# Model Calibration of the Liquid Mercury Spallation Target using Evolutionary Neural Networks and Sparse Polynomial Expansions

arXiv: https://arxiv.org/abs/2202.09353 · HTML: https://mlsanity.com/paper/2202.09353/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 59 references that are in the map.
- First posted on arXiv 18 Feb 2022.

## Builds on (most cited first, 7 of 7)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [A Rewriting System for Convex Optimization Problems](https://mlsanity.com/paper/1709.04494/) (2017)
- [A Theoretical and Empirical Comparison of Gradient Approximations in Derivative-Free Optimization](https://mlsanity.com/paper/1905.01332/) (2019)
- [NEORL: NeuroEvolution Optimization with Reinforcement Learning](https://mlsanity.com/paper/2112.07057/) (2021)
- [Accelerating Reinforcement Learning with a Directional-Gaussian-Smoothing Evolution Strategy](https://mlsanity.com/paper/2002.09077/) (2020)
- [AdaDGS: An adaptive black-box optimization method with a nonlocal directional Gaussian smoothing gradient](https://mlsanity.com/paper/2011.02009/) (2020)

## Built on by (most cited first, 4 of 4)

- [Variational Digital Twins](https://mlsanity.com/paper/2507.01047/) (2025)
- [Multi-module based CVAE to predict HVCM faults in the SNS accelerator](https://mlsanity.com/paper/2304.10639/) (2023)
- [Multifidelity Surrogate Modeling of Depressurized Loss of Forced Cooling in High-temperature Gas Reactors](https://mlsanity.com/paper/2603.14143/) (2026)
- [MAEO: Multiobjective Animorphic Ensemble Optimization for Scalable Large-scale Engineering Applications](https://mlsanity.com/paper/2604.26973/) (2026)

## Abstract (arXiv)

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.