Yield Optimization based on Adaptive Newton-Monte Carlo and Polynomial Surrogates

In this paper we present an algorithm for yield estimation and optimization exploiting Hessian based optimization methods, an adaptive Monte Carlo (MC) strategy, polynomial surrogates and several error indicators. Yield estimation is used to quantify the impact of uncertainty in a manufacturing process. Since computational efficiency is one main issue in uncertainty quantification, we propose a hybrid method, where a large part of a MC sample is evaluated with a surrogate model, and only a small subset of the sample is re-evaluated with a high fidelity finite element model. In order to determine this critical fraction of the sample, an adjoint error indicator is used for both the surrogate error and the finite element error. For yield optimization we propose an adaptive Newton-MC method. We reduce computational effort and control the MC error by adaptively increasing the sample size. The proposed method minimizes the impact of uncertainty by optimizing the yield. It allows to control the finite element error, surrogate error and MC error. At the same time it is much more efficient than standard MC approaches combined with standard Newton algorithms.