ASRR-PINN: Adaptive Sub-Regional Random Resampling-Based PINN for Thermal Analysis of 3D-ICs

The physics-informed neural network (PINN) is a promising technology to accelerate thermal analysis of integrated circuits (ICs). However, the application of PINN to threedimensional (3D) scenarios is faced with numerous challenges, including the requirement of a vast number of sampling points as well as the high-level fitting capability of the network. This paper introduces an Adaptive Sub-regional Random Resamplingbased PINN (ASRR-PINN) to accelerate the thermal analysis of 3D-ICs. The adaptive sub-regional random resampling (ASRR) algorithm is proposed for efficient sampling in PINN, which divides the solution domain into a series of sub-regions and further adaptively decomposes these sub-regions during the training process. Besides, the sampling points are randomly resampled within each sub-region. By this means, the solution accuracy is enhanced significantly, especially in cases of a limited number of sampling points. To accelerate the convergence of the network, the thermal boundary conditions are incorporated into the ASRRPINN, ensuring that the network outputs automatically satisfy these constraints. Furthermore, the capability of parameterization of ASRR-PINN is achieved by training an additional reduced network. Numerical results show that the ASRR algorithm reduces the maximum absolute error (AE) by more than $56 \%$ compared with other non-uniform sampling methods while the runtime is shortened by at least $28 \%$. Moreover, using the parameterized ASRR-PINN to explore the design space of 3D-ICs achieves speeds over 200 times faster than the original ASRR-PINN.