# Surrogate models for non-smooth outputs with multiple failure domains

Hi! I am investigating methods (or combinations thereof) to surrogate complex, highly dimensional models whose outputs are non-smooth and where there exist multiple disjointed low probability failure domains. I bumped into a paper by Cadini et al. (2014) “An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability” which seems to describe something close to what I want (metaAK-IS). However, it’s been 6 years since the publication of this paper and I am not an expert in the reliability field. Does someone know the state-of-the-art for this specific issue?

Thanks!

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Hi voulpiotis! This sounds similar to work I’m getting around to, using non-stationary Gaussian process (GP) emulators. GP emulators are approximations of an aspect of a more complex model’s output, based on a set of perturbed input parameters and the corresponding output. GP emulators don’t cope well with discontinuities or sharp changes in the model output, which makes sense since the model output is assumed to be smooth when emulating. However there are some adaptions that can be made to emulate non-stationary behaviour.

Some of them have been around a while, like Gramacy and Lee, 2008, Bayesian Treed Gaussian Process Models With an Application to Computer Modeling. This one is a bit limited and maybe not the best for high-dimensions. But there has been more interest in recent years:

• using multiple stationary GPs (Montagna and Tokdar, 2016, Computer Emulation with Nonstationary Gaussian Processes)
• deriving underlying covariance functions using multiple covariance kernels (Volodina and Williamson, 2018, Nonstationary Gaussian Process Emulators
with Kernel Mixtures)
• splitting the parameter space into Voronoi tessellations and emulating over each region (Pope et al., 2019, Gaussian Process Modeling of Heterogeneity and Discontinuities Using Voronoi Tessellations)
• using neural net kernels (Mohammadi et al., 2019, Emulating computer models with step-discontinuous outputs using Gaussian processes)

I’m aware these aren’t exactly in the reliability field, but maybe these methods might be of use to you!

Thanks @rsans, I will have a look!