Physics-augmented machine learning enables resource-efficient design of Eri silkworm protein-enriched frozen desserts

Abstract

Inefficient formulation hinders integrating sustainable insect proteins into complex food matrices. This study develops and demonstrates a hybrid Physics-Augmented Machine Learning (PAML) framework to accelerate the design of Eri silkworm ( Philosamia ricini ) protein-enriched frozen desserts. A sequential hybrid framework combined Arrhenius kinetics with Ensemble Smoother with Multiple Data Assimilation (ES-MDA) for thermodynamic modeling, alongside Random Forest for sensory characterization. The framework was tested using Leave-One-Out Cross-Validation (LOOCV) on a sparse dataset derived from six prototypes (0–5% w/w protein). The mechanistic module achieved exceptional calibration fidelity for melting behavior ( R ² = 0.989, RMSE = 2.254), while the machine learning component successfully predicted texture attributes ( R ² = 0.771). However, flavor prediction was limited ( R ² < 0.3), indicating that the model is primarily effective for structural and thermal screening while flavor requires empirical verification. Multi-domain optimization identified 1–2% protein incorporation as optimal, balancing sensory acceptance (scores >6.0/9.0) with a 60% reduction in ingredient-level carbon footprint (0.80 vs 2.00 kg CO<inf>2</inf> eq /kg dairy). Crucially, the framework reduced the experimental burden by an estimated 87% compared to a theoretical full factorial design (6 validation runs vs. 45 required). To ensure safety alongside sustainability, enzymatic hydrolysis was validated to reduce IgE binding allergenicity by 85%. This work demonstrates that hybrid physics-augmented frameworks bridge the gap between in-silico design and physical implementation, offering a resource-efficient pathway for sustainable food innovation.