[论文解读] Data-scarce surrogate modeling of shock-induced pore collapse process

Siu Wun Cheung, Youngsoo Choi+2 more|arXiv (Cornell University)|May 31, 2023

Seismic Imaging and Inversion TechniquesEarth and Planetary Sciences被引用 3

一句话总结

本论文提出了一种针对冲击诱导孔隙坍塌的低数据量代理建模方法，结合物理信息动态模态分解（DW-DMD）与条件生成对抗网络（CcGAN），以冲击压力作为条件输入。参数化DW-DMD在再现性任务中实现0.3%的相对误差，在插值任务中误差为1.3%–5%，在准确性和效率方面均优于CcGAN，尤其在数据稀缺条件下表现更优。

ABSTRACT

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.

研究动机与目标

• 解决在多孔材料中模拟冲击诱导孔隙坍塌时计算成本过高的挑战。
• 在训练数据有限的条件下，开发高效代理模型以预测不同冲击压力下的孔隙坍塌动力学。
• 通过将物理约束整合到数据驱动模型中，克服数据稀缺与复杂对流主导的物理特性。
• 比较动态模态分解（DW-DMD）与条件生成对抗网络（CcGAN）在预测准确性和训练效率方面的表现。
• 验证模型在未见冲击压力下的插值与外推情形下的鲁棒性。

提出的方法

• 采用带窗函数的动态模态分解（DW-DMD）从高保真度仿真快照中提取时空模态。
• 在DW-DMD中引入冲击压力的参数化插值作为条件输入，以建模压力依赖的动力学行为。
• 应用窗函数以在时间上局部化降阶模型，提升降维效果与稳定性。
• 采用基于U-Net的条件生成对抗网络（CcGAN），以冲击压力作为条件输入，生成孔隙坍塌动力学。
• 将物理信息作为指示符或条件输入，引导模型学习并提升泛化能力。
• 在ALE3D流体动力学代码生成的代表性冲击压力下的稀疏仿真数据上训练模型，最大限度减少对大规模数据集的依赖。

Fig. 1: Schematic diagram for illustration of shock-induced pore collapse process. At first, the shock approaches and travels through the pore. The pore eventually deforms and develops into a high-temperature profile after the interaction with the shock.

实验结果

研究问题

• RQ1 在数据稀缺条件下，结合参数化插值的物理信息DW-DMD能否实现孔隙坍塌的高精度与高效率预测？
• RQ2 在训练集中未包含的冲击压力下，DW-DMD与CcGAN在插值与外推情形下的预测准确性如何比较？
• RQ3 增加训练数据量对CcGAN与DW-DMD捕捉复杂对流主导动力学性能的影响如何？
• RQ4 DW-DMD中的窗函数在时间局部区域中在多大程度上提升了降阶模型的稳定性和准确性？
• RQ5 在有限数据下训练的代理模型是否能在插值与外推两种情形下有效泛化至未见的冲击压力？

主要发现

• 参数化DW-DMD模型在再现性任务中最终时刻的相对误差约为0.3%，表明在极小数据量下仍具有极高精度。
• 在插值情形下，DW-DMD模型在未见冲击压力下的相对误差范围为1.3%至5%，表明其具备强大的泛化能力。
• 在外推情形下，DW-DMD模型的相对误差为8%至9%，显著低于全局CcGAN在相同条件下20%的误差水平。
• 单个DW-DMD模型的训练时间仅需约30秒（CPU），而CcGAN模型的训练需8小时（GPU），凸显DW-DMD在效率上的显著优势。
• 增加更多训练冲击压力可略微提升CcGAN的性能，但误差始终稳定在约20%，表明在数据稀缺条件下其可扩展性有限。
• 在两种模型中引入冲击压力作为条件输入，显著增强了其在不同压力区间间的泛化能力，尤其在参数化DW-DMD结构中表现更优。

Fig. 2: Schematics of non-intrusive surrogate models of the discrete dynamics of pore collapse. In the offline phase, the snapshot data from training shock pressures are used as the input and the output of the recurrence relation in the discrete dynamics, and dynamic mode decomposition or U-Net gene