Fused ensembles of dynamic-rupture earthquake simulations to accelerate Bayesian inference

Understanding earthquake dynamics is essential for seismic hazard assessment and risk mitigation. In this context, Bayesian inference provides valuable insights into model parameters by combining simulation models with real-world data. Such Bayesian parameter inference with uncertainty quantification (UQ) requires numerous simulation runs and is therefore often computationally infeasible. Already, a single high-fidelity earthquake simulation - governed by a linear hyperbolic seismic wave equation coupled nonlinearly to a friction law and plastic deformation - is computationally expensive. In this study, we investigate the use of fused ensemble simulations to accelerate large earthquake simulation workflows and UQ studies. We implement and evaluate this approach in SeisSol, a high-performance computing software for the simulation of complex earthquake events that uses an Arbitrary high-order DERivative Discontinuous Galerkin (ADER-DG) scheme. Via fused ensembles, we turn the element-local small sparse/dense matrix operations into tensor contractions working on a dense rank-3 tensor and sparse matrices. These are again executed via loops of small, sparse/dense matrix operations, but with better computational efficiency, due to better exploitation of SIMD instructions on CPUs. We also compare two implementation variants (with different implementation effort) for kernels modeling non-linear dynamic rupture and effects of material plasticity. Our results demonstrate that fused simulations can be up to 5.54 times faster than a single execution - though this depends strongly on the discretization order, the problem size, and the compute architecture. For a full UQ example workflow, we demonstrate a speedup of 1.6, resulting in 36% savings in node hours for the entire workflow.