Uncertainty quantification and stochastic modelling of photonic device from experimental data through polynomial chaos expansion

Waqas, Abi; Melati, Daniele; Mushtaq, Zarlish; Melloni, Andrea

doi:10.1117/12.2290540

Cited by 3 publications

(5 citation statements)

References 12 publications

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“…However, (28) is a non-convex optimization problem and is hard to optimize in general. The subproblems (26) and (27) help to provide a good initial guess for the joint optimization.…”

Section: B How To Build the Surrogate Models?mentioning

confidence: 99%

“…We first build the surrogate models for both the objective and constraints by the second-order polynomial basis functions. The optimized quadrature points {x l , v l } 6 l=1 for the design variables by (26) and {ξ l , u l } 6 l=1 for the random parameter by (27) are shown in Fig. 3 (a) and (b), respectively.…”

Section: A Synthetic Examplementioning

confidence: 99%

“…2. Initialize the quadrature points for design variables {x l , v l } M1 l=1 by (26), and quadrature points for stochastic parameters {ξ l , u l } M2 l=1 by the optimization problem (27), respectively. Then co-optimize the quadrature rule to obtain {x k , ξ k , w k } M k=1 by (28).…”

Section: B How To Build the Surrogate Models?mentioning

confidence: 99%

“…(1, Σ) + 1 2 N (−1, Σ) with Σ The quadrature points and weights in the synthetic experiment. (a) and (b): The initial 2-D quadrature points for the design variables x and uncertain parameters ξ by solving(26) and(27), respectively. (c) and (d): The optimized quadrature points for the joint 4-D space of x and ξ by solving(28).…”

mentioning

confidence: 99%

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Chance-Constrained and Yield-Aware Optimization of Photonic ICs With Non-Gaussian Correlated Process Variations

Cui

Liu

Zhang

2020

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Uncertainty quantification has become an efficient tool for yield prediction, but its power in yield-aware optimization has not been well explored from either theoretical or application perspectives. Yield optimization is a much more challenging task. On one side, optimizing the generally non-convex probability measure of performance metrics is difficult. On the other side, evaluating the probability measure in each optimization iteration requires massive simulation data, especially when the process variations are non-Gaussian correlated. This paper proposes a data-efficient framework for the yield-aware optimization of the photonic IC. This framework optimizes design performance with a yield guarantee, and it consists of two modules: a modeling module that builds stochastic surrogate models for design objectives and chance constraints with a few simulation samples, and a novel yield optimization module that handles probabilistic objectives and chance constraints in an efficient deterministic way. This deterministic treatment avoids repeatedly evaluating probability measures at each iteration, thus it only requires a few simulations in the whole optimization flow. We validate the accuracy and efficiency of the whole framework by a synthetic example and two photonic ICs. Our optimization method can achieve more than 30× reduction of simulation cost and better design performance on the test cases compared with a recent Bayesian yield optimization approach.

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“…However, (28) is a non-convex optimization problem and is hard to optimize in general. The subproblems (26) and (27) help to provide a good initial guess for the joint optimization.…”

Section: B How To Build the Surrogate Models?mentioning

confidence: 99%

Section: A Synthetic Examplementioning

confidence: 99%

Section: B How To Build the Surrogate Models?mentioning

confidence: 99%

mentioning

confidence: 99%

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Chance-Constrained and Yield-Aware Optimization of Photonic ICs With Non-Gaussian Correlated Process Variations

Cui

Liu

Zhang

2020

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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“…Generalized Polynomial Chaos Expansion (gPC), proposed several years ago [6], is a popular and classical choice to build stochastic surrogate models and several advanced techniques have been recently reported to deal also with a large number of variables and variable correlation [7]- [9]. A few gPC implementations have been proposed also for stochastic analysis of photonics devices [10]- [14]. As a drawback, both gPC and Monte Carlo based techniques are circuit-specific and the entire analysis has to be repeated each time the BB parameters or the circuit layout change, with a large expense of time and resources.…”

Section: Introductionmentioning

confidence: 99%

Efficient Variability Analysis of Photonic Circuits by Stochastic Parametric Building Blocks

Waqas

Melati

Chowdhry

et al. 2020

IEEE J. Select. Topics Quantum Electron.

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This paper presents a method to build stochastic parametric building blocks to be used in photonic process design kits. The building blocks are based on parametric macromodels computed by means of the generalized Polynomial Chaos Expansion technique. These macro-models can be built upfront and stored in process design kits. Being parametric, they do not have to be recalculated if the value of their design or statistical parameters change. It is shown that a single deterministic simulation performed with a classical circuit simulator is sufficient to perform the statistical analysis of any arbitrary photonic circuit realized combining these building blocks with different parameters, without the need of time-consuming Monte Carlo approach. Relevant numerical examples are used to demonstrate that the proposed macro-models are truly parametric, inherently stochastic and have greater simulation efficiency compared to

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Chance-Constrained and Yield-aware Optimization of Photonic ICs with Non-Gaussian Correlated Process Variations

Cui¹,

Liu²,

Zhang³

2019

Preprint

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Uncertainty quantification and stochastic modelling of photonic device from experimental data through polynomial chaos expansion

Cited by 3 publications

References 12 publications

Chance-Constrained and Yield-Aware Optimization of Photonic ICs With Non-Gaussian Correlated Process Variations

Chance-Constrained and Yield-Aware Optimization of Photonic ICs With Non-Gaussian Correlated Process Variations

Efficient Variability Analysis of Photonic Circuits by Stochastic Parametric Building Blocks

Chance-Constrained and Yield-aware Optimization of Photonic ICs with Non-Gaussian Correlated Process Variations

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