In this paper, we investigate data-driven parameterized modeling of insertion loss for transmission lines with respect to design parameters. We first show that direct application of neural networks can lead to non-physics models with negative insertion loss. To mitigate this problem, we propose two deep learning solutions. One solution is to add a regulation term, which represents the passive condition, to the final loss function to enforce the negative quantity of insertion loss. In the second method, a third-order polynomial expression is defined first, which ensures positiveness, to approximate the insertion loss, then DeepONet neural network structure, which was proposed recently for function and system modeling, was employed to model the coefficients of polynomials. The resulting neural network is applied to predict the coefficients of the polynomial expression. The experimental results on an open-sourced SI/PI database of a PCB design show that both methods can ensure the positiveness for the insertion loss. Furthermore, both methods can achieve similar prediction results, while the polynomial-based DeepONet method is faster than DeepONet based method in training time.

翻译：在本文中,我们根据设计参数调查传输线插入损失的数据驱动参数模型; 我们首先显示神经网络的直接应用可能导致非物理模型,产生负插入损失; 为了缓解这一问题,我们建议了两个深层次的学习解决办法。 一个办法是在最后损失函数中添加一个监管术语,代表被动状态,以强制执行负插入损失的负数。 在第二种方法中,首先定义了第三阶多位表达式,以确保插入损失的正值,近似插入损失,然后采用最近为功能和系统建模提议的DeepONet神经网络结构,以模拟多语言的系数。由此产生的神经网络用于预测多语言表达的系数。多氯联苯设计中开源的SI/PI数据库的实验结果显示,这两种方法都能够确保插入损失的积极性。此外,两种方法都能够取得类似的预测结果,而基于多层次的DeepONet方法在培训时间比基于DeepONet的方法更快。