[Paper Review] 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 Sciences3 citations

TL;DR

This paper proposes data-scarce surrogate modeling for shock-induced pore collapse using physics-informed dynamic mode decomposition (DW-DMD) and conditional generative adversarial networks (CcGAN), with shock pressure as a conditional input. The parametric DW-DMD achieves 0.3% relative error in reproduction and 1.3–5% in interpolation, outperforming CcGAN in accuracy and efficiency, especially under data scarcity.

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.

Motivation & Objective

• Address the challenge of high computational cost in simulating shock-induced pore collapse in porous materials.
• Develop efficient surrogate models for predicting pore collapse dynamics under varying shock pressures with limited training data.
• Overcome data scarcity and complex advection-dominated physics by integrating physical constraints into data-driven models.
• Compare the performance of dynamic mode decomposition (DW-DMD) and conditional generative adversarial networks (CcGAN) in predictive accuracy and training efficiency.
• Demonstrate robustness of the models in both interpolatory and extrapolatory cases for unseen shock pressures.

Proposed method

• Employ dynamic mode decomposition with windowing (DW-DMD) to extract spatiotemporal modes from high-fidelity simulation snapshots.
• Introduce parametric interpolation of shock pressure as a conditional input in DW-DMD to model pressure-dependent dynamics.
• Apply windowing to localize reduced-order models in time, improving dimensionality reduction and stability.
• Use U-Net-based conditional generative adversarial networks (CcGAN) with shock pressure as conditional input to generate pore collapse dynamics.
• Incorporate physics information as indicators or conditional inputs to guide model learning and improve generalization.
• Train models on sparse simulation data from ALE3D hydrocode at representative shock pressures, minimizing reliance on large datasets.

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.

Experimental results

Research questions

• RQ1 Can physics-informed dynamic mode decomposition with parametric interpolation achieve accurate and efficient prediction of pore collapse under data scarcity?
• RQ2 How does the predictive accuracy of DW-DMD compare to CcGAN in interpolatory and extrapolatory cases for shock pressures not in the training set?
• RQ3 What is the impact of increasing training data size on the performance of CcGAN and DW-DMD in capturing complex advection-dominated dynamics?
• RQ4 To what extent does windowing in DW-DMD enhance the stability and accuracy of reduced-order models in time-localized regions?
• RQ5 Can surrogate models trained on limited data generalize effectively to unseen shock pressures in both interpolation and extrapolation regimes?

Key findings

• The parametric DW-DMD model achieves a final-time relative error of approximately 0.3% in reproductive cases, demonstrating high accuracy with minimal data.
• In interpolatory cases, the DW-DMD model maintains a relative error range of 1.3% to 5% at unseen shock pressures, indicating strong generalization capability.
• For extrapolatory cases, the DW-DMD model shows a relative error of 8% to 9%, which is significantly lower than the 20% error observed in global CcGAN under the same conditions.
• Training a single DW-DMD model takes only about 30 seconds on CPU, while training a CcGAN model requires 8 hours on GPU, highlighting a major efficiency advantage for DW-DMD.
• Adding more training shock pressures improves CcGAN performance slightly, but the error remains consistently around 20%, indicating limited scalability under data scarcity.
• The integration of shock pressure as a conditional input in both models enhances their ability to generalize across pressure regimes, especially in the parametric DW-DMD formulation.

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