Muis Muhtadi, M. Zainalarifin, Harits Ar Rosyid
Physics-Informed Neural Networks (PINNs) provide a mesh-free, data-efficient framework for solving partial differential equations (PDEs) by incorporating physical laws into the training objective. This study proposes a computationally efficient PINN for solving the 1D heat equation by analytically computing second-order spatial derivatives, thereby eliminating costly higher-order automatic differentiation. The model is benchmarked on three canonical problems: transient heat conduction, steady-state with source, and mixed boundary conditions. Despite not reaching the specified convergence threshold, the model achieves high fidelity in boundary and initial condition enforcement, and competitive L2 errors in transient and steady-state cases. The steady-state problem achieves the best performance with a 0.0033 ~L2 error and 0.10% relative error in just 190 seconds. However, performance degrades under mixed boundary conditions, suggesting the need for architectural or loss-balancing adaptations. These findings validate the effectiveness of analytically differentiated PINNs for heat transfer simulations and highlight pathways for future improvements. © 2025 IEEE.
State University of Malang, Electrical Engineering and Informatics, Malang, Indonesia
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