Abstract Pair potentials or kernels, ψ ( | r | ) , play a critical role in a number of areas; these include biophysics, electrical engineering, fluid dynamics, diffusion physics, solid state physics, and many more. The need to evaluate these potentials rapidly for N particles gives rise to the classical N -body problem. In this paper, we present scalable parallel algorithms for evaluation of these potentials for highly non-uniform distributions. The underlying methodology for evaluating these potentials relies on the accelerated Cartesian expansion (ACE) framework that is quasi-kernel-independent with the requirement that the kernel be differentiable with known derivatives. The results presented demonstrate the accuracy control, low cost, and parallel scalability offered by this method for several example kernels and distributions of up to 5 billion particles on 16384 CPU cores. Potential applications of the algorithm include various disciplines of computational physics, engineering, machine learning, among others.

中文翻译：

---

成对电位的快速且可扩展的评估

摘要 对势或核 ψ ( | r | ) 在许多领域发挥着关键作用。其中包括生物物理学、电气工程、流体动力学、扩散物理学、固态物理学等等。需要快速评估 N 粒子的这些势，这就产生了经典的 N 体问题。在本文中，我们提出了可扩展的并行算法，用于评估高度非均匀分布的这些潜力。评估这些潜力的基本方法依赖于准内核独立的加速笛卡尔扩展 (ACE) 框架，并要求内核可与已知导数微分。所呈现的结果证明了精确控制、低成本、以及此方法为多个示例内核和 16384 个 CPU 内核上多达 50 亿个粒子的分布提供的并行可扩展性。该算法的潜在应用包括计算物理、工程、机器学习等各个学科。