Physics-informed neural networks for forward and inverse problem solving using DeepXDE

Physics-Informed Neural Networks (PINNs) offer a powerful framework to solve forward and inverse problems by embedding governing physical laws into the training process. In this study, we applied PINNs to model steady-state thermal conduction in an insulating slab, aiming to predict temperature distribution and estimate the hemispherical total emissivity (ε). Using the DeepXDE framework, we incorporated the governing PDE into the loss function, enabling accurate predictions even from sparse data. Various activation functions (sigmoid, tanh, swish) were evaluated in combination with optimizers (Adam, L-BFGS-B, hybrid). The best prediction accuracy (loss ≈ 1.67 × 10 −7 ) was achieved using the Swish + Adam configuration, while the fastest convergence (≈1.12 s) with moderate accuracy resulted from Sigmoid + L-BFGS-B. For the inverse problem, the Tanh + Adam setup estimated ε = 0.42 with a loss of 8.08e+01 and a convergence time of 119.39 s. These results underscore the robustness and efficiency of PINNs for thermal modeling tasks.