PEGNN: A physics embedded graph neural network for out-of-distribution temperature field reconstruction

Amidst the intricate landscape of microelectronic systems, where accurate state estimation and health assessment stand as formidable challenges, the reconstruction of temperature fields from sparse sensors emerges as a particularly daunting task. These challenges are further compounded by the occurrence of out-of-distribution scenarios, commonly encountered in atypical operating conditions or iterative design phases. To address this issue, we propose a novel methodology that integrates fundamental physical principles within a graph neural network framework. This method is achieved by imitating heat diffusion based on the concept of iterative solution and pseudo transient, thereby deriving the forward propagation of a physical layer. Subsequently, we approximate the gradient and divergence operators within the physical layer by generalizing finite differences onto graphs. Along with a readin layer and a readout layer, we construct the physics embedded graph neural network by several physical layers, effectively encapsulating the essence of the governing physical laws. Through comparative analysis with baselines under several out-of-distribution tests, our methodology exhibits remarkable superiority, achieving an average of 45% and 22% improvements in MAE and MaxAE compared to the leading baseline. Furthermore, our method enables reconstructions to more authentically reflect the physical reality, as validated by the results of empirical reconstructions.