A Data Compression Strategy for the Efficient Uncertainty Quantification of Time-Domain Circuit Responses

Abstract

This paper presents an innovative modeling strategy for the construction of efficient and compact surrogate models for the uncertainty quantification of time-domain responses of digital links. The proposed approach relies on a two-step methodology. First, the initial dataset of available training responses is compressed via principal component analysis (PCA). Then, the compressed dataset is used to train compact surrogate models for the reduced PCA variables using advanced techniques for uncertainty quantification and parametric macromodeling. Specifically, in this work sparse polynomial chaos expansion and least-square support-vector machine regression are used, although the proposed methodology is general and applicable to any surrogate modeling strategy. The preliminary compression allows limiting the number and complexity of the surrogate models, thus leading to a substantial improvement in the efficiency. The feasibility and performance of the proposed approach are investigated by means of two digital link designs with 54 and 115 uncertain parameters, respectively. INDEX TERMS High-speed link, least-squares support-vector machine, machine learning, polynomial chaos expansion, principal component analysis, signal integrity, uncertainty quantification. PAOLO MANFREDI (Senior Member, IEEE) received the M.Sc. degree in electronic engineering from the Politecnico di Torino, Turin, Italy, in 2009, and the Ph.D. degree in information and communication technology from the Scuola Interpolitecnica di Dottorato, Politecnico di Torino, in 2013.

Fast Stochastic Surrogate Modeling via Rational Polynomial Chaos Expansions and Principal Component Analysis

“…In order to reduce the exorbitant number of MQ regression solutions that is required by the full characterization of the model ( 6) for all port responses and frequency points, a compression strategy is introduced using PCA [23]. This approach is motivated by the fact that the responses of a linear system exhibit some amount of interdependency between different ports and frequency points, which can be effectively handled by compressing the data into a reduced subset by means of PCA [24].…”

“…In order to alleviate this shortcoming, we introduce here a compression strategy, based on principal component analysis (PCA) [23], that allows for a considerable reduction of the number of regression problems to be solved, thus remarkably improving the efficiency in large-size problems. This approach was recently used in conjunction with generic surrogate modeling techniques to improve the efficiency of stochastic time-domain circuit simulations [24]. In this paper, it is adapted for the use with rational PCEs in the FD.…”

“…In this paper, it is adapted for the use with rational PCEs in the FD. Therefore, compared to [24], the main novel contribution is in the use of rational PCEs as surrogate models, which were shown to provide remarkably better accuracy for the uncertainty quantification of FD network responses. Moreover, novel theoretical insights are provided, and the behavior of the PCA coefficients w.r.t.…”

Compressed Machine Learning Models for the Uncertainty Quantification of Power Distribution Networks

“…To overcome this limitation, we introduce a compression strategy based on PCA [39,46]. Let us consider again a set of L training pairs {(…”

“…As the model parameters have to be optimized separately for each output variable, the computational complexity is proportional to the number of variables of interest which, for a power distribution network, usually amount to thousands of steady-state voltages at the network nodes. To overcome this detrimental limitation, principal component analysis (PCA) is used to compress the number of output variables that need to be effectively modeled [39], thus reducing the model building cost typically by some order of magnitude.…”