Estimation of morphological properties in aggregates from 2D data based on machine learning method

Two-dimensional (2D) imaging techniques, particularly Transmission Electron Microscopy (TEM), offer high spatial resolution and grayscale information, yet accurately interpreting three-dimensional (3D) aggregate structures from 2D projections remains challenging, especially for aggregates spanning broad ranges of fractal and structural properties. This study developed an artificial neural network (ANN) to estimate fractal dimension ( D f ) and the number of primary particles ( N p ) of aggregates from synthetic TEM images. A comprehensive dataset of 3D aggregates was generated using a particle-cluster aggregation model, covering D f = 1.8–3.0, N p = 10–500, and primary particle size polydispersity 0–20 %, each aggregate was randomly rotated 50 times to produce synthetic 2D TEM projections. Morphological features extracted via the 2D box-counting method, Relative Optical Density (ROD), and Circular Hough Transform (CHT) served as ANN inputs. For monodisperse aggregates, the ANN delivered highly reliable estimations (R 2 > 0.998 for N p and R 2 > 0.968 for D f ), significantly outperforming conventional methods such as the projection area method and the ROD-based method, particularly for aggregates with higher D f . For aggregates formed by polydisperse primary particles, the ANN maintained robust performance across a broad range of primary particle size polydispersity, achieving R 2 ≥ 0.998 for N P and approximately 0.964 for D f . Subgroup analysis confirmed the ability of the model to capture structural variability under different combinations of N P , D f , and primary particle size polydispersity. Furthermore, validation using aggregates formed by polydisperse primary particles generated via the cluster-cluster aggregation model confirmed the strong generalization capability of ANN across structurally complex and heterogeneous systems. • ANN accurately predicts aggregate fractal dimension and number of primary particles from 2D TEM images. • Method integrates box-counting, ROD, and Circular Hough Transform for feature extraction. • Outperforms traditional methods and generalizes well to diverse aggregate structures.