A Bayesian approach to adaptive frequency sampling

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

A novel methodology to create generative statistical models of interconnects

This paper addresses the problem of constructing a generative statistical model for an interconnect starting from a limited set of S-parameter samples, which are obtained by simulating or measuring the interconnect for a few random realizations of its stochastic physical properties. These original samples are first converted into a pole-residue representation with common poles. The corresponding residues are modeled as a correlated stochastic process by means of principal component analysis and kernel density estimation. The obtained model allows generating new samples with similar statistics as the original data. A passivity check is performed over the generated samples to retain only passive data. The proposed approach is applied to a representative coupled microstrip line example

Statistical modeling of frequency responses using linear Bayesian vector fitting

This article presents a Bayesian extension of the vector fitting (VF) procedure for rational approximation of frequency-domain responses. The proposed method treats the linear part of VF in a Bayesian way, while propagating distributions through the nonlinear part by sampling. As such, it is capable of providing data-driven uncertainty information along with the rational fit. The Bayesian VF technique is applied to two realistic design examples, a double folded stub filter and a RAM memory channel, demonstrating its validity and highlighting three potential applications of this novel framework

Generation of stochastic interconnect responses via gaussian process latent variable models

We introduce a novel generative model for stochastic device responses using limited available data. This model is oblivious to any varying design parameters or their distribution and only requires a small set of "training" responses. Using this model, new responses are efficiently generated whose distribution closely matches that of the real data, e.g., for use in Monte-Carlo-like analyses. The modeling methodology consists of a vector fitting step, where device responses are represented by a rational model, followed by the optimization of a Gaussian process latent variable model. Passivity is guaranteed by a posteriori discarding of nonpassive responses. The novel model is shown to considerably outperform a previous generative model, as evidenced by comparing accuracies of distribution estimation for the case of differential-to-common mode conversion in two coupled microstrip lines

Adaptive frequency sampling using linear Bayesian vector fitting

The authors present a novel Bayesian approach to adaptively select frequency samples to obtain a rational macromodel of device responses over a broad frequency range while performing as few electromagnetic simulations as possible. The method leverages a Bayesian approach to vector fitting to construct a data-driven uncertainty measure. The presented technique is demonstrated by application to a double semi-circular patch antenna and is shown to accurately and efficiently construct a rational macromodel over the frequency range of interest

A novel generative stochastic model for high-speed interconnection links

In this paper we introduce a new modeling approach to create a generative model for stochastic link responses. The proposed scheme starts from a limited set of simulated or measured ‘training samples’, which are first represented by a rational model using vector fitting with common poles. Next, the generative model is built, leveraging the residues' stochastic distribution, via a principal component analysis and kernel density estimation. Then, in a post-processing phase, non-passive samples are discarded. The novel method is applied to a commercial connector footprint, a multi-conductor transmission line, and a complete link composed of the cascade connection of the former components

Machine-learning-based hybrid random-fuzzy uncertainty quantification for EMC and SI assessment

Modeling the effects of uncertainty is of crucial importance in the signal integrity and Electromagnetic Compatibility assessment of electronic products. In this article, a novel machine-learning-based approach for uncertainty quantification problems involving both random and epistemic variables is presented. The proposed methodology leverages evidence theory to represent probabilistic and epistemic uncertainties in a common framework. Then, Bayesian optimization is used to efficiently propagate this hybrid uncertainty on the performance of the system under study. Two suitable application examples validate the accuracy and efficiency of the proposed method

A generative modeling framework for statistical link analysis based on sparse data

This paper proposes a novel strategy for creating generative models of stochastic link responses starting from limited available data. Whereas state-of-the-art techniques, e.g., based on generalized polynomial chaos expansions, require a considerable amount of (expensive) input data, here we start from a small set of "training" responses. These responses are obtained either from simulations or measurements to construct a comprehensive stochastic model. Using this model, new response samples can be generated with a distribution as similar as possible to the real data distribution, for use in Monte Carlo-like analyses. The methodology first uses the standard Vector Fitting algorithm to fit the S-parameter data with rational functions having common poles. Then, a generative model for the residues is created by means of principal component analysis and kernel density estimation. An a posteriori selection of passive samples is performed on the generated data to ensure the new samples are physically consistent. The proposed modeling approach is applied to a commercial connector and to a set of differential striplines. Both are concatenated to produce the stochastic analysis of a complete link. Comparisons on the prediction of time-domain responses are also provided

Machine learning-based hybrid random-fuzzy modeling framework for antenna design

A machine learning-based framework is proposed to evaluate the effect of design parameters, affected by both aleatory and epistemic uncertainty, on the performance of antennas. In particular, possibility theory is leveraged to define aleatory and epistemic uncertainty in a common framework. Then, a method combining Bayesian optimization and Polynomial Chaos expansion is applied to accurately and efficiently propagate both uncertainties throughout the system under study. A suitable application example validates the proposed method