Physics-constrained Gaussian Processes for Predicting Shockwave Hugoniot Curves

Silicon Carbide (SiC) possesses exceptional physical properties, such as low density, high stiffness and high hardness, which renders it a highly versatile engineering material for hypervelocity and armor protection applications. However, the characterization of SiC in response to shock is significantly challenging. From an experimental point of view, a the large number of variables such as sample confinement, impact angle, leads to a large number of experimental scenarios. This is coupled with extremely fast timescales, on the order of picoseconds, during which the material transitions from the unloaded to the shocked state, characterized by a shock wave front with a near-atomic thickness. To circumvent these difficulties, the research community has recently focused on computational modeling and, in particular, atomic-level simulations to provide insights into the underlying physics of the shock response of SiC. Despite yielding results in good agreement with experimental data, large-scale molecular dynamics (MD) simulations can be computationally daunting. In an effort to accelerate these computations, this work proposes a physics-informed Gaussian Process (GP) framework as an inexpensive predictive model for deriving the Hugoniot Elastic Limit (HEL) curves of SiC. The proposed approach leverages the Rankine-Hugoniot conditions between the different regions of shocked state, in conjunction with a Taylor expansion in which the associated thermodynamic quantities are assumed to be Gaussian variables. This yields a multi-output GP model which is consistent with the laws of thermodynamics and is capable of predicting plastic and phase transformation waves with quantifiable uncertainty. The GP is further parameterized to define a dependency between Us-Up Hugoniot curves and crystallographic orientation.