PISOV: Physics-Informed Separation of Variables Solvers for Full-Chip Thermal Analysis

Thermal issues are becoming increasingly critical due to rising power densities in high-performance chip design. The need for fast and precise full-chip thermal analysis is evident. Although machine learning (ML)-based methods have been widely used in thermal simulation, their training time remains a challenge. In this article, we proposed a novel physics-informed separation of variables solver (PISOV) to significantly reduce training time for fast full-chip thermal analysis. Inspired by the recently proposed ThermPINN, we employ a least-square regression method to calculate the unknown coefficients of the cosine series. The proposed PISOV method combines physics-informed neural network (PINN) and separation of variables (SOVs) methods. Due to the matrix-solving method of PISOV, its speed is much faster than that of ThermPINN. On top of PISOV, we parameterize effective convection coefficients and power values for surrogate model-based uncertainty quantification (UQ) analysis by using neural networks, a task that cannot be accomplished by the SOV method. In the parameterized PISOV, we only need to calculate once to obtain all parameterized results of the hyperdimensional partial differential equations. Additionally, we study the impact of sampling methods (such as grid, uniform, Sobol, Latin hypercube sampling (LHS), Halton, and Hammersly) and hybrid sampling methods on the accuracy of PISOV and parameterized PISOV. Numerical results show that PISOV can achieve a speedup of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$245\times $ </tex-math></inline-formula>, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{4}\times $ </tex-math></inline-formula> over ThermPINN, and PINN, respectively. Among different sampling methods, the Hammersley sampling method yields the best accuracy.