Comparative application of machine learning techniques and response surface methodology for predicting final pH and salt diffusion coefficients in rennet-induced micellar casein concentrate gels

Background

Effective prediction of salt diffusion and pH in dairy matrices is vital for optimising cheese salting, ensuring microbial safety, controlling enzymatic activity and enhancing product consistency. While mechanistic and regression-based approaches have been used in prior studies, they are often inefficient to capture complex interactions among multiple process variables.

Aim(s)

This study aimed to compare the predictive performance of multiple machine learning (ML) techniques—including artificial neural networks (ANNs), support vector machines (SVMs), Gaussian process regression (GPR) and bootstrap forest—with response surface methodology (RSM) for modelling salt diffusion coefficients and final pH in rennet-induced micellar casein concentrate (MCC) gels.

Methods

A dataset was derived by varying four key process variables: salting temperature, MCC concentration, calcium content and GDL addition. RSM models were developed and used as linear baselines. Machine learning models were constructed using the JMP Pro software, with model performance evaluated via R², RMSE and MAE. ANN architectures were varied by activation type and layer configuration, while SVM, GPR and bootstrap forest models were fine-tuned via cross-validation and hyperparameter selection.

Major Findings

Gaussian process regression yielded the highest predictive accuracy for both salt diffusion (R² = 0.9976) and pH (R² = 0.9858), followed by SVM (R² = 0.9911 and 0.9859, respectively). Artificial neural network performance was moderate (R² = 0.8128 for diffusion, 0.9852 for pH), showing sensitivity to dataset size. The RSM model achieved an R² of 0.94 for pH prediction. This study is among the first to systematically benchmark these methods using a single, experimentally consistent dataset.

Industrial Implications

The results highlight the utility of kernel-based models (SVM and GPR) in data-limited dairy systems and support their integration into process analytical technologies for cheese manufacturing. These models offer enhanced predictive accuracy over classical methods and enable data-driven process optimisation in industrial salting applications.