A Portable Numerical Library for the Calculation of Multi-Dimensional Integrals

Multi-dimensional numerical integration is a prevalent task in physics and other scientific fields, e.g., in the simulation of particle-beam dynamics and Bayesian parameter estimation. Scientific computing applications that simulate complex phenomena may require the solution to numerous multi-variate integrals. However, functions that have features such as sharp peaks or oscillations in high dimensional spaces, can result in an exorbitant number of computations. For many cases, convergence to accurate results in a reasonable amount of time is infeasible with existing numerical libraries. One approach towards making multi-dimensional integration viable is to parallelize existing algorithms. No commonly available algorithms or libraries exist that are tailored for parallel execution. Existing parallel implementations in CUDA have demonstrated some degree of success but their exclusive compatibility with NVIDIA GPUs incurs limitations on execution platform portability. The emergence of exascale computing and GPU clusters that have non-NVIDIA GPUs make portability increasingly more relevant. This dissertation focuses on enabling largescale and platform-agnostic numerical integration of computationally intense multi-dimensional functions. The plethora of integrands with various peculiarities make it impossible for any existing algorithm to guarantee convergence or performance on all functions. Additionally, efficient parallelization is challenging to achieve due to workload imbalances that occur when there is no apriori information on a function’s behavior. As such, we create two parallel algorithms based on the deterministic CUHRE and probabilistic VEGAS routines. First, we demonstrate the performance and robustness of our algorithms through a CUDA implementation. Then, we evaluate our parallel algorithms in two platform-agnostic programming models: Kokkos, and oneAPI. This allows us to investigate the performance and limitations of two of the most prominent portability options.