An enhanced physics-informed deep learning framework for solving variable-coefficient heat conduction problems with temperature-dependent thermal conductivity and nonlinear source terms

Physics-Informed Neural Networks (PINNs) have demonstrated significant potential for solving nonlinear PDEs; however, while handling variable coefficients, discontinuities, and complex boundary conditions, their accuracy frequently declines. To address these limitations, this study proposes an enhanced variable-coefficient PINN (VC-PINN) framework for solving transient nonlinear heat conduction problems with temperature-dependent conductivity and nonlinear source terms. The framework provided a unified multiple boundary condition within a single architecture while effectively handling discontinuous conductivity coefficients, which remain challenging for standard PINNs and many classical numerical methods. Numerical experiments show that the proposed method achieves L2 and L∞ errors as low as 10−6 and mean squared errors reaching 10−8. For problems with discontinuous coefficients, the framework reduced the maximum error reported in previous studies to approximately 10−6. Comparisons with standard PINNs, finite difference methods, and finite element methods demonstrated improved accuracy, stability, and robustness using only moderate collocation points and training iterations.