Machine Learning Approaches to Surpass the Limitations of the Beer-Lambert Law

Many scientific and industrial applications depend on the precise measurement of chemical concentrations. The current study demonstrates how an inventive method of combining photographic images with a machine learning (ML) model successfully estimates the concentration of a chemical compound in solution. A machine learning model using linear regression with L2 regularization (ridge regression model) was developed as a part of a predictive model. The model was trained on captured images of K₂Cr₂O₇ solutions following the standard setup. After completing the training, the model was evaluated using a data set of test samples. The prediction precision of the model had been evaluated using 210 images and a high correlation between actual and predicted K₂Cr₂O₇ concentrations was obtained with MAE, MSE, and RMSE of 1.4 × 10^-5, 3.4 × 10^-10, and 1.0 × 10^-5, respectively. The ridge regression model is also extended to predict the concentration of potassium permanganate (KMnO₄) and highlights the potential of integrating machine learning techniques with image analysis to accurately quantify the concentration of any chemical species in the solution state. As this model depends solely on the color intensity of the sample without any molecular interactions, it exceeds the limitations of the Beer-Lambert law. The created machine learning model also minimizes the requirement of substantial expertise and training and hence bridges the gap between experienced and novice analysts.