Fast scalable implicit solver with convergence of equation-based modeling and data-driven learning: earthquake city simulation on low-order unstructured finite element

We developed a new approach in converging equation-based modeling and data-driven learning on high-performance computing resources to accelerate physics-based earthquake simulations. Here, data-driven learning based on data generated while conducting equation-based modeling was used to accelerate the convergence process of an implicit low-order unstructured finite-element solver. This process involved a suitable combination of data-driven learning for estimating high-frequency components and coarsened equation-based models for estimating low-frequency components of the problem. The developed solver achieved a 12.8-fold speedup over the state-of-art solver with a 96.4% size-up scalability up to 24,576 nodes (98,304 MPI processes × 12 OpenMP threads = 1,179,648 CPU cores) of Fugaku with 126,581,788,413 degrees-of-freedom, leading to solving a huge city earthquake shaking analysis in a 10.1-fold shorter time than the previous state-of-the-art solver. Furthermore, to show that the developed method attains high performance on variety of systems with small implementation costs, we ported the developed method to recent GPU systems by use of directive based methods (OpenACC). The equation based modeling and the data-driven learning are of utterly different characteristics, and hence they are rarely combined. The developed approach of combining them is effective, and remarkable results mentioned above are achieved.