CPU and GPU based acceleration of high-dimensional population balance models via the vectorization and parallelization of multivariate aggregation and breakage integral terms

The development of mathematical models for physical systems often necessitates the use of high-dimensional spaces and fine discretizations to accurately capture complex dynamics. These models, which involve large matrices and extensive mathematical operations, tend to be computationally intensive, leading to slow execution times. In this study, we analyzed various acceleration strategies by comparing the simulation accuracy, computational time, and resource utilization of various vectorization and parallelization methods on both CPUs and GPUs, using a multi-dimensional Population Balance Model simulated in MATLAB and Python. Our findings revealed that GPU-based vectorization provided the highest performance, achieving a 40-fold speedup compared to the serial implementations. Unlike simulations on CPUs, where run time is often limited by processing power, GPUs simulations are limited by the available memory, especially at high resolution. This work highlights the importance of using appropriate resources and code optimization strategies to reduce computational time, for development of an efficient model. • 3-dimensional Population Balance Models ran on CPUs and GPUs using MATLAB and Python. • Speed comparison of vectorized and unvectorized code ran in serial and parallel. • A speedup of up to 40x was observed with GPU execution of the vectorized code.