• Optimized bivariate Monte Carlo simulations enable efficient aggregate descriptor prediction • SPSD attainment in volume and surface area depends on characteristic time scales • CNN surrogate model accelerates prediction, reducing computation time 15 000-fold • Differentiable surrogate model enables efficient reactor temperature optimization Precise control over nanoparticle synthesis in gas-phase processes such as flame and plasma reactors remains a significant challenge because of the complex, non-linear particle formation dynamics governed by coagulation and sintering. This paper presents a computational methodology that combines a Monte Carlo (MC) simulation framework and a convolutional neural network (CNN)-based surrogate model to accelerate predictions of bivariate particle descriptor vector distributions. The MC framework, optimized for computational efficiency, predicts the evolution of the particle surface area and volume distributions over time under isothermal conditions. This bivariate description enables accurate representation of particle morphology, which in turn influences formation dynamics and final product performance. Evaluation against established models demonstrates high agreement, emphasizing its precision in capturing particle formation dynamics. Indications and restrictions are identified for the achievement of a self-preserving size distribution (SPSD) for both aggregate volume and surface area, offering the potential to simplify and facilitate bivariate modeling approaches. The CNN-based surrogate model leverages bivariate histograms to predict time-dependent distributions for variable temperatures, achieving a 15 000-fold reduction in computation time compared to the MC framework and thus reaching real-time capability, while maintaining sufficient accuracy. In addition, the differentiable nature of the model enables the optimization of temperature profiles. This paper demonstrates the potential for integrating advanced MC frameworks with neural networks to balance computational efficiency and predictive accuracy.
Fuchs et al. (Wed,) studied this question.