Pseudo adjoint optimization: harnessing the solution curve for SPICE acceleration

Pseudo transient analysis (PTA) has been a promising solution for direct current (DC) analysis of transistor-level circuit simulation. Despite its popularity, PTA requires meticulous hyperparameter tuning for optimal performance. In this paper, we propose pseudo adjoint optimization, Soda-PTA, which models the PTA solution curve (which is used to measure convergence) using a neural ordinary differential equation (Neural ODE) and deriving explicit gradients of the Newton-Raphson (NR) iteration w.r.t. the PTA hyperparameters through the classic adjoint method, enabling effective optimization of the PTA hyperparameters. To generalize Soda-PTA for unseen circuits, we further introduce a graph convolution network to transfer optimal PTA hyperparameters from the other circuits to the target one. Soda-PTA is implemented in an out-of-the-box SPICE simulator. Through extensive experiments, Soda-PTA demonstrates superior acceleration performance: an average speedup of 1.53x over the state-of-the-art BoA-PTA while ensuring superior convergence and up to 22.12x speedup compared to the native PTA solver.