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

Manfredi, Paolo; Trinchero, Riccardo

doi:10.1109/tcad.2021.3112138

Cited by 15 publications

(13 citation statements)

References 70 publications

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“…Fortunately, closed-form expressions can be derived at least for the predicted mean and variance of y and, specifically, for their expectation and standard deviation. Some preliminary results in this regard were presented in [43]. This article provides more accurate results for the prediction of the variance, and it extends the framework to complex-valued outputs.…”

Section: Probabilistic Uq Via Gpr Surrogatesmentioning

confidence: 87%

“…In [43], the expected value and standard deviation of (12) were approximatively derived under the simplifying assumption that μy ≈ E μy . For a more rigorous calculation, it is useful to rewrite (12) as the quadratic form [65]…”

Section: B Probabilistic Gpr Estimate Of the Variancementioning

confidence: 99%

“…A simpler, though rigorous probabilistic framework based on GPR for the UQ of electronic circuits with the inclusion of confidence bounds for the statistical estimates, such as moments and probability distributions of the outputs of interest, has been recently developed [43]. The idea is to derive statistical estimates from pointwise predictions by suitably taking into account their uncertainty.…”

mentioning

confidence: 99%

“…Moreover, for problems with multiple outputs of interest, PCA is leveraged to compress data and make the model training more efficient [43], [44], [45], [46]. In this context, the use of PCA compression is not per se new, yet it fits particularly well in the context of GPR, because its linearity allows retaining the convenient properties of Gaussian random variables.…”

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confidence: 99%

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Probabilistic Uncertainty Quantification of Microwave Circuits Using Gaussian Processes

Manfredi

2023

IEEE Trans. Microwave Theory Techn.

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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.

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Section: Probabilistic Uq Via Gpr Surrogatesmentioning

confidence: 87%

Section: B Probabilistic Gpr Estimate Of the Variancementioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Probabilistic Uncertainty Quantification of Microwave Circuits Using Gaussian Processes

Manfredi

2023

IEEE Trans. Microwave Theory Techn.

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“…In particular, stochastic spectral methods based on the generalised polynomial chaos have emerged as a promising alternative, significantly outperforming Monte Carlo. Sparse implementations (e.g., least-angle regression, sparse interpolations, and low-rank tensor decompositions) are also appropriate for high-dimensional problems 19 – 22 . All these techniques, including the sparse ones, are however parametric, meaning that the form of the predictor must be specified beforehand.…”

Section: Introductionmentioning

confidence: 99%

Stochastic and multi-objective design of photonic devices with machine learning

Manfredi,

Waqas,

Melati

2024

Sci Rep

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Compact and highly performing photonic devices are characterized by non-intuitive geometries, a large number of parameters, and multiple figures of merit. Optimization and machine learning techniques have been explored to handle these complex designs, but the existing approaches often overlook stochastic quantities. As an example, random fabrication uncertainties critically determines experimental device performance. Here, we present a novel approach for the stochastic multi-objective design of photonic devices combining unsupervised dimensionality reduction and Gaussian process regression. The proposed approach allows to efficiently identify promising alternative designs and model the statistic of their response. Incorporating both deterministic and stochastic quantities into the design process enables a comprehensive analysis of the device and of the possible trade-offs between different performance metrics. As a proof-of-concept, we investigate surface gratings for fiber coupling in a silicon-on-insulator platform, considering variability in structure sizes, silicon thickness, and multi-step etch alignment. We analyze 86 alternative designs presenting comparable performance when neglecting variability, discovering on the contrary marked differences in yield and worst-case figures for both fiber coupling efficiency and back-reflections. Pareto frontiers demonstrating optimized device robustness are identified as well, offering a powerful tool for the design and optimization of photonic devices with stochastic figures of merit.

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Application of different learning methods for arrays sensitivity analysis with uncertain excitation and location tolerances

Boozari

Yasi

Khalaj‐Amirhosseini

2022

AEU - International Journal of Electronics and Communications

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

Cited by 15 publications

References 70 publications

Probabilistic Uncertainty Quantification of Microwave Circuits Using Gaussian Processes

Probabilistic Uncertainty Quantification of Microwave Circuits Using Gaussian Processes

Stochastic and multi-objective design of photonic devices with machine learning

Application of different learning methods for arrays sensitivity analysis with uncertain excitation and location tolerances

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