Machine Learning and Physics-Informed Neural Networks for Thermal Behavior Prediction in Porous TPMS Metals

Mohammed Yahya, Mohamad Ziad Saghir

Triply periodic minimal surface (TPMS) structures provide high surface area to volume ratios and tunable conduction pathways, but predicting their thermal behavior across different metallic materials remains challenging because multi-material experimentation is costly and full-scale simulations require extremely fine meshes to resolve the complex geometry. This study develops a physics-informed neural network (PINN) that reconstructs steady-state temperature fields in TPMS Gyroid structures using only two experimentally measured materials, Aluminum and Silver, which were tested under identical heat flux and flow conditions. The model incorporates conductivity ratio physics, Fourier-based thermal scaling, and complete spatial temperature profiles directly into the learning process to maintain physical consistency. Validation using the complete Aluminum and Silver datasets confirms excellent agreement for Aluminum and strong accuracy for Silver despite its larger temperature gradients. Once trained, the PINN can generalize the learned behavior to nine additional metals using only their conductivity ratios, without requiring new experiments or numerical simulations. A detailed heat transfer analysis is also performed for Magnesium, a lightweight material that is increasingly considered for thermal management applications. Since no published TPMS measurements for Magnesium currently exist, the predicted Nusselt numbers obtained from the PINN-generated temperature fields represent the first model-based evaluation of its convective performance. The results demonstrate that the proposed PINN provides an efficient, accurate, and scalable surrogate model for predicting thermal behavior across multiple metallic TPMS structures and supports the design and selection of materials for advanced porous heat technologies.