As circuits’ speed and frequency increase, fast and accurate capture of the details of the parasitics in metal structures, such as inductors and clock trees, becomes more critical. However, conducting high-fidelity 3D electromagnetic (EM) simulations within the design loop is very time consuming and computationally expensive. To address this issue, we propose a surrogate-based optimization methodology flow, namely multi-fidelity surrogate-based optimization with candidate search (MFSBO-CS), which integrates the concept of multi-fidelity to reduce the full-wave EM simulation cost in analog/RF simulation-based optimization problems. To do so, a statistical co-kriging model is adapted as the surrogate to model the response surface, and a parallelizable perturbation-based adaptive sampling method is used to find the optima. Within the proposed method, low-fidelity fast RC parasitic extraction tools and high-fidelity full-wave EM solvers are used together to model the target design and then guide the proposed adaptive sample method to achieve the final optimal design parameters. The sampling method in this work not only delivers additional coverage of design space but also helps increase the accuracy of the surrogate model efficiently by updating multiple samples within one iteration. Moreover, a novel modeling technique is developed to further improve the multi-fidelity surrogate model at an acceptable additional computation cost. The effectiveness of the proposed technique is validated by mathematical proofs and numerical test function demonstration. In this article, MFSBO-CS has been applied to two design cases, and the result shows that the proposed methodology offers a cost-efficient solution for analog/RF design problems involving EM simulation. For the two design cases, MFSBO-CS either reaches comparably or outperforms the optimization result from various Bayesian optimization methods with only approximately one- to two-thirds of the computation cost.

中文翻译：

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基于多保真代理的电磁仿真加速优化

随着电路速度和频率的提高，快速、准确地捕捉金属结构（如电感器和时钟树）中的寄生细节变得更加关键。然而，在设计循环中进行高保真 3D 电磁 (EM) 仿真非常耗时且计算量大。为了解决这个问题，我们提出了一种基于代理的优化方法流程，即基于候选搜索的多保真代理优化（MFSBO-CS），它集成了多保真概念以降低全波电磁仿真成本基于模拟/射频仿真的优化问题。为此，采用统计协克里金模型作为响应面建模的代理，并使用可并行化的基于扰动的自适应采样方法来寻找最优值。在建议的方法中，低保真快速 RC 寄生参数提取工具和高保真全波 EM 求解器一起使用，对目标设计进行建模，然后指导所提出的自适应样本方法，以实现最终的最优设计参数。这项工作中的采样方法不仅提供了额外的设计空间覆盖，而且还通过在一次迭代中更新多个样本来有效地提高代理模型的准确性。此外，开发了一种新颖的建模技术，以在可接受的额外计算成本下进一步改进多保真代理模型。通过数学证明和数值测试功能演示验证了所提出技术的有效性。在本文中，MFSBO-CS 已应用于两个设计案例，结果表明，所提出的方法为涉及电磁仿真的模拟/射频设计问题提供了一种经济高效的解决方案。对于这两种设计案例，MFSBO-CS 要么达到相当的效果，要么优于各种贝叶斯优化方法的优化结果，而计算成本只有大约三分之二。