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

• Main Authors: Fuhrländer, Mona, Georg, Niklas, Römer, Ulrich, Schöps, Sebastian
• Format: Journal Article
• Language: English
• Published: 09-10-2020
• Subjects: Computer Science - Computational Engineering, Finance, and Science
• DOI: 10.48550/arxiv.1912.09908

Int.J.UncertaintyQuantification 10, 4 (2020) p. 351-373 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.