ML-assisted optimization method for the prediction of 3-dimensional fractal structures from microscopic images

Aggregated aerosol particles released from high temperature processes and combustion processes are often described as quasi-fractal aggregates, where the shape of these particles is represented by the scaling law. A detailed understanding of the morphology is quite important as various properties are strongly dependent on the particle shape. Electron microcopy based image analysis is the most commonly used technique to visualize and study the morphological features. In this study, we propose a machine learning (ML)-assisted retrieval method where ML techniques are combined with optimization algorithms to predict the morphological features and the corresponding 3-dimensional structures from microscopic images. The proposed algorithm is comprehensively tested with “synthetic” images as well as Transmission Electron Microcopy images. Various ML models, including Linear regression, Artificial Neural Network, K-nearest neighbours, Random Forest regression, and XGBoost are used for preliminary prediction of the morphological features (Number of monomers (N), fractal prefactor (k_f) and fractal Dimension (D_f)). These are used to narrow down the search space in the optimization algorithms. Random Forest and XGBoost methods achieved approximately 0.96 R2 score for N, 0.85 for D_f and 0.73 for k_f. Multiple optimization methods, including PSO, JAYA, and JAYA-SA, were tested in the study. The method was tested across a wide range of parameters, including N (up to 500), D_f (1.1–2.7), and k_f (0.6–2.1), and the results are quite promising while comparing various 3-dimensional properties of the retrieved structures. The retrieved fractal parameters, N and D_f, exhibited errors under 10%, and the predicted k_f values were found within approximately 15% using the proposed method. Results also show that the 3-dimensional properties of the predicted structure are quite close to the structures used for testing the algorithm. The algorithm was also parallelized to improve the computational time. The results show that the predicted fractal parameters and the retrieved 3-dimensional structures are quite similar to the structures used for testing across a wide range of particle morphologies. The incorporation of ML models has significantly improved the accuracy and computational speed, compared to the existing retrieval techniques.