Estimating the execution time of fully-online multiscale numerical simulations
Resumo
In this paper, we propose a methodology for estimating the execution time of simulations driven by multiscale numerical methods. The methodology explores the idiosyncrasies of multiscale simulators to reduce the uncertainty of predictions. We use the multiscale hybrid-mixed (MHM) finite element method to validate our methodology. We compare our proposed technique with prediction models automatically selected and calibrated by Auto-WEKA. We show that the models obtained with our technique are competitive when compared with the models coming from Auto-WEKA, being interpretable and with much less computational effort during the learning process.Referências
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R. Araya, C. Harder, A. H. Poza, and F. Valentin. Multiscale hybrid-mixed method for the Stokes and Brinkman equations – The method. Computer Methods in Applied Mechanics and Engineering, 324:29–53, 2017.
T. Arbogast, G. Pencheva, M. F. Wheeler, and I. Yotov. A multiscale mortar mixed nite element method. Multiscale Modeling & Simulation, 6(1):319–346, 2007.
T. Chaumont-Frelet and F. Valentin. A multiscale hybrid-mixed method for the Helmholtz equation in heterogeneous domains. SIAM Journal on Numerical Analysis, 58(2):1029– 1067, 2020.
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J. H. L. Fabian, A. T. A. Gomes, and E. Ogasawara. Estimating the execution time of In The Latin America High the coupled stage in multiscale numerical simulations. Performance Computing Conference (to appear), 2020.
I. Farmaga, P. Shmigelskyi, P. Spiewak, and L. Ciupinski. Evaluation of computational complexity of nite element analysis. In 11th International Conference The Experience of Designing and Application of CAD Systems in Microelectronics (CADSM), pages 213–214, 2011.
R. T. Guiraldello, R. F. Ausas, F. S. Sousa, F. Pereira, and G. C. Buscaglia. The multiscale robin coupled method for ows in porous media. Journal of Computational Physics, 355:1–21, 2018.
C. Harder, D. Paredes, and F. Valentin. A family of Multiscale Hybrid-Mixed nite element methods for the Darcy equation with rough coefcients. Journal of Computational Physics, 245:107–130, 2013.
D. N. Hieu, T. Tieu Minh, T. Van Quang, B. X. Giang, and T. Van Hoai. A Machine Learning-Based Approach for Predicting the Execution Time of CFD Applications on Cloud Computing Environment. In Future Data and Security Engineering, pages 40– 52, 2016.
S. Kim, Y. Suh, and J. Kim. EXTES: An Execution-Time Estimation Scheme for Efcient Computational Science and Engineering Simulation via Machine Learning. IEEE Access, 7:98993–99002, 2019.
L. Kotthoff, C. Thornton, H. H. Hoos, F. Hutter, and K. Leyton-Brown. Auto-weka 2.0: Automatic model selection and hyperparameter optimization in weka. Journal of Machine Learning Research, 18(25):1–5, 2017.
P. Malakar, P. Balaprakash, V. Vishwanath, V. Morozov, and K. Kumaran. Benchmarking machine learning methods for performance modeling of scientic applications. In 2018 IEEE/ACM Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems (PMBS), pages 33–44, 2018.
V. Martínez, F. Dupros, M. Castro, and P. Navaux. Performance Improvement of Stencil Computations for Multi-core Architectures based on Machine Learning. Procedia Computer Science, 108:305–314, 2017.
R. J. Quinlan. Learning with Continuous Classes. In 5th Australian Joint Conference on Articial Intelligence, pages 343–348, Singapore, 1992. World Scientic.
H. Silverman. Cahuachi in the Ancient Nasca World. University of Iowa Press, 1993. ISBN 9780877454076.
A. Tiwari, M. A. Laurenzano, L. Carrington, and A. Snavely. Modeling Power and Energy In 2012 IEEE 26th International Parallel and Distributed Usage of HPC Kernels. Processing Symposium Workshops PhD Forum, pages 990–998, 2012.
E. Weinan. Principles of Multiscale Modeling. Cambridge University Press, 2011. I. H. Witten, E. Frank, and M. A. Hall. Data Mining: Practical Machine Learning Tools and Techniques. Morgan Kaufmann, Amsterdam, 3 edition, 2011. ISBN 978-0-12374856-0.
R. Araya, C. Harder, A. H. Poza, and F. Valentin. Multiscale hybrid-mixed method for the Stokes and Brinkman equations – The method. Computer Methods in Applied Mechanics and Engineering, 324:29–53, 2017.
T. Arbogast, G. Pencheva, M. F. Wheeler, and I. Yotov. A multiscale mortar mixed nite element method. Multiscale Modeling & Simulation, 6(1):319–346, 2007.
T. Chaumont-Frelet and F. Valentin. A multiscale hybrid-mixed method for the Helmholtz equation in heterogeneous domains. SIAM Journal on Numerical Analysis, 58(2):1029– 1067, 2020.
J. G. Cleary and L. E. Trigg. K*: An instance-based learner using an entropic distance In 12th International Conference on Machine Learning, pages 108–114, measure. 1995.
Y. Efendiev and T. Y. Hou. Multiscale Finite Element Methods. Springer, 2009. B. Efron and R. J. Tibshirani. An Introduction to the Bootstrap. Number 57 in Monographs on Statistics and Applied Probability. Chapman & Hall/CRC, Boca Raton, Florida, USA, 1993.
J. H. L. Fabian, A. T. A. Gomes, and E. Ogasawara. Estimating the execution time of In The Latin America High the coupled stage in multiscale numerical simulations. Performance Computing Conference (to appear), 2020.
I. Farmaga, P. Shmigelskyi, P. Spiewak, and L. Ciupinski. Evaluation of computational complexity of nite element analysis. In 11th International Conference The Experience of Designing and Application of CAD Systems in Microelectronics (CADSM), pages 213–214, 2011.
R. T. Guiraldello, R. F. Ausas, F. S. Sousa, F. Pereira, and G. C. Buscaglia. The multiscale robin coupled method for ows in porous media. Journal of Computational Physics, 355:1–21, 2018.
C. Harder, D. Paredes, and F. Valentin. A family of Multiscale Hybrid-Mixed nite element methods for the Darcy equation with rough coefcients. Journal of Computational Physics, 245:107–130, 2013.
D. N. Hieu, T. Tieu Minh, T. Van Quang, B. X. Giang, and T. Van Hoai. A Machine Learning-Based Approach for Predicting the Execution Time of CFD Applications on Cloud Computing Environment. In Future Data and Security Engineering, pages 40– 52, 2016.
S. Kim, Y. Suh, and J. Kim. EXTES: An Execution-Time Estimation Scheme for Efcient Computational Science and Engineering Simulation via Machine Learning. IEEE Access, 7:98993–99002, 2019.
L. Kotthoff, C. Thornton, H. H. Hoos, F. Hutter, and K. Leyton-Brown. Auto-weka 2.0: Automatic model selection and hyperparameter optimization in weka. Journal of Machine Learning Research, 18(25):1–5, 2017.
P. Malakar, P. Balaprakash, V. Vishwanath, V. Morozov, and K. Kumaran. Benchmarking machine learning methods for performance modeling of scientic applications. In 2018 IEEE/ACM Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems (PMBS), pages 33–44, 2018.
V. Martínez, F. Dupros, M. Castro, and P. Navaux. Performance Improvement of Stencil Computations for Multi-core Architectures based on Machine Learning. Procedia Computer Science, 108:305–314, 2017.
R. J. Quinlan. Learning with Continuous Classes. In 5th Australian Joint Conference on Articial Intelligence, pages 343–348, Singapore, 1992. World Scientic.
H. Silverman. Cahuachi in the Ancient Nasca World. University of Iowa Press, 1993. ISBN 9780877454076.
A. Tiwari, M. A. Laurenzano, L. Carrington, and A. Snavely. Modeling Power and Energy In 2012 IEEE 26th International Parallel and Distributed Usage of HPC Kernels. Processing Symposium Workshops PhD Forum, pages 990–998, 2012.
E. Weinan. Principles of Multiscale Modeling. Cambridge University Press, 2011. I. H. Witten, E. Frank, and M. A. Hall. Data Mining: Practical Machine Learning Tools and Techniques. Morgan Kaufmann, Amsterdam, 3 edition, 2011. ISBN 978-0-12374856-0.
Publicado
21/10/2020
Como Citar
FABIAN, Juan; GOMES, Antônio; OGASAWARA, Eduardo.
Estimating the execution time of fully-online multiscale numerical simulations. In: SIMPÓSIO EM SISTEMAS COMPUTACIONAIS DE ALTO DESEMPENHO (SSCAD), 21. , 2020, Online.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2020
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p. 191-202.
DOI: https://doi.org/10.5753/wscad.2020.14069.