Toward Fully Automated High-Dimensional Parameterized Macromodeling

This article presents a fully automated algorithm for the extraction of parameterized macromodels from frequency responses. The reference framework is based on a frequency-domain rational approximation combined with a parameter-space expansion into Gaussian radial basis functions (RBFs). An iterative least-squares fitting with positivity constraints is used to optimize model coefficients, with a guarantee of uniform stability over the parameter space. The main novel contribution of this work is a set of algorithms, supported by strong theoretical arguments with associated proofs, for the automated determination of all the hyperparameters that define model orders, placement, and width of RBFs. With respect to standard approaches, which tune these parameters using time-consuming tentative model extractions following a trial-and-error strategy, the presented technique allows much faster tuning of the model structure. The numerical results show that models with up to ten independent parameters are easily extracted in few minutes.