Nonlinear Mode Decomposition and Reduced-Order Modeling for Three-Dimensional Cylinder Flow by Distributed Learning on Fugaku

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).