HierPINN-EM: Fast Learning-Based Electromigration Analysis for Multi-Segment Interconnects Using Hierarchical Physics-Informed Neural Network
HierPINN-EM: Fast Learning-Based Electromigration Analysis for Multi-Segment Interconnects Using Hierarchical Physics-Informed Neural Network
复制标题
HierPINN-EM：使用分层物理信息神经网络对多段互连进行基于快速学习的电迁移分析
DOI：
10.1145/3508352.3549371
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Tan, Sheldon X.-D.
中科院分区：
文献类型：
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作者：
Jin, Wentian;Chen, Liang;Lamichhane, Subed;Kavousi, Mohammadamir;Tan, Sheldon X.-D.
随着纳米技术的发展，电迁移（EM）成为VLSI电路的主要问题。问题的关键是求解偏微分Korhonen方程，这仍然是具有挑战性的，由于不断增加的集成密度。最近，由于深度神经网络的突破性成功，科学机器学习已经被探索用于解决偏微分方程（PDE），并且现有方法（如物理信息神经网络（PINN））在一些小的PDE问题上显示出有希望的结果。然而，对于大型工程问题，如大型互连树的EM分析，结果表明，由于大量的变量，普通PINN不能很好地工作。在这项工作中，我们提出了一种新的分层PINN方法，HierPINN-EM快速EM诱导应力分析的多段互连。而不是解决作为一个整体的互连树，我们首先解决EM问题的一个线段在不同的边界和几何参数使用监督学习。然后，我们应用无监督PINN的概念来解决整个互连线的边界，强制执行的物理定律的所有线段。这样，HierPINN-EM可以大大减少PINN求解器中的变量数量。对多棵合成互连树的仿真结果表明，HierPINN-EM方法的训练速度提高了几个数量级，精度提高了79倍以上.此外，HierPINN-EM比最近提出的基于图神经网络的EM求解器EMGraph的精度高19%，训练成本降低99%。
Electromigration (EM) becomes a major concern for VLSI circuits as the technology advances in the nanometer regime. The crux of problem is to solve the partial differential Korhonen equations, which remains challenging due to the increasing integrated density. Recently, scientific machine learning has been explored to solve partial differential equations (PDE) due to breakthrough success in deep neural networks and existing approach such as physics-informed neural networks (PINN) shows promising results for some small PDE problems. However, for large engineering problems like EM analysis for large interconnect trees, it was shown that the plain PINN does not work well due the to large number of variables. In this work, we propose a novel hierarchical PINN approach,HierPINN-EMfor fast EM induced stress analysis for multi-segment interconnects. Instead of solving the interconnect tree as a whole, we first solve EM problem for one wire segment under different boundary and geometrical parameters using supervised learning. Then we apply unsupervised PINN concept to solve the whole interconnects by enforcing the physics laws in the boundaries for all wire segments. In this way,HierPINN-EMcan significantly reduce the number of variables at plain PINN solver. Numerical results on a number of synthetic interconnect trees show thatHierPINN-EMcan lead to orders of magnitude speedup in training and more than 79× better accuracy over the plain PINN method. Furthermore,HierPINN-EMyields 19% better accuracy with 99% reduction in training cost over recently proposed Graph Neural Network-based EM solver, EMGraph.