PISOV:全芯片热分析的物理信息分离变量求解器

IF 2.7 3区 计算机科学 Q2 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE
Liang Chen;Wenxing Zhu;Min Tang;Sheldon X.-D. Tan;Jun-Fa Mao;Jianhua Zhang
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引用次数: 0

摘要

由于高性能芯片设计中功率密度的提高,热问题变得越来越重要。对快速、精确的全芯片热分析的需求是显而易见的。尽管基于机器学习(ML)的方法已广泛应用于热模拟,但其训练时间仍然是一个挑战。在本文中,我们提出了一种新的物理变量分离求解器(PISOV),以显着减少快速全芯片热分析的训练时间。受最近提出的ThermPINN的启发,我们采用最小二乘回归方法来计算余弦级数的未知系数。提出的PISOV方法结合了物理信息神经网络(PINN)和变量分离(sov)方法。由于PISOV的矩阵求解方法,其速度比ThermPINN快得多。在PISOV的基础上,利用神经网络参数化有效对流系数和功率值,实现基于代理模型的不确定性量化(UQ)分析,这是SOV方法无法实现的。在参数化PISOV中,我们只需要计算一次就可以得到所有的超维偏微分方程的参数化结果。此外,我们还研究了采样方法(如网格采样、均匀采样、Sobol采样、拉丁超立方采样(LHS)、Halton采样和Hammersly采样)和混合采样方法对PISOV和参数化PISOV精度的影响。数值结果表明,与ThermPINN和PINN相比,PISOV的加速速度分别提高了245倍和10倍。在不同的采样方法中,Hammersley采样方法的精度是最好的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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 $245\times $ , and $10^{4}\times $ over ThermPINN, and PINN, respectively. Among different sampling methods, the Hammersley sampling method yields the best accuracy.
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来源期刊
CiteScore
5.60
自引率
13.80%
发文量
500
审稿时长
7 months
期刊介绍: The purpose of this Transactions is to publish papers of interest to individuals in the area of computer-aided design of integrated circuits and systems composed of analog, digital, mixed-signal, optical, or microwave components. The aids include methods, models, algorithms, and man-machine interfaces for system-level, physical and logical design including: planning, synthesis, partitioning, modeling, simulation, layout, verification, testing, hardware-software co-design and documentation of integrated circuit and system designs of all complexities. Design tools and techniques for evaluating and designing integrated circuits and systems for metrics such as performance, power, reliability, testability, and security are a focus.
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