A refined PINN framework for parametric modeling and inverse design of thermal conductivity in TPMS-based composites

Architected materials with tailored microstructures, particularly triply periodic minimal surfaces (TPMS), offer significant potential for advanced thermal management. This paper presents a refined physics-informed neural network (PINN) framework for modeling steady-state heat conduction in high-contrast Schwarz Primitive TPMS composites. To address convergence issues and spectral bias inherent in PINN modeling of heterogeneous media, we evaluate mitigation techniques including property smoothing, adaptive activation functions, and domain decomposition. Analysis confirms that domain decomposition combined with hard constraints delivers superior accuracy. The framework is rigorously validated against finite element method (FEM) and experimental data, demonstrating exceptional stability in extreme high-contrast scenarios—specifically AlSi10Mg composites with a conductivity ratio of ~ 3800:1—where standard methods often falter. Additionally, a Hybrid Physics-Data training strategy is introduced, assimilating sparse experimental data to enhance prediction fidelity by compensating for manufacturing-induced geometric imperfections. Finally, the framework facilitates inverse design by treating geometry as a learnable parameter. A multi-stage Transfer Learning strategy is implemented to tackle the non-convex optimization landscape involving simultaneous material and topological variations. These findings establish PINNs as a powerful, efficient alternative to FEM for the analysis and optimization of complex material architectures.