Scaled Block Vecchia Approximation for High-Dimensional Gaussian Process Emulation on GPUs

Emulating computationally intensive scientific simulations is crucial for enabling uncertainty quantification, optimization, and informed decision-making at scale. Gaussian Processes (GPs) offer a flexible and data-efficient foundation for statistical emulation, but their poor scalability limits applicability to large datasets. We introduce the Scaled Block Vecchia (SBV) algorithm for distributed GPU-based systems. SBV integrates the Scaled Vecchia approach for anisotropic input scaling with the Block Vecchia (BV) method to reduce computational and memory complexity while leveraging GPU acceleration techniques for efficient linear algebra operations. To the best of our knowledge, this is the first distributed implementation of any Vecchia-based GP variant. Our implementation employs MPI for inter-node parallelism and the MAGMA library for GPU-accelerated batched matrix computations. We demonstrate the scalability and efficiency of the proposed algorithm through experiments on both synthetic and real-world workloads, including a 50M-point simulation from a respiratory disease model. SBV achieves near-linear scalability on up to 512 A100 and GH200 GPUs, handles 2.56 B points, and reduces energy use relative to exact GP solvers, establishing SBV as a scalable and energy-efficient framework for emulating large-scale scientific models on GPU-based distributed systems.