Few-Shot Bayesian Performance Modeling for Silicon Photonic Devices Under Process Variation

We develop and apply a Bayesian linear regression technique for few-shot performance modeling of silicon photonic devices under process variation. The key contribution is to leverage information from low-fidelity simulations which are cheap to obtain, and to encode that information into the prior distribution under a Bayesian framework. We then evaluate the maximum-a-posteriori (MAP) estimator according to Bayes' theorem. Our numerical experiments on a rectangular waveguide and a Y-branch show that compared to linear regression, ridge regression, and a multi-layer feedforward neural network, this approach can achieve 7x smaller error given the same number of samples, or reduce running time by 2.4x to reach the same accuracy. Most importantly, we demonstrate that with only 10 expensive high-fidelity simulations and a small number of cheap low-fidelity simulations, our approach can obtain a model with good performance.