Physics-Informed Neural Networks for modeling heat diffusion in anisotropic solids

Abstract

Accurate simulation of heat diffusion in anisotropic solids is essential for the design and optimization of advanced engineering materials and thermal management systems. However, conventional numerical approaches often require computationally intensive mesh generation and repeated solution procedures, particularly for transient problems involving directional heat transport. This study investigates the application of Physics-Informed Neural Networks for modeling transient heat diffusion in anisotropic solid materials. The proposed framework incorporates the governing heat conduction equation, initial conditions, and boundary conditions directly into the neural network training process, enabling physically consistent predictions without extensive labeled datasets. The model was trained using a combination of Adam and L-BFGS optimization algorithms and validated against finite element method simulations. The influence of thermal anisotropy was evaluated for conductivity ratios ranging from isotropic conditions to strongly anisotropic cases. The developed Physics-Informed Neural Networks demonstrated excellent agreement with finite element method solutions, achieving a root mean square error of 0.014 K, a mean absolute error of 0.010 K, a maximum absolute error of 0.061 K, and a coefficient of determination of 0.9997. Although prediction errors increased slightly with increasing anisotropy, the model maintained high accuracy and stable convergence across all investigated scenarios. The results confirm that Physics-Informed Neural Networks provide an accurate and physically consistent alternative to traditional numerical methods for anisotropic heat transfer analysis. The proposed approach offers significant potential for rapid thermal simulations, inverse heat transfer problems, digital twin development, and real-time engineering applications involving complex anisotropic materials.