A physics-constrained Gaussian Process regression framework is developed for predicting shocked material states and their associated uncertainties along the Hugoniot curve using data from a small number of shockwave simulations. The proposed Gaussian process is constrained by 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. Shock Hugoniots are an important measure for understanding material behavior under extreme conditions, including for the development of equations of state and determining material properties such as the Hugoniot Elastic Limit, but they are costly to generate through large-scale molecular dynamics simulations or shock 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 Molecular Dynamics simulations are performed using a reverse ballistic approach. The framework reproduces the Hugoniot curve with satisfactory accuracy while also quantifying the uncertainty in the predictions using the Gaussian Process posterior. These uncertain Hugoniot predictions can then be used to calibrate equation of state models, estimate material properties, or inform future experimental and/or simulation campaigns.

翻译：针对仅使用少量冲击波模拟数据预测雨贡纽线上受冲击材料状态及其相关不确定性的问题，本文提出了一种基于物理约束的高斯过程回归框架。该高斯过程受不同受冲击材料状态间的Rankine-Hugoniot跳跃条件约束，构建了热力学一致的协方差函数。由此可建立关于少量可解释超参数的优化问题，并识别从领先弹性波到尾随塑性波及相变波的区域转变。冲击雨贡纽线是理解材料在极端条件下行为的重要度量，包括用于开发状态方程及确定雨贡纽弹性极限等材料属性，但通过大规模分子动力学模拟或冲击实验生成代价高昂。在此约束下，本方法仅需有限数量的分子动力学模拟即可建立雨贡纽曲线。以碳化硅为代表材料，采用反向弹道方法执行分子动力学模拟。该框架能以令人满意的精度复现雨贡纽曲线，同时利用高斯过程后验量化预测不确定性。这些含不确定性的雨贡纽预测可用于标定状态方程模型、估计材料属性，或为未来的实验/模拟方案提供依据。