Thermal Conductivity Analysis of Functional Gradient Materials Based on Physically Informed Neural Networks

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This paper investigates transient heat conduction problems in functionally graded materials (FGMs) using Physics-Informed Neural Networks (PINNs) and Augmented Lagrangian Physics-Informed Neural Networks (AL-PINNs). By constructing residual loss functions for the governing equations and boundary initial conditions, this method trains the neural network without relying on sample data, thereby enhancing the model’s generalisation capability and reducing the reliance on the pre-processing tasks, such as the derivation of differential equations, complex modelling, and mesh generation, required by traditional numerical methods. This paper investigates the applicability of PINN and AL-PINN in solving transient heat conduction problems in FGMs and analyses the impact of network architecture on prediction accuracy. The results indicate that AL-PINN exhibits lower error than conventional PINN when addressing transient FGM heat conduction problems with complex boundaries. Although the training cost of PINN-based methods is still higher than that of the conventional Finite Element Method for small-scale benchmark problems, the proposed framework offers greater flexibility for problems with irregular geometries and variable material properties, without requiring mesh generation.

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