MINNs: MNA-Informed Neural Networks for Fast Transient Simulation of Nonlinear Transmission Lines Subject to Parametric Uncertainty

In this paper, a new artificial neural network (ANN) formulation is presented for the transient simulation of nonlinear transmission lines (NLTLs) in the presence of parametric uncertainty. The key attribute of the proposed formulation is that it minimizes a loss function expressed as the sum of the residuals of the modified nodal analysis (MNA) equations and the initial conditions describing NLTLs instead of the classical data-driven loss function. The resultant ANNs are referred to as MNA informed neural networks (MINNs). MINNs exhibit a completely data-free and highly efficient training unlike conventional ANNs that are trained on large datasets extracted from time and memory-intensive SPICE simulations of NLTLs. Furthermore, by virtue of its more fundamental MNA-based training, MINNs are more accurate than conventional ANNs when predicting NLTL responses for parameter values lying outside the training range. In this paper, additional techniques such as dynamic weighting and multistep multi-fidelity training are developed to mitigate the inherently slow convergence of MINNs. Overall, MINNs are demonstrated to enable highly accurate and efficient Monte Carlo driven uncertainty quantification of NLTLs that is not possible using conventional ANNs or brute force SPICE simulations.