Modeling complex mechanical computer codes with functional input via Gaussian processes

Resumo

Surrogate models based on Gaussian processes (GPs) have been successfully used as a complement
of costly-to-evaluate complex computer codes. They are capable to provide accurate predictions with confident
intervals but require fewer costs (in both time and resources). Here, we focus on a class of mechanical codes
with functional inputs and output force-displacement curves. We further investigate a GP framework where inputs
are handled in a continuous setting, which results in more tractable and scalable models. Both input and output
information are correlated using a composite kernel function that can be efficiently computed (and inverted) when
tensor-structured data are considered. We demonstrate the reliability and scalability of the GP in a synthetic
example with highly variable input and output curves, as well as on a real-world mechanical application modeling
the self-piercing riveting (SPR) in a single hat component. Our experiments show that the methodology is able to
correctly detect the maximum forces and the displacements at peak force where the failure of SPR appears.