Identification of input random field samples causing extreme responses

Abstract Consider a physical system modeled by a differential equation that depends on a coefficient random field. The objective of this work is to identify samples of this random field which yield extreme response as a means to: study the law of the input conditioned on rare events and predict if a random field sample causes such an event. This differs from reliability engineering which focuses on computation of failure probabilities. We investigate two classification schemes that identify these samples of interest: physics-based indicators which are functionals of the input random field and surrogate models which approximate the response. As an alternative to these approaches, we propose a general framework consisting of two stages that combines the use of a physics-based surrogate model and a machine learning classifier. In the first stage, a multifidelity surrogate that requires infrequent evaluations of the full model is designed. This surrogate is then used to generate a sufficient number of samples of random fields that yield extreme events to train a machine learning classifier in the second stage. We study the analytical properties required of the surrogate model and demonstrate through numerical examples the synergy of the proposed approach.