  The mercury constitutive model predicting the strain and stress in the target
vessel plays a central role in improving the lifetime prediction and future
target designs of the mercury targets at the Spallation Neutron Source (SNS).
We leverage the experiment strain data collected over multiple years to improve
the mercury constitutive model through a combination of large-scale simulations
of the target behavior and the use of machine learning tools for parameter
estimation. We present two interdisciplinary approaches for surrogate-based
model calibration of expensive simulations using evolutionary neural networks
and sparse polynomial expansions. The experiments and results of the two
methods show a very good agreement for the solid mechanics simulation of the
mercury spallation target. The proposed methods are used to calibrate the
tensile cutoff threshold, mercury density, and mercury speed of sound during
intense proton pulse experiments. Using strain experimental data from the
mercury target sensors, the newly calibrated simulations achieve 7\% average
improvement on the signal prediction accuracy and 8\% reduction in mean
absolute error compared to previously reported reference parameters, with some
sensors experiencing up to 30\% improvement. The proposed calibrated
simulations can significantly aid in fatigue analysis to estimate the mercury
target lifetime and integrity, which reduces abrupt target failure and saves a
tremendous amount of costs. However, an important conclusion from this work
points out to a deficiency in the current constitutive model based on the
equation of state in capturing the full physics of the spallation reaction.
Given that some of the calibrated parameters that show a good agreement with
the experimental data can be nonphysical mercury properties, we need a more
advanced two-phase flow model to capture bubble dynamics and mercury
cavitation.
