A digital twin approach for optimizing okara-based Greek-style yogurt using hybrid Gompertz–LSTM modeling and data assimilation

Plant-based yogurts frequently exhibit inadequate structural integrity and pronounced syneresis. This study formulated a novel okara and coconut milk Greek-style plant-based yogurt and developed a physics-augmented digital twin for robust process control. Rheological and microstructural analyses, yielding a fractal dimension ( D f = 1.686), demonstrated that the okara–coconut matrix aggregates via diffusion-limited cluster aggregation (DLCA), forming a compact, space-filling network. Multi-objective Pareto optimization identified an optimal formulation (14% okara, 18% coconut milk) that minimized syneresis (1.86%) while maximizing storage modulus ( G′ = 886 Pa) and overall sensory acceptability (8.46/9.0). To monitor fermentation and gelation, a hybrid framework fusing a mechanistic Gompertz prior with a Long Short-Term Memory–Support Vector Regression (LSTM-SVR) residual corrector was developed. This digital twin achieved high predictive accuracy ( R 2 = 0.9928), outperforming standalone machine learning approaches. Furthermore, integrating an Ensemble Smoother with Multiple Data Assimilation (ES-MDA) enabled dynamic parameter self-calibration for Avrami gelation kinetics, successfully reducing prediction uncertainty for G′ and syneresis by 58% and 74%, respectively. Ultimately, this hybrid physics–AI approach provides highly interpretable, risk-aware process control, establishing a scalable Industry 4.0 paradigm for managing raw material variability in plant-based food manufacturing.