Adaptive Newton-Monte Carlo for efficient and fully error controlled yield optimization
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In this paper we present an efficient and fully error controlled algorithm for yield estimation and yield optimization. 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 Monte Carlo (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 adaptivly 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.
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