Multi-objective Bayesian optimization for the retrieval of aggregated aerosol structures from microscopic images

Abstract

Aerosol particles are increasingly recognized for their significant impacts on human health and climate. Often found in aggregated form, the morphology of these particles plays a crucial role in influencing their physicochemical properties. Owing to the sub-micron size, electron microscopy is the most commonly used technique to visualize the aggregated particles. In a prior study, we proposed a combination of forward modelling coupled with optimization techniques for the prediction of 3-dimensional structures from microscopic images. Here, we extend the methodology to a multi-objective optimization approach for the specific cases where aggregated particles are classified and sampled based on specific properties such as mobility diameter, aerodynamic diameter etc. The comparison of 2-dimensional features of the microscopic image with the projections of computationally generated aggregates forms the first objective function, while the comparison of the measured 3-dimensional property, mobility diameter, is used as the second objective function. The estimation of the mobility diameter often requires the calculation of the hydrodynamic radius (R_h) and the orientationally averaged projected area (PA), which can be computationally expensive for larger aggregates and for frequent calculations. Bayesian optimization is used for the retrieval process, as it can provide much faster convergence with significantly fewer function evaluations compared to metaheuristic algorithms. The multi-objective Bayesian optimization-based retrieval algorithm has been validated using synthetically generated and experimentally collected microscopic images. The process is found to be about 5–10 times faster than previously reported methods. The algorithm is further extended to retrieve aggregates with polydisperse and overlapping monomers. The retrieval process demonstrated strong accuracy, with fractal parameters showing around 10–15% error compared to the original values. This includes a mobility diameter difference of less than 10%, indicating high similarity between retrieved and input structures. Furthermore, tests are conducted on welding fume particles of varying mobility diameters, where retrieved structures consistently exhibited mobility diameters within a 10% difference from original values.