Physics-Informed Neuro-Symbolic Recommender System: A Dual-Physics Approach for Personalized Nutrition

Traditional e-commerce recommender systems primarily optimize for user engagement and purchase likelihood, often neglecting the rigid physiological constraints required for human health. Standard collaborative filtering algorithms are structurally blind to these hard limits, frequently suggesting bundles that fail to meet specific total daily energy expenditure and macronutrient balance requirements. To address this disconnect, this paper introduces a Physics-Informed Neuro-Symbolic Recommender System that integrates nutritional science directly into the recommendation pipeline via a dual-layer architecture. The framework begins by constructing a semantic knowledge graph using sentence-level encoders to strictly align commercial products with authoritative nutritional data. During the training phase, an implicit physics regularizer applies a differentiable thermodynamic loss function, ensuring that learned latent embeddings reflect nutritional plausibility rather than simple popularity. Subsequently, during the inference phase, an explicit physics optimizer employs simulated annealing and elastic quantity optimization to generate discrete grocery bundles that strictly adhere to the user's protein and caloric targets.