Structural features modeling of substituted hydroxyapatite nanopowders as bone fillers via machine learning

Abstract In the present study, both experimental and modeling approaches were employed to explore the solid-state formation mechanisms and estimate the structural behavior of nanosized substituted hydroxyapatite (HA) powders using different machine learning (ML) techniques. In the phase of modeling, an artificial neural network (ANN)-based method, called multi-layer perceptron (MLP), was used to truthfully approximate structural characteristics of the as-received nanopowders. In the next round of modeling, the genetic programming (GP) technique was employed to appraise the strength of the predictive model. Following the modeling procedure, a few case studies were conducted to evaluate the results obtained by the modeling framework, where the microstructural alterations of the mechanosynthesized substituted nanopowders were examined in terms of the dopant agent. The Rietveld refinement showed a good fit of the observed and calculated profiles over the full diffraction patterns. With the effect of dopant type, different levels of weight loss were observed in the thermal analysis curves. The comparison between the proposed models ascertained that both models were truthful for the estimation of the structural features of HA-based bioceramics for different bone regeneration applications. From the statistical assessments, the values of Mean Squared Error (MSE) and Correlation Coefficient (R) of the MLP-ANN in the training phase for the crystallite size were 5.757 and 0.93, which in prediction reached 3.429 and 0.995, respectively.