Physics-constrained Gaussian Process Regression Equation-of-State Model for Shock Simulations

We present the ongoing development of a data-driven equation of state (EOS) model and its integration with hydrodynamics simulations. The EOS model is based on a non-parametric, thermodynamically constrained Gaussian process regression (GPR) framework, which is trained with first-principles simulations and experimental Hugoniot data and capable of capturing both model and data uncertainties. The approach is demonstrated using aluminum and diamond data, where we integrate custom EOS tables with data generated from the GPR model to shock simulations using the HYADES hydrocode. Finally, we discuss our current effort in developing a multiphase formulation with uncertainty quantification, and its potential applications to inform future high compression experiments.