In this talk, I will introduce our recent work on scalable finite-element earthquake simulation methods. First I will introduce a scalable finite-element solver accelerated by data-driven methods. Here, the accuracy of initial solutions used in iterative solvers in time-history simulations are improved using past time-step data, leading to significant speedup on Fugaku. Second, I will introduce a scalable solver based on a stochastic finite-element method to conduct uncertainty quantification of huge-scale problems. Last, I will introduce our work on OpenACC-based acceleration of these finite-element methods on GPU-based systems.