Variable-fidelity electromagnetic simulations and co-kriging for accurate modeling of antennas

Accurate and fast models are indispensable in contemporary antenna design. In this paper, we describe the low-cost antenna modeling methodology involving variable-fidelity electromagnetic (EM) simulations and co-Kriging. Our approach exploits sparsely sampled accurate (high-fidelity) EM data as well as densely sampled coarse-discretization (low-fidelity) EM simulations that are accommodated into one model using the co-Kriging technique. By using coarse-discretization simulations, the computational cost of creating the antenna model is greatly reduced compared to conventional approaches, where high-fidelity simulations are directly used to set up the model. At the same time, the modeling accuracy is not compromised. The proposed technique is demonstrated using three examples of antenna structures. Comparisons with conventional modeling based on high-fidelity data approximation, as well as applications for antenna design, are also discussed

Surrogate-based Analysis and Design Optimization of Power Delivery Networks

As microprocessor architectures continue to increase computing performance under low-energy consumption, the combination of signal integrity, electromagnetic interference, and power delivery is becoming crucial in the computer industry. In this context, power delivery engineers make use of complex and computationally expensive models that impose time-consuming industrial practices to reach an adequate power delivery design. In this paper, we propose a general surrogate-based methodology for fast and reliable analysis and design optimization of power delivery networks (PDN). We first formulate a generic surrogate model methodology exploiting passive lumped models optimized by parameter extraction to fit PDN impedance profiles. This PDN modeling formulation is illustrated with industrial laboratory measurements of a 4th generation server CPU motherboard. We next propose a black box PDN surrogate modeling methodology for efficient and reliable power delivery design optimization. To build our black box PDN surrogate, we compare four metamodeling techniques: support vector machines, polynomial surrogate modeling, generalized regression neural networks, and Kriging. The resultant best metamodel is then used to enable fast and accurate optimization of the PDN performance. Two examples validate our surrogate-based optimization approach: a voltage regulator with dual power rail remote sensing intended for communications and storage applications, by finding optimal sensing resistors and loading conditions; and a multiphase voltage regulator from a 6th generation Intel® server motherboard, by finding optimal compensation settings to reduce the number of bulk capacitors without losing CPU performance.ITESO, A.C

A Probabilistic Machine Learning Approach for the Uncertainty Quantification of Electronic Circuits Based on Gaussian Process Regression

This paper introduces a probabilistic machine learning framework for the uncertainty quantification (UQ) of electronic circuits based on Gaussian process regression (GPR). As opposed to classical surrogate modeling techniques, GPR inherently provides information on the model uncertainty. The main contribution of this work is twofold. First, it describes how, in an UQ scenario, the model uncertainty can be combined with the uncertainty of the input design parameters to provide confidence bounds for the statistical estimates of the system outputs, such as moments and probability distributions. These confidence bounds allows assessing the accuracy of the predicted statistics. Second, in order to deal with dynamic multi-output systems, principal component analysis (PCA) is effectively employed to compress the time-dependent output variables into a smaller set of components, for which the training of individual GPR models becomes feasible. The uncertainty on the principal components is then propagated back to the original output variables. Several application examples, ranging from a trivial RLC circuit to real-life designs, are used to illustrate and validate the advocated approach

Machine learning for the performance assessment of high-speed links

This paper investigates the application of support vector machine to the modeling of high-speed interconnects with largely varying and/or highly uncertain design parameters. The proposed method relies on a robust and well-established mathematical framework, yielding accurate surrogates of complex dynamical systems. An identification procedure based on the observation of a small set of system responses allows generating compact parametric relations, which can be used for design optimization and/or stochastic analysis. The feasibility and strength of the method are demonstrated based on a benchmark function and on the statistical assessment of a realistic printed circuit board interconnect, highlighting the main features and benefits of this technique over state-of-the-art solutions. Emphasis is given to the effects of the initial sample size and of input noise on the model estimation

Polynomial-based surrogate modeling of RF and microwave circuits in frequency domain exploiting the multinomial theorem

A general formulation to develop EM-based polynomial surrogate models in frequency domain utilizing the multinomial theorem is presented in this paper. Our approach is especially suitable when the number of learning samples is very limited and no physics-based coarse model is available. We compare our methodology against other four surrogate modeling techniques: response surface modeling, support vector machines, generalized regression neural networks, and Kriging. Results confirm that our modeling approach has the best performance among these techniques when using a very small amount of learning base points on relatively small modeling regions. We illustrate our technique by developing a surrogate model for an SIW interconnect with transitions to microstrip lines, a dual band T-slot PIFA handset antenna, and a high-speed package interconnect. Examples are simulated on a commercially available 3D FEM simulator

Probabilistic Uncertainty Quantification of Microwave Circuits Using Gaussian Processes

In this article, a probabilistic machine learning framework based on Gaussian process regression (GPR) and principal component analysis (PCA) is proposed for the uncertainty quantification (UQ) of microwave circuits. As opposed to most surrogate modeling techniques, GPR models inherently carry information on the model prediction uncertainty due to unseen data. This article shows how the inherent uncertainty of GPR pointwise predictions can be combined with the uncertainty of the design parameters to provide global statistical information on the device performance with the inclusion of confidence bounds. The model confidence is possibly improved by increasing the amount of training data. In addition, PCA is employed to effectively deal with problems with multiple and possibly complex-valued output components, such as those involving the UQ of time-domain responses or multiport scattering parameters. The proposed technique is successfully applied to two low-noise amplifier designs subject to the process variation of up to 25 parameters. Comparisons against the state-of-the-art polynomial chaos expansion method demonstrates that GPR achieves superior accuracy, while additionally providing information on the prediction confidence

Selecting Surrogate-Based Modeling Techniques for Power Integrity Analysis

In recent years, extensive usage of simulated power integrity (PI) models to predict the behavior of power delivery networks (PDN) on a chip has become more relevant. Predicting adequate performance against power consumption can yield to either cheap or costly design solutions. Since PI simulations including high-frequency effects are becoming more and more computationally complex and expensive, it is critical to develop reliable and fast models to understand system’s behavior to accelerate decision making during design stages. Hence, metamodeling techniques can help to overcome this challenge. In this work, a comparative study between different surrogate modeling techniques as applied to PI analysis is described. We model and analyze a PDN that includes two different power domains and a combination of remote sense resistors for communication and storage CPU applications. We aim at developing reliable and fast coarse models to make trade off decisions while complying with voltage levels and power consumption requirements

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

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