Fast Full-Chip Parametric Thermal Analysis Based on Enhanced Physics Enforced Neural Networks

In this work, we propose a fast full-chip thermal numerical analysis approach based on an enhanced physics-informed neural networks (PINN) framework. The new method, called ThermPINN, leverages both PINN-based DNN optimization framework and analytic solutions of simplified thermal problems for solving thermal partial differential equations (PDE). The resulting ThermPINN leads to more efficient training speed of DNN networks and more scalability for solving large PDE problems. Specifically, we propose to partially enforce physics laws based on closely related analytic solutions to simpler problems. As a result, we are able to significantly reduce the number of variables in the loss function and easily meet boundary conditions. To consider the impact of various ambient temperatures and effective convection coefficients, which are influenced by different design parameters and run-time conditions, we develop a parameterized thermal analysis technique. This technique enables design space exploration and uncertainty quantification (UQ), which are critical for ensuring the reliability of integrated circuits under various operating conditions. The numerical results on alpha21264 processor show that the proposed ThermPINN has 2x speedup and 3x better accuracy over the state-of-the-art thermal simulator, VarSim. The experimental results for 2-D full-chip thermal analysis of 3171 cases show that the proposed parameterized ThermPINN considering both training and inference time can achieve a 6x speedup over commercial COMSOL with an average mean absolute error (AE) of 0.47 K. In terms of training time, the proposed parameterized ThermPINN is 11x faster than the parameterized plain PINN with similar accuracy. The UQ analysis with 5000 samples for maximum temperature propagated from ambient temperature shows that the parameterized ThermPINN and parameterized plain PINN are 113x and 22x faster than COMSOL, respectively.