Optimizing parallel particle tracking in Brownian motion using machine learning

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 220 Rn 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.