GBEES-GPU: An efficient parallel GPU algorithm for high-dimensional nonlinear uncertainty propagation

TL;DR

This paper introduces a GPU-optimized version of the GBEES algorithm for high-dimensional nonlinear uncertainty propagation, achieving over 1000x speedup while maintaining accuracy.

Contribution

It adapts the GBEES algorithm to CUDA for GPU execution, significantly enhancing computational efficiency in high-dimensional systems.

Findings

Over 1000x speedup on GPU compared to CPU implementation

Validated accuracy and convergence for Lorenz models

Effective handling of high-dimensional probability distributions

Abstract

Eulerian nonlinear uncertainty propagation methods often suffer from finite domain limitations and computational inefficiencies. A recent approach to this class of algorithm, Grid-based Bayesian Estimation Exploiting Sparsity, addresses the first challenge by dynamically allocating a discretized grid in regions of phase space where probability is non-negligible. However, the design of the original algorithm causes the second challenge to persist in high-dimensional systems. This paper presents an architectural optimization of the algorithm for CPU implementation, followed by its adaptation to the CUDA framework for single GPU execution. The algorithm is validated for accuracy and convergence, with performance evaluated across distinct GPUs. Tests include propagating a three-dimensional probability distribution subject to the Lorenz '63 model and a six-dimensional probability distribution subject to the Lorenz '96 model. The results imply that the improvements made result in a speedup of over 1000 times compared to the original implementation.