Mathematical Model Coupled to Neural Networks Calculates the Extraction Recovery of Polycyclic Aromatic Hydrocarbons in Problematic Matrix

Unknown extraction recovery from solid matrix samples leads to meaningless chemical analysis results. It cannot always be determined, and it depends on the complexity of the matrix and properties of the extracted substances. This paper combines a mathematical model with the machine learning method - neural networks that predict liquid extraction recovery from solid matrices. The prediction of the three-stage extraction recovery of polycyclic aromatic hydrocarbons from a wooden railway sleeper matrix is demonstrated. Calculation of the extraction recovery requires the extract's volume to be measured and the polycyclic aromatic hydrocarbons' concentration to be determined for each stage. These data are used to calculate the input values for a neural network model. Lowest mean-squared error (0.014) and smallest retraining relative standard deviation (20.7%) were achieved with the neural network setup 6:5:5:4:1 (six inputs, three hidden layers with five, five, and four neurons in a layer, and one output). To train such a neural network, it took less than 8000 steps - less than a second - using an average-performance laptop. The relative standard deviation of the extraction recovery predictions ranged between 1.13 and 5.15%. The three-stage recovery of the extracted dry sample showed 104% of three different polycyclic aromatic hydrocarbons. The extracted wet sample recovery was 71, 98, and 55% for phenanthrene, anthracene, and pyrene, respectively. This method is applicable in the environmental, food processing, pharmaceutical, biochemical, biotechnology, and space research areas where extraction should be performed autonomously without human interference.