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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.

Physics-Enforced Modeling for Insertion Loss of Transmission Lines by Deep Neural Networks