Understanding the mechanisms of shock-induced pore collapse is of great interest in various disciplines in sciences and engineering, including materials science, biological sciences, and geophysics. However, numerical modeling of the complex pore collapse processes can be costly. To this end, a strong need exists to develop surrogate models for generating economic predictions of pore collapse processes. In this work, we study the use of a data-driven reduced order model, namely dynamic mode decomposition, and a deep generative model, namely conditional generative adversarial networks, to resemble the numerical simulations of the pore collapse process at representative training shock pressures. Since the simulations are expensive, the training data are scarce, which makes training an accurate surrogate model challenging. To overcome the difficulties posed by the complex physics phenomena, we make several crucial treatments to the plain original form of the methods to increase the capability of approximating and predicting the dynamics. In particular, physics information is used as indicators or conditional inputs to guide the prediction. In realizing these methods, the training of each dynamic mode composition model takes only around 30 seconds on CPU. In contrast, training a generative adversarial network model takes 8 hours on GPU. Moreover, using dynamic mode decomposition, the final-time relative error is around 0.3% in the reproductive cases. We also demonstrate the predictive power of the methods at unseen testing shock pressures, where the error ranges from 1.3% to 5% in the interpolatory cases and 8% to 9% in extrapolatory cases.

翻译：理解冲击诱发孔洞坍塌的机理在材料科学、生物科学和地球物理学等科学与工程领域具有重要研究价值。然而，对复杂孔洞坍塌过程进行数值模拟往往代价高昂。因此，迫切需要开发替代模型以实现孔洞坍塌过程的经济性预测。本研究探讨了两种方法：基于数据驱动的降阶模型（动态模态分解）和深度生成模型（条件生成对抗网络），以模拟代表性训练冲击压力下的孔洞坍塌过程数值仿真。由于仿真成本高昂，训练数据极为稀缺，这给构建精确的替代模型带来了挑战。为克服复杂物理现象带来的困难，我们对方法的原始基础形式进行了若干关键改进，以增强其逼近和预测动力学行为的能力。具体而言，利用物理信息作为指示因子或条件输入来引导预测。在实现过程中，动态模态分解模型的训练在CPU上仅需约30秒，而生成对抗网络模型在GPU上训练需8小时。此外，采用动态模态分解时，再现案例的最终时间相对误差约为0.3%。我们同时验证了该方法在未观测测试冲击压力下的预测能力：插值案例的误差范围为1.3%-5%，外推案例的误差范围为8%-9%。