In this paper, we present a generic, scalable and adaptive load balancing parallel Lagrangian particle tracking approach in Wiener type processes such as Brownian motion. The approach is particularly suitable in problems involving particles with highly variable computation time, like deposition on boundaries that may include decay, when particle lifetime obeys exponential distribution. At first glance, Lagranginan tracking is highly suitable for a distributed programming model due to the independence of motion of separate particles. However, the commonly employed Decomposition Per Particle (DPP) method, where each process is in charge of a certain number of particles, actually displays poor parallel efficiency due to the high particle lifetime variability when dealing with a wide set of deposition problems that optionally include decay. The proposed method removes DPP defects and brings a novel approach to discrete particle tracking. The algorithm introduces master/slave model dubbed Partial Trajectory Decomposition (PTD), in which a certain number of processes produce partial trajectories and put them into the shared queue, while the remaining processes simulate actual particle motion using previously generated partial trajectories. Our approach also introduces meta-heuristics for determining the optimal values of partial trajectory length, chunk size and the number of processes acting as producers/consumers, for the given total number of participating processes (Optimized Partial Trajectory Decomposition, OPTD). The optimization process employs a surrogate model to estimate the simulation time. The surrogate is based on historical data and uses a coupled machine learning model, consisting of classification and regression phases. OPTD was implemented in C, using standard MPI for message passing and benchmarked on a model of 220Rn progeny in the diffusion chamber, where particle motion is characterized by an exponential lifetime distribution and Maxwell velocity distribution. The speedup improvement of OPTD is approximatelly 320% over standard DPP, reaching almost ideal speedup on up to 256 CPUs.

中文翻译：

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使用机器学习优化布朗运动中的并行粒子跟踪

在本文中，我们提出了一种通用的、可扩展的、自适应的负载平衡并行拉格朗日粒子跟踪方法，用于维纳类型的过程，如布朗运动。当粒子寿命服从指数分布时，该方法特别适用于涉及计算时间高度可变的粒子的问题，例如可能包括衰减的边界上的沉积。乍一看，由于分离粒子运动的独立性，拉格朗日南跟踪非常适合分布式编程模型。然而，通常采用的每粒子分解 (DPP) 方法，其中每个过程负责一定数量的粒子，在处理广泛的沉积问题时，由于粒子寿命的高可变性，实际上显示出较差的并行效率，这些问题可选地包括衰变。所提出的方法消除了 DPP 缺陷，并为离散粒子跟踪带来了一种新方法。该算法引入了称为部分轨迹分解（PTD）的主/从模型，其中一定数量的进程产生部分轨迹并将它们放入共享队列，而其余进程使用先前生成的部分轨迹模拟实际粒子运动。我们的方法还引入了元启发式，用于确定部分轨迹长度、块大小和作为生产者/消费者的进程数量的最优值，对于给定的参与进程总数（优化的部分轨迹分解，OPTD）。优化过程采用代理模型来估计仿真时间。代理基于历史数据并使用耦合机器学习模型，由分类和回归阶段组成。OPTD 在 C 中实现，使用标准 MPI 进行消息传递，并在扩散室中的 220Rn 后代模型上进行基准测试，其中粒子运动的特征在于指数寿命分布和麦克斯韦速度分布。OPTD 的加速比标准 DPP 提高了大约 320%，在多达 256 个 CPU 上达到几乎理想的加速。