arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2007.09684cs.LGphysics.app-phphysics.comp-phstat.ML
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基于自动编码器和图像梯度的片上热方程无监督学习方法

An unsupervised learning approach to solving heat equations on chip based on Auto Encoder and Image Gradient

Ansys Inc.(Ansys公司)

Haiyang He, Jay Pathak

摘要:

在即将到来的5G和AI芯片封装系统中,解决芯片上的传热方程变得非常关键。然而,对于数据驱动的监督机器学习模型,必须执行批量仿真。数据驱动的方法是数据饥饿的,为了解决这个问题,已经提出了物理信息神经网络(PINN)。然而,vanilla PINN模型一次解决一个固定的热方程,因此必须针对具有不同源项的热方程重新训练模型。此外,多目标优化的相关问题必须解决,而使用PINN,以最大限度地减少PDE残差,满足边界条件,并符合观察到的数据等,因此,本文研究了一种无监督学习的方法来解决芯片上的传热方程,而不使用解决方案的数据和推广的训练网络预测解决方案的热方程与看不见的源项。具体而言,设计了一种基于自动编码器(AE)和图像梯度(IG)的混合网络框架。AE用于编码热方程的不同源项。基于IG的网络实现了结构化网格的二阶中心差分算法,并使PDE残差最小化。通过求解各种用例的热方程来评估所设计网络的有效性。证明了在有限的源项训练AE网络的情况下,该框架不仅可以用一次训练过程解决给定的传热问题,而且可以对未知的情况(含新源项的热方程)进行合理的预测,而不需要重新训练。

英文摘要:

Solving heat transfer equations on chip becomes very critical in the upcoming 5G and AI chip-package-systems. However, batches of simulations have to be performed for data driven supervised machine learning models. Data driven methods are data hungry, to address this, Physics Informed Neural Networks (PINN) have been proposed. However, vanilla PINN models solve one fixed heat equation at a time, so the models have to be retrained for heat equations with different source terms. Additionally, issues related to multi-objective optimization have to be resolved while using PINN to minimize the PDE residual, satisfy boundary conditions and fit the observed data etc. Therefore, this paper investigates an unsupervised learning approach for solving heat transfer equations on chip without using solution data and generalizing the trained network for predicting solutions for heat equations with unseen source terms. Specifically, a hybrid framework of Auto Encoder (AE) and Image Gradient (IG) based network is designed. The AE is used to encode different source terms of the heat equations. The IG based network implements a second order central difference algorithm for structured grids and minimizes the PDE residual. The effectiveness of the designed network is evaluated by solving heat equations for various use cases. It is proved that with limited number of source terms to train the AE network, the framework can not only solve the given heat transfer problems with a single training process, but also make reasonable predictions for unseen cases (heat equations with new source terms) without retraining.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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