A Bayesian Approach to Adaptive Frequency Sampling

Abstract

This paper introduces an adaptive frequency sampling scheme, based on a Bayesian approach to the well-known vector fitting algorithm. This Bayesian treatment results in a data-driven measure of intrinsic model uncertainty. This uncertainty measure can in turn be leveraged to sample sequentially in an efficient and robust way. A realistic example is used to visualize the proposed scheme, and to confirm its proficiency.

Adaptive Frequency Sampling Based on Local Rational Modeling for Microwave Electromagnetic Simulations

“…Over the years, numerous adaptive frequency sampling algorithms have been developed, using global rational macromodeling techniques [5]- [10]. These algorithms employ a global rational macromodel, represented by a partial fraction expansion…”

“…Incorporation of the crowding distance in the sampling metric therefore favors exploration independently of the model uncertainty. As the value of the crowding distance in (10) relies on the absolute difference between frequencies, it needs to be normalized to obtain a uniform metric accross different frequency ranges. The normalized crowding distance is defined as [31]…”

“…In the literature, adaptive sampling is also sometimes denoted as active learning. Current AFS algorithms add additional frequency data samples in an iterative way without requiring any prior system knowledge [5]- [10]. In each consecutive iteration, a data-driven Model Order Reduction (MOR) method is used to steer the frequency sampling process.…”

Use of an Active Learning Strategy Based on Gaussian Process Regression for the Uncertainty Quantification of Electronic Devices

“…The statistical information provided by the probabilistic model constructed via the GPR can be suitably adopted to efficiently explore the parameter space X , in order to get the optimal set of training samples [8][9][10][11]. The proposed AL approach is iterative.…”

“…This work investigates the possible advantages and the performance of an alternative approach for the sampling selection given by the combination of an active learning (AL) scheme and the GPR [8][9][10][11][12]. The effectiveness of the proposed AL technique has been investigated by considering the uncertainty quantification of the DC efficiency of a switching converter as a function of seven uncertain parameters.…”