parallelizable both inter-block and intra-block ² No data dependency between data points Ø Controlled error propagation ² Error would propagate to at most one block
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u Regression works better under large error bound Ø Cannot model sharp change because of the reconstructed hyperplane is always linear ² Lorenzo: constant for 1D data, linear for 2D data, quadratic for 3D data etc.. Ø High storage cost for regression coefficients ² 1/54 overhead for 6x6x6 block, although it could be further compressed Ø Higher computational cost ² More multiplications than the Lorenzo predictor
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u Sampling + prediction error estimation Ø Regression error can be estimated accurately ² error = !" ∗ $ + !& ∗ ' + !( ∗ ) + !* − data Ø Add some penalty term for Lorenzo ² error = fL − data + 1.22 ∗ 4
Diagonal sampling Penalty estimation
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u Sampling + prediction error estimation Ø Regression error can be estimated accurately ² error = !" ∗ $ + !& ∗ ' + !( ∗ ) + !* − data Ø Add some penalty term for Lorenzo ² error = fL − data + 1.22 ∗ 4
20 30 40 50 60 70 80 90 100 110 1 2 3 4 5 6 PSNR (dB) Bit-rate Our sol. w/ penalty coeff. Our sol. w/o penalty coeff. All regression
40 50 60 70 80 90 0.5 1 1.5 2 2.5 PSNR (dB)
Bit-rate
Our sol. w/ penalty coeff. Our sol. w/o penalty coeff. All regression
20% 40% 60% 80% 100% 0.5 1 1.5 2 2.5 Percentage of regression blocks
Bit-rate
Our sol. w/ penalty coeff. Our sol. w/o penalty coeff. All regression
Rate-distortion on ISABEL (overall) Rate-distortion on TCf48 (single field)
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u Evaluated Datasets Ø CSEM-ATM:
2D, climate simulation
Ø Hurricane-ISABEL:
3D, meteorological simulation
Ø NYX:
3D, cosmological simulation
Ø SCALE-LETKF:
3D, weather simulation
u Experimental platforms Ø Bebop cluster at ANL – up to 128 nodes, each with two Intel Xeon E5-2695 v4 processors
and 128 GB of memory, and each processor with 16 cores
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24 10 20 30 40 50 60 70 80 90 5 10 15 20 25 30 PSNR Bit Rate OurSol SZ ZFP VAPOR FPZIP ISABELA 30 40 50 60 70 80 90 0.5 1 1.5 2 2.5 3
CESM rate distortion
10 20 30 40 50 60 70 80 90 5 10 15 20 25 30 35 PSNR Bit Rate OurSol SZ ZFP VAPOR FPZIP ISABELA TTHRESH 40 50 60 70 80 1 2 3 4 5
Hurricane rate distortion
10 20 30 40 50 60 70 80 90 2 4 6 8 10 12 14 16 18 20 PSNR Bit Rate OurSol SZ ZFP VAPOR FPZIP ISABELA TTHRESH 30
40 50 60 70 80 0.5 1 1.5 2 2.5 3
NYX rate distortion
10 20 30 40 50 60 70 80 90 5 10 15 20 25 30 PSNR Bit Rate OurSol SZ ZFP VAPOR FPZIP ISABELA TTHRESH 30 40 50 60 70 80 90 0.5 1 1.5 2 2.5 3
S-L rate distortion
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down-sampling + tricubic interpolation ZFP decompressed SZ 1.4 decompressed OurSol decompressed
10 20 30 40 50 60 70 80 90 5 10 15 20 25 30 35 PSNR Bit Rate OurSol SZ ZFP VAPOR FPZIP ISABELA TTHRESH 40 50 60 70 80 1 2 3 4 5
Overall rate distortion
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down-sampling + tricubic interpolation ZFP decompressed SZ 1.4 decompressed OurSol decompressed Overall rate distortion
10 20 30 40 50 60 70 80 90 2 4 6 8 10 12 14 16 18 20 PSNR Bit Rate OurSol SZ ZFP VAPOR FPZIP ISABELA TTHRESH 30
40 50 60 70 80 0.5 1 1.5 2 2.5 3
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u Data dumping time: time to dump data to parallel file system
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Data compression time + writing compressed file time
u Data loading time: time to load data from parallel file system
Ø
Reading compressed file time + data decompression time
100 200 300 400 500 600 700 800 900 1000 S Z Z F P O u r S
S Z Z F P O u r S
S Z Z F P O u r S
Elapsed Time(s) Number of Cores compression time data writing time 8192 4096 2048 200 400 600 800 1000 1200 Elapsed Time(s) S Z Z F P O u r S
S Z Z F P O u r S
S Z Z F P O u r S
Number of Cores 8192 4096 2048 decompression time data reading time
Data dumping time Data loading time
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u We propose an adaptive lossy compression framework by dividing a dataset into blocks and
select the best-fit predictor for each block
u We propose two new predictors to mitigate the impact of decompressed data in traditional
Lorenzo predictor under large error bounds
u We develop an algorithm to adaptively select the best-fit predictor u We evaluate the proposed method with six other state-of-the-art lossy compressors in terms
parallel experiments for the dumping/loading performance on parallel file system
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This research was supported by the Exascale Computing Project (17-SC-20-SC), a joint project of the U.S. Department
Nuclear Security Administration, responsible for delivering a capable exascale ecosystem, including software, applications, and hardware technology, to support the nation’s exascale computing imperative.
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