Predicting Thermal Conductivity of Foamed Concrete via Physics-Informed Neural Networks Coupled with the Maxwell–Eucken Model

This study investigates a neural network model regularized by the Maxwell–Eucken formulation for predicting the thermal conductivity of foamed concrete. Backed by experimental measurements, the modeling workflow incorporates augmented samples derived from the empirical dataset. A total of 30 experimental records, categorized into five distinct mixture groups, provide the foundational data basis. Bulk density and density-derived porosity serve as model inputs, both reflecting the same underlying variation in material density. Evaluation results demonstrate that the proposed hybrid model achieves a coefficient of determination (R2) of 0.7701, substantially outperforming the standalone Maxwell–Eucken model (R2 = 0.4546) and the effective medium theory (R2 = 0.3041). Although these indicators reflect an improved in-sample fit, they neither isolate the explicit contribution of the physics-informed penalty nor establish the model’s predictive capability for unseen mixtures. The Maxwell–Eucken term functions as an approximate constitutive regularizer, whereas the clustered residuals highlight specific boundary conditions where further model refinement is warranted. Overall, this study validates the feasibility of the hybrid modeling approach within the tested material domain; group-separated validation and comparative benchmarks against purely data-driven models are required to assess its broader generalizability.