Stochastic Barnes-Hut Approximation for Fast Summation on the GPU

We present a novel stochastic version of the Barnes-Hut approximation. Regarding the level-of-detail (LOD) family of approximations as control variates, we construct an unbiased estimator of the kernel sum being approximated. Through several examples in graphics applications such as winding number computation and smooth distance evaluation, we demonstrate that our method is well-suited for GPU computation, capable of outperforming a GPU-optimized implementation of the deterministic Barnes-Hut approximation by achieving equal median error in up to 9.4x less time.

@article{madan2025_2506.02219,
  title={ Stochastic Barnes-Hut Approximation for Fast Summation on the GPU },
  author={ Abhishek Madan and Nicholas Sharp and Francis Williams and Ken Museth and David I.W. Levin },
  journal={arXiv preprint arXiv:2506.02219},
  year={ 2025 }
}