sppexa · performance prediction of multigrid -solver configurations plackett-burman design (pbd)...
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![Page 1: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/1.jpg)
Performance Prediction of Multigrid-Solver Configurations
Performance Prediction of Multigrid-Solver Configurations
Norbert Siegmund
Harald Köstler
Alexander Grebhahn
Sven Apel
![Page 2: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/2.jpg)
Performance Prediction of Multigrid-Solver Configurations
General Challenge: Finding the Optimal Configuration for a Given Hardware Platform?
2
cgs
preS
preS
preS postS
postS
postS
restriction à
prol
onga
tion à
Stencil code
![Page 3: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/3.jpg)
Performance Prediction of Multigrid-Solver Configurations
General Challenge: Finding the Optimal Configuration for a Given Hardware Platform?
2
cgs
preS
preS
preS postS
postS
postS
restriction à
prol
onga
tion à
Stencil code
![Page 4: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/4.jpg)
Performance Prediction of Multigrid-Solver Configurations
General Challenge: Finding the Optimal Configuration for a Given Hardware Platform?
2
cgs
preS
preS
preS postS
postS
postS
restriction à
prol
onga
tion à
Stencil code
![Page 5: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/5.jpg)
Performance Prediction of Multigrid-Solver Configurations
What is the Influence of Configuration Options on Performance?
3
![Page 6: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/6.jpg)
Performance Prediction of Multigrid-Solver Configurations
What is the Influence of Configuration Options on Performance?
3
![Page 7: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/7.jpg)
Performance Prediction of Multigrid-Solver Configurations
What is the Influence of Configuration Options on Performance?
3
Binary options
![Page 8: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/8.jpg)
Performance Prediction of Multigrid-Solver Configurations
What is the Influence of Configuration Options on Performance?
3
Binary options Numeric options
![Page 9: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/9.jpg)
Performance Prediction of Multigrid-Solver Configurations
What is the Influence of Configuration Options on Performance?
3
Binary options Numeric options
![Page 10: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/10.jpg)
Performance Prediction of Multigrid-Solver Configurations
What is the Influence of Configuration Options on Performance?
3
Binary options Numeric options
![Page 11: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/11.jpg)
Performance Prediction of Multigrid-Solver Configurations
What is the Influence of Configuration Options on Performance?
3
Binary options Numeric options
![Page 12: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/12.jpg)
Performance Prediction of Multigrid-Solver Configurations
What is the Influence of Configuration Options on Performance?
3
Binary options Numeric options
Perf
orm
ance
![Page 13: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/13.jpg)
Performance Prediction of Multigrid-Solver Configurations
Vision: Performance-Influence Models
4
![Page 14: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/14.jpg)
Performance Prediction of Multigrid-Solver Configurations
Vision: Performance-Influence Models
Determine the influence of configuration options and their interactions
4
![Page 15: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/15.jpg)
Performance Prediction of Multigrid-Solver Configurations
Vision: Performance-Influence Models
Determine the influence of configuration options and their interactions
4
![Page 16: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/16.jpg)
Performance Prediction of Multigrid-Solver Configurations
Vision: Performance-Influence Models
Determine the influence of configuration options and their interactions
4
![Page 17: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/17.jpg)
Performance Prediction of Multigrid-Solver Configurations
Vision: Performance-Influence Models
Determine the influence of configuration options and their interactions
– Understanding
4
and use it for:
![Page 18: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/18.jpg)
Performance Prediction of Multigrid-Solver Configurations
Vision: Performance-Influence Models
Determine the influence of configuration options and their interactions
– Understanding – Debugging
4
and use it for:
![Page 19: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/19.jpg)
Performance Prediction of Multigrid-Solver Configurations
Vision: Performance-Influence Models
Determine the influence of configuration options and their interactions
– Understanding – Debugging – Prediction and optimization
4
14.3 + 113.3 - 4.5 - 73.9 + 171.7 = 219.9
and use it for:
![Page 20: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/20.jpg)
Performance Prediction of Multigrid-Solver Configurations
Learning Procedure
5
![Page 21: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/21.jpg)
Performance Prediction of Multigrid-Solver Configurations
Learning Procedure
5
Sampling
![Page 22: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/22.jpg)
Performance Prediction of Multigrid-Solver Configurations
Learning Procedure
5
Sampling Learning
![Page 23: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/23.jpg)
Performance Prediction of Multigrid-Solver Configurations
Learning Procedure
5
Sampling Learning Performance-Influence Model
![Page 24: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/24.jpg)
Performance Prediction of Multigrid-Solver Configurations
Learning Procedure
5
Sampling Learning Performance-Influence Model
![Page 25: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/25.jpg)
Performance Prediction of Multigrid-Solver Configurations
Sampling Binary and Numeric Options
Structured sampling approaches for the different kinds of options
6
![Page 26: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/26.jpg)
Performance Prediction of Multigrid-Solver Configurations
Sampling Binary and Numeric Options
Binary Options
Structured sampling approaches for the different kinds of options
6
![Page 27: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/27.jpg)
Performance Prediction of Multigrid-Solver Configurations
Sampling Binary and Numeric Options
Binary Options Numeric Options
Structured sampling approaches for the different kinds of options
6
![Page 28: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/28.jpg)
Performance Prediction of Multigrid-Solver Configurations
Sampling Binary and Numeric Options
Binary Options Numeric Options
Structured sampling approaches for the different kinds of options
6
Exponential number!
![Page 29: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/29.jpg)
Performance Prediction of Multigrid-Solver Configurations
Sampling Binary and Numeric Options
Binary Options Numeric Options
Structured sampling approaches for the different kinds of options
6
Exponential number!
![Page 30: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/30.jpg)
Performance Prediction of Multigrid-Solver Configurations
Heuristics for Binary-Option Sampling
• Random? – Unlikely to select a valid configuration – Locally clustered solutions using SAT
7
![Page 31: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/31.jpg)
Performance Prediction of Multigrid-Solver Configurations
Heuristics for Binary-Option Sampling
• Random? – Unlikely to select a valid configuration – Locally clustered solutions using SAT
• Heuristics
– Option-Wise (OW): { }, { }, { }, { }, {}
7
Siegmund et al., ICSE‘12
![Page 32: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/32.jpg)
Performance Prediction of Multigrid-Solver Configurations
Heuristics for Binary-Option Sampling
• Random? – Unlikely to select a valid configuration – Locally clustered solutions using SAT
• Heuristics
– Option-Wise (OW): { }, { }, { }, { }, {} – Negative Option-Wise (nOW): { }, { }, { }, { }, { }
7
Siegmund et al., ICSE‘12
![Page 33: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/33.jpg)
Performance Prediction of Multigrid-Solver Configurations
Heuristics for Binary-Option Sampling
• Random? – Unlikely to select a valid configuration – Locally clustered solutions using SAT
• Heuristics
– Option-Wise (OW): { }, { }, { }, { }, {} – Negative Option-Wise (nOW): { }, { }, { }, { }, { } – Pair-Wise (PW) : { }, { }, { }, { }, { },
{ } 7
Siegmund et al., ICSE‘12
![Page 34: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/34.jpg)
Performance Prediction of Multigrid-Solver Configurations
Numeric-Option Sampling (Experimental Designs)
• Fractional factorial designs • Optimal designs
8
![Page 35: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/35.jpg)
Performance Prediction of Multigrid-Solver Configurations
Numeric-Option Sampling (Experimental Designs)
• Fractional factorial designs • Optimal designs
• Pre-study:
8
cgs
preS
preS
preS postS
postS
postS
restriction à
prol
onga
tion à
Multi-grid solver as subject systems
![Page 36: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/36.jpg)
Performance Prediction of Multigrid-Solver Configurations
Numeric-Option Sampling (Experimental Designs)
• Fractional factorial designs • Optimal designs
• Pre-study:
Plackett-Burman Design as best design
8
cgs
preS
preS
preS postS
postS
postS
restriction à
prol
onga
tion à
Multi-grid solver as subject systems
![Page 37: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/37.jpg)
Performance Prediction of Multigrid-Solver Configurations
Plackett-Burman Design (PBD)
• Minimizes the variance of the estimates of the independent variables (numeric options)
• …while using a limited number of measurements
9
![Page 38: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/38.jpg)
Performance Prediction of Multigrid-Solver Configurations
Plackett-Burman Design (PBD)
• Minimizes the variance of the estimates of the independent variables (numeric options)
• …while using a limited number of measurements • Design specifies seeds depending on the number of experiments to
be conducted (i.e., configurations to be measured)
9
Numeric options
Conf
igur
atio
ns
![Page 39: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/39.jpg)
Performance Prediction of Multigrid-Solver Configurations
Plackett-Burman Design (PBD)
• Minimizes the variance of the estimates of the independent variables (numeric options)
• …while using a limited number of measurements • Design specifies seeds depending on the number of experiments to
be conducted (i.e., configurations to be measured)
9
Numeric options
Conf
igur
atio
ns
Min Center Max
Value range of a numeric option
![Page 40: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/40.jpg)
Performance Prediction of Multigrid-Solver Configurations
Plackett-Burman Design (PBD)
• Minimizes the variance of the estimates of the independent variables (numeric options)
• …while using a limited number of measurements • Design specifies seeds depending on the number of experiments to
be conducted (i.e., configurations to be measured)
9
Numeric options
Conf
igur
atio
ns
Min Center Max
Value range of a numeric option
![Page 41: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/41.jpg)
Performance Prediction of Multigrid-Solver Configurations
Plackett-Burman Design (PBD)
• Minimizes the variance of the estimates of the independent variables (numeric options)
• …while using a limited number of measurements • Design specifies seeds depending on the number of experiments to
be conducted (i.e., configurations to be measured)
9
Numeric options
Conf
igur
atio
ns
Min Center Max
Value range of a numeric option
![Page 42: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/42.jpg)
Performance Prediction of Multigrid-Solver Configurations
Learning Procedure
10
Sampling Learning Performance-Influence Model
![Page 43: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/43.jpg)
Performance Prediction of Multigrid-Solver Configurations
Learning Procedure
10
Sampling Learning Performance-Influence Model
![Page 44: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/44.jpg)
Performance Prediction of Multigrid-Solver Configurations
20
50
100
50
20
100
100
0
16
32
32
32
0
16
0
1
1
0
1
0
1
0
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Regression Learning
11
1
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Conf
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![Page 45: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/45.jpg)
Performance Prediction of Multigrid-Solver Configurations
20
50
100
50
20
100
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16
32
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0
16
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Regression Learning
11
1
0
1
1
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Perf.
833
411
290
799
753
514
416
=
Individual Options
Conf
igur
atio
ns
![Page 46: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/46.jpg)
Performance Prediction of Multigrid-Solver Configurations
20
50
100
50
20
100
100
0
16
32
32
32
0
16
0
1
1
0
1
0
1
0
1
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1
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1
Regression Learning
11
1
0
1
1
1
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Perf.
833
411
290
799
753
514
416
=
β1 β2 β3 β4 β5
Individual Options
Conf
igur
atio
ns
* * * * *
![Page 47: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/47.jpg)
Performance Prediction of Multigrid-Solver Configurations
20
50
100
50
20
100
100
0
16
32
32
32
0
16
0
1
1
0
1
0
1
0
1
0
1
1
0
1
Regression Learning
11
1
0
1
1
1
0
1
Perf.
833
411
290
799
753
514
416
=
β1 β2 β3 β4 β5
Individual Options
102.4 84.3 54.1 5.4 1.3
Error:
41%
Conf
igur
atio
ns
* * * * *
![Page 48: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/48.jpg)
Performance Prediction of Multigrid-Solver Configurations
0
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0 1600
20
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16
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Regression Learning
11
1
0
1
1
1
0
1
Perf.
833
411
290
799
753
514
416
=
β1 β2 β3 β4 β5 β6 β7 β8
Individual Options Interactions
102.4 84.3 54.1 5.4 1.3
Error:
41%
Conf
igur
atio
ns
* * * * * * * *
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Performance Prediction of Multigrid-Solver Configurations
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Regression Learning
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Perf.
833
411
290
799
753
514
416
=
β1 β2 β3 β4 β5 β6 β7 β8
Individual Options Interactions
102.4 84.3 54.1 5.4 1.3
132.3 81.3 56.6 3.5 1.9 -14.1 -5.4 2.4
Error:
41%
25%
Conf
igur
atio
ns
* * * * * * * *
![Page 50: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/50.jpg)
Performance Prediction of Multigrid-Solver Configurations
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Regression Learning
11
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N/A
1.2
0.9
1.5
1.5
N/A
1.2
2 Log( ) Perf.
833
411
290
799
753
514
416
=
β1 β2 β3 β4 β5 β6 β7 β8 β9 β10
Individual Options Interactions Functions
102.4 84.3 54.1 5.4 1.3
132.3 81.3 56.6 3.5 1.9 -14.1 -5.4 2.4
Error:
41%
25%
Conf
igur
atio
ns
* * * * * * * * * *
![Page 51: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/51.jpg)
Performance Prediction of Multigrid-Solver Configurations
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Regression Learning
11
1
0
1
1
1
0
1
N/A
1.2
0.9
1.5
1.5
N/A
1.2
2 Log( ) Perf.
833
411
290
799
753
514
416
=
β1 β2 β3 β4 β5 β6 β7 β8 β9 β10
Individual Options Interactions Functions
102.4 84.3 54.1 5.4 1.3
132.3 81.3 56.6 3.5 1.9 -14.1 -5.4 2.4
130.3 83.5 54.2 0.01 0 -14.1 -5.4 1.4 2.1 8.8
Error:
41%
25%
7.4%
Conf
igur
atio
ns
* * * * * * * * * *
![Page 52: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/52.jpg)
Performance Prediction of Multigrid-Solver Configurations
0
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1
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1
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1
0
1
1
0
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Regression Learning
11
1
0
1
1
1
0
1
N/A
1.2
0.9
1.5
1.5
N/A
1.2
2 Log( ) Perf.
833
411
290
799
753
514
416
=
β1 β2 β3 β4 β5 β6 β7 β8 β9 β10
Individual Options Interactions Functions
102.4 84.3 54.1 5.4 1.3
132.3 81.3 56.6 3.5 1.9 -14.1 -5.4 2.4
130.3 83.5 54.2 0.01 0 -14.1 -5.4 1.4 2.1 8.8
Error:
41%
25%
7.4%
Conf
igur
atio
ns
* * * * * * * * * *
Exponential number!
![Page 53: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/53.jpg)
Performance Prediction of Multigrid-Solver Configurations
0
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0 1600
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1
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Regression Learning
11
1
0
1
1
1
0
1
N/A
1.2
0.9
1.5
1.5
N/A
1.2
2 Log( ) Perf.
833
411
290
799
753
514
416
=
β1 β2 β3 β4 β5 β6 β7 β8 β9 β10
Individual Options Interactions Functions
102.4 84.3 54.1 5.4 1.3
132.3 81.3 56.6 3.5 1.9 -14.1 -5.4 2.4
130.3 83.5 54.2 0.01 0 -14.1 -5.4 1.4 2.1 8.8
Error:
41%
25%
7.4%
Conf
igur
atio
ns
* * * * * * * * * *
Exponential number! Unlimited candidates!
![Page 54: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/54.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
![Page 55: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/55.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1
![Page 56: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/56.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1
![Page 57: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/57.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1 β0+ * β1
β0+ * β1
β0+ * β1
β0+ * β1
![Page 58: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/58.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1 β0+ * β1 50%
125%
72%
35%
β0+ * β1
β0+ * β1
β0+ * β1
![Page 59: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/59.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1 β0+ * β1 50%
125%
72%
35% 2 2
log( )
β0+ * β1
β0+ * β1
β0+ * β1
β0+ * β1
β0+ log( ) * β1
![Page 60: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/60.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1 β0+ * β1 50%
125%
72%
35% 2 2
log( )
29%
34%
β0+ * β1
β0+ * β1
β0+ * β1
β0+ * β1
β0+ log( ) * β1
![Page 61: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/61.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1 β0+ * β1 50%
125%
72%
35% 2 2
log( )
29%
34%
β0+ * β1
β0+ * β1
β0+ * β1
β0+ * β1
β0+ log( ) * β1
![Page 62: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/62.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1 β0+ * β1 50%
125%
72%
35% 2 2
log( )
29%
34%
β0 + * β1 2
β0+ * β1
β0+ * β1
β0+ * β1
β0+ * β1
β0+ log( ) * β1
![Page 63: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/63.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1 β0+ * β1 50%
125%
72%
35% 2 2
log( )
29%
34%
β0 + * β1 2
2
…
log( )
β0+ * β1
β0+ * β1
β0+ * β1
β0+ * β1
β0+ log( ) * β1
![Page 64: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/64.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1 β0+ * β1 50%
125%
72%
35% 2 2
log( )
29%
34%
β0 + * β1 2
2
…
* β2
…
log( )
β0 + * β1 + 2
* β2 β0 + * β1 + 2
* β2 β0 + * β1 + 2
* β2 β0 + * β1 + 2
* β2 β0 + * β1 +log( ) 2
β0+ * β1
β0+ * β1
β0+ * β1
β0+ * β1
β0+ log( ) * β1
![Page 65: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/65.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1 β0+ * β1 50%
125%
72%
35% 2 2
log( )
29%
34%
β0 + * β1 2
2
…
* β2 5% …
12%
18%
27%
… …
log( )
β0 + * β1 + 2
* β2 β0 + * β1 + 2
* β2 β0 + * β1 + 2
* β2 β0 + * β1 + 2
* β2 β0 + * β1 +log( ) 2
β0+ * β1
β0+ * β1
β0+ * β1
β0+ * β1
β0+ log( ) * β1
![Page 66: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/66.jpg)
Performance Prediction of Multigrid-Solver Configurations 12
Multiple Regression with Feature Subset Selection
Compression Encryption CacheSize PageSize
Candidates: Models: Errors: Winner:
1 β0+ * β1 50%
125%
72%
35% 2 2
log( )
29%
34%
β0 + * β1 2
2
…
* β2 5% …
12%
18%
27%
… …
2
log( )
β0 + * β1 + 2
* β2 β0 + * β1 + 2
* β2 β0 + * β1 + 2
* β2 β0 + * β1 + 2
* β2 β0 + * β1 +log( ) 2
β0+ * β1
β0+ * β1
β0+ * β1
β0+ * β1
β0+ log( ) * β1
β0 + * β1 + * β2
![Page 67: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/67.jpg)
Performance Prediction of Multigrid-Solver Configurations
Learning Procedure
13
Sampling Learning Performance-Influence Model
![Page 68: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/68.jpg)
Performance Prediction of Multigrid-Solver Configurations
Learning Procedure
13
Sampling Learning Performance-Influence Model
![Page 69: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/69.jpg)
Performance Prediction of Multigrid-Solver Configurations
1. Experiment: Leveraging Domain Knowledge
• Test system: HSMGP
– Different smoothers, coarse-grid solvers, # pre-smoothing, # post-smoothing, # cores
14
![Page 70: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/70.jpg)
Performance Prediction of Multigrid-Solver Configurations
1. Experiment: Leveraging Domain Knowledge
• Test system: HSMGP
– Different smoothers, coarse-grid solvers, # pre-smoothing, # post-smoothing, # cores
14
![Page 71: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/71.jpg)
Performance Prediction of Multigrid-Solver Configurations
1. Experiment: Leveraging Domain Knowledge
15
• Assumptions: 1. The runtime of the coarse-grid solver is not affected
by the selection of the smoother and the number of pre-smoothing and post-smoothing steps.
2. Pre-smoothing sweeps and post-smoothing sweeps needs the same time.
![Page 72: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/72.jpg)
Performance Prediction of Multigrid-Solver Configurations
1. Experiment: Leveraging Domain Knowledge
15
• Assumptions: 1. The runtime of the coarse-grid solver is not affected
by the selection of the smoother and the number of pre-smoothing and post-smoothing steps.
2. Pre-smoothing sweeps and post-smoothing sweeps needs the same time.
![Page 73: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/73.jpg)
Performance Prediction of Multigrid-Solver Configurations
1. Experiment: Leveraging Domain Knowledge
15
• Assumptions: 1. The runtime of the coarse-grid solver is not affected
by the selection of the smoother and the number of pre-smoothing and post-smoothing steps.
2. Pre-smoothing sweeps and post-smoothing sweeps needs the same time.
![Page 74: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/74.jpg)
Performance Prediction of Multigrid-Solver Configurations
1. Experiment: Leveraging Domain Knowledge
15
• Assumptions: 1. The runtime of the coarse-grid solver is not affected
by the selection of the smoother and the number of pre-smoothing and post-smoothing steps.
2. Pre-smoothing sweeps and post-smoothing sweeps needs the same time.
![Page 75: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/75.jpg)
Performance Prediction of Multigrid-Solver Configurations
1. Experiment: Leveraging Domain Knowledge
15
• Assumptions: 1. The runtime of the coarse-grid solver is not affected
by the selection of the smoother and the number of pre-smoothing and post-smoothing steps.
2. Pre-smoothing sweeps and post-smoothing sweeps needs the same time.
![Page 76: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/76.jpg)
Performance Prediction of Multigrid-Solver Configurations
2. Experiment: Code Generator
• 20 configuration options from different domains (hardware-specific, multigrid-specific, optimizations)
• Global Model vs. Local Model
16
![Page 77: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/77.jpg)
Performance Prediction of Multigrid-Solver Configurations
2. Experiment: Code Generator
• 20 configuration options from different domains (hardware-specific, multigrid-specific, optimizations)
• Global Model vs. Local Model
16
![Page 78: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/78.jpg)
Performance Prediction of Multigrid-Solver Configurations
2. Experiment: Code Generator
• 20 configuration options from different domains (hardware-specific, multigrid-specific, optimizations)
• Global Model vs. Local Model
16
![Page 79: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/79.jpg)
Performance Prediction of Multigrid-Solver Configurations
Findings and Future Work
17
![Page 80: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/80.jpg)
Performance Prediction of Multigrid-Solver Configurations
Findings and Future Work
17
![Page 81: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/81.jpg)
Performance Prediction of Multigrid-Solver Configurations
Findings and Future Work
17
![Page 82: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/82.jpg)
Performance Prediction of Multigrid-Solver Configurations
Findings and Future Work
17
![Page 83: SPPEXA · Performance Prediction of Multigrid -Solver Configurations Plackett-Burman Design (PBD) •Minimizes the variance of the estimates of the independent variables (numeric](https://reader036.vdocuments.us/reader036/viewer/2022081613/5fbec0a3c996e9791b1fe41c/html5/thumbnails/83.jpg)
Performance Prediction of Multigrid-Solver Configurations
Findings and Future Work
17
https://github.com/nsiegmun/SPLConqueror http://fosd.de/SPLConqueror/
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Performance Prediction of Multigrid-Solver Configurations
Findings and Future Work
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