A physics-constrained Gaussian Process regression framework is developed for predicting shocked material states along the Hugoniot curve using data from a small number of shockwave simulations. The proposed Gaussian process employs a probabilistic Taylor series expansion in conjunction with the Rankine-Hugoniot jump conditions between the various shocked material states to construct a thermodynamically consistent covariance function. This leads to the formulation of an optimization problem over a small number of interpretable hyperparameters and enables the identification of regime transitions, from a leading elastic wave to trailing plastic and phase transformation waves. This work is motivated by the need to investigate shock-driven material response for materials discovery and for offering mechanistic insights in regimes where experimental characterizations and simulations are costly. The proposed methodology relies on large-scale molecular dynamics which are an accurate but expensive computational alternative to experiments. Under these constraints, the proposed methodology establishes Hugoniot curves from a limited number of molecular dynamics simulations. We consider silicon carbide as a representative material and atomic-level simulations are performed using a reverse ballistic approach together with appropriate interatomic potentials. The framework reproduces the Hugoniot curve with satisfactory accuracy while also quantifying the uncertainty in the predictions using the Gaussian Process posterior.

翻译：本文提出了一种物理约束的高斯过程回归框架，用于利用少量冲击波模拟数据预测沿雨贡纽曲线的冲击材料状态。该高斯过程采用概率泰勒级数展开，并结合不同冲击材料状态之间的兰金-雨贡纽跳跃条件，构建了热力学一致性的协方差函数。由此构建了一个可解释超参数数量较少的优化问题，并能够识别从主导弹性波到后续塑性波及相变波的机制转变。本研究的动机源于探索冲击驱动材料响应的需求，以用于材料发现，并在实验表征和模拟成本高昂的机制中提供机理见解。所提出的方法依赖于大规模分子动力学模拟，这是一种精确但计算成本较高的实验替代方案。在此约束下，该方法通过有限数量的分子动力学模拟建立了雨贡纽曲线。我们以碳化硅作为代表性材料，采用反向弹道方法与适当的原子间势函数进行原子级模拟。该框架以令人满意的精度复现了雨贡纽曲线，同时利用高斯过程后验量化了预测的不确定性。