Tsui-Wei Weng

Uncertainty quantification of silicon photonic devices with correlated and non-Gaussian random parameters

Process variations can significantly degrade device performance and chip yield in silicon photonics. In order to reduce the design and production costs, it is highly desirable to predict the statistical behavior of a device before the final fabrication. Monte Carlo is the mainstream computational technique used to estimate the uncertainties caused by process variations. However, it is very often too expensive due to its slow convergence rate. Recently, stochastic spectral methods based on polynomial chaos expansions have emerged as a promising alternative, and they have shown significant speedup over Monte Carlo in many engineering problems. The existing literature mostly assumes that the random parameters are mutually independent. However, in practical applications such assumption may not be necessarily accurate. In this paper, we develop an efficient numerical technique based on stochastic collocation to simulate silicon photonics with correlated and non-Gaussian random parameters. The effectiveness of our proposed technique is demonstrated by the simulation results of a silicon-on-insulator based directional coupler example. Since the mathematic formulation in this paper is very generic, our proposed algorithm can be applied to a large class of photonic design cases as well as to many other engineering problems.

Stochastic simulation and robust design optimization of integrated photonic filters

Abstract Manufacturing variations are becoming an unavoidable issue in modern fabrication processes; therefore, it is crucial to be able to include stochastic uncertainties in the design phase. In this paper, integrated photonic coupled ring resonator filters are considered as an example of significant interest. The sparsity structure in photonic circuits is exploited to construct a sparse combined generalized polynomial chaos model, which is then used to analyze related statistics and perform robust design optimization. Simulation results show that the optimized circuits are more robust to fabrication process variations and achieve a reduction of 11%–35% in the mean square errors of the 3 dB bandwidth compared to unoptimized nominal designs.

Big-Data Tensor Recovery for High-Dimensional Uncertainty Quantification of Process Variations

Fabrication process variations are a major source of yield degradation in the nanoscale design of integrated circuits (ICs), microelectromechanical systems (MEMSs), and photonic circuits. Stochastic spectral methods are a promising technique to quantify the uncertainties caused by process variations. Despite their superior efficiency over Monte Carlo for many design cases, stochastic spectral methods suffer from the curse of dimensionality, i.e., their computational cost grows very fast as the number of random parameters increases. In order to solve this challenging problem, this paper presents a high-dimensional uncertainty quantification algorithm from a big data perspective. Specifically, we show that the huge number of (e.g.,

Fast Stochastic Simulation of Silicon Waveguide with Non-Gaussian Correlated Process Variations

1.5 \times 10^{27}

Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach

) simulation samples in standard stochastic collocation can be reduced to a very small one (e.g., 500) by exploiting some hidden structures of a high-dimensional data array. This idea is formulated as a tensor recovery problem with sparse and low-rank constraints, and it is solved with an alternating minimization approach. The numerical results show that our approach can efficiently simulate some IC, MEMS, and photonic problems with over 50 independent random parameters, whereas the traditional algorithm can only deal with a small number of random parameters.

Towards Fast Computation of Certified Robustness for ReLU Networks

In this paper, we develop an efficient statistical simulation technique based on stochastic collocation for silicon photonics process variations with non-Gaussian correlated random parameters. Our algorithm has achieved 57-times speedup compared with standard Monte-Carlo simulation.