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Failure probability estimation problem is an crucial task in engineering. Inthis work we consider this problem in the situation that the underlyingcomputer models are extremely expensive, which often arises in the practice,and in this setting, reducing the calls of computer model is of essentialimportance. We formulate the problem of estimating the failure probability withexpensive computer models as an sequential experimental design for the limitstate (i.e., the failure boundary) and propose a series of efficient adaptivedesign criteria to solve the design of experiment (DOE). In particular, theproposed method employs the deep neural network (DNN) as the surrogate of limitstate function for efficiently reducing the calls of expensive computerexperiment. A map from the Gaussian distribution to the posterior approximationof the limit state is learned by the normalizing flows for the ease ofexperimental design. Three normalizing-flows-based design criteria are proposedin this work for deciding the design locations based on the differentassumption of generalization error. The accuracy and performance of theproposed method is demonstrated by both theory and practical examples.

Adaptive design of experiment via normalizing flows for failure probability estimation