Abstract
Nonlinear modes of the three-dimensional flow field around a cylinder were extracted by distributed learning on Fugaku. Mode decomposition is an approach used to decompose flow fields into physically important flow structures known as modes. In this study, convolutional neural network-based mode decomposition was applied to the three-dimensional flow field. However, because this process is costly in terms of calculation and memory usage for even a small flow field problem, the enormous computational and memory resources of the supercomputer Fugaku were employed. A hybrid parallelism method combining the distribution of network structure (model parallelism) and the input data (data parallelism) using up to 10,500 nodes on Fugaku was employed for learning. Further, we constructed a reduced-order model to predict the time evolution of latent vector, using the long short-term memory networks. Finally, we compared the reproduced flow field of the model with that of the original full-order model. In addition, we evaluated the execution performance of the learning process. Using a single core memory group, the whole learning process indicates a value of 129.50 GFLOPS being achieved, 7.57% of the single-precision floating-point arithmetic peak performance. Notably, the convolution calculation for backward-propagation achieved 1103.09 GFLOPS, which is 65.39% of the peak. Furthermore, with the weak scaling test, the whole learning process indicates 72.9% with 25,250 nodes (1,212,000 cores) relative to 750 nodes, the sustained performance is 7.8 PFLOPS. In particular, the convolution calculation for backward-propagation indicates a result of 113 PFLOPS (66.2% of the peak performance).
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Notes
- 1.
At the time of this calculation, Fugaku was not yet in operation.
- 2.
Single-precision is sufficient for precise learning and can increase FLOPS by utilizing the SIMD register.
- 3.
The first two modes, learned by two and 20 mode models, are not the same because if the number of modes when learning is different, the optimal set of modes to reconstruct the energy of the original field are different.
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Acknowledgment
We sincerely appreciate the advice and support of Prof. Koji Fukagata, Mr. Kai Fukami, and Mr. Takaaki Murata of Keio University. This work used computational resources of the supercomputer Fugaku provided by RIKEN.
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Ando, K., Onishi, K., Bale, R., Tsubokura, M., Kuroda, A., Minami, K. (2021). Nonlinear Mode Decomposition and Reduced-Order Modeling for Three-Dimensional Cylinder Flow by Distributed Learning on Fugaku. In: Jagode, H., Anzt, H., Ltaief, H., Luszczek, P. (eds) High Performance Computing. ISC High Performance 2021. Lecture Notes in Computer Science(), vol 12761. Springer, Cham. https://doi.org/10.1007/978-3-030-90539-2_8
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