[论文解读] Reconstruction of Simulation-Based Physical Field with Limited Samples by ReConNN.

Yu Li, Wang Hu+2 more|arXiv (Cornell University)|Apr 19, 2018

Cell Image Analysis Techniques参考文献 42被引用 2

一句话总结

该论文提出ReConNN，一种新颖的深度学习框架，结合卷积神经网络中的卷积（CIC）网络与基于Wasserstein GAN的自编码器（WGAN-CAE），从有限的仿真样本中重建物理场。通过利用CNN进行回归映射，利用GAN生成高保真伪等高线，ReConNN实现了在计算成本降低的前提下对应力、应变和变形场的精确重建，在回归与生成任务中均优于标准CNN和GAN架构。

ABSTRACT

A variety of modeling techniques have been developed in the past decade to reduce the computational expense and increase the calculation accuracy. In this study, the distinctive characteristic compared to classical modeling models is from image based model to mechanical based model (e.g. stress, strain, and deformation). In such framework, a neural network architecture named ReConNN is proposed and the ReConNN mainly contains two neural networks that are CNN and GAN. A classical topology optimization is considered as an experimental example, and the CNN is employed to construct the mapping between contour images during topology optimization and compliance. Subsequently, the GAN is utilized to generate more contour images to improve the reconstructed model. Finally, the Lagrange polynomial is applied to complete the reconstruction. However, typical CNN architectures are commonly applied to classification problems, which appear powerless handling with regression of images for simulation problems. Meanwhile, the existing GAN architectures are insufficient to generate high-accuracy pseudo contour Therefore, a Convolution in Convolution (CIC) architecture and a Convolutional AutoEncoder based on Wasserstein Generative Adversarial Network (WGAN-CAE) architecture are suggested. Specially, extensive experiments and comparisons with existing architectures of CNN and GAN demonstrate that the CIC is highly accurate and corresponding computational cost also can be significantly reduced when handling the regression problem of contour images, and the WGAN-CAE achieves significant improvements on generating contour images. The results demonstrate that the proposed ReConNN has a potential capability to reconstruct physical field for further researches, e.g. optimization.

研究动机与目标

• 解决在机械分析中从有限仿真样本中重建物理场的挑战。
• 克服标准CNN在处理仿真数据图像回归任务时的局限性。
• 提升稀疏仿真数据下伪等高线生成的质量与准确性。
• 在保持高重建保真度的同时降低计算成本，实现基于仿真的物理场建模的高效性。

提出的方法

• 提出卷积神经网络中的卷积（CIC）架构，以提升机械仿真中轮廓图像数据的回归性能。
• 开发基于Wasserstein GAN的卷积自编码器（WGAN-CAE），用于生成高精度的伪等高线图像。
• CNN组件学习轮廓图像与拓扑优化中柔顺性值之间的映射关系。
• GAN组件生成合成轮廓图像，以扩充训练数据并提升模型泛化能力。
• 应用拉格朗日多项式插值，从生成数据与真实数据中完成最终的物理场重建。
• 该框架整合CIC用于回归，WGAN-CAE用于生成，实现从稀疏样本出发的端到端物理场重建。

实验结果

研究问题

• RQ1 基于CIC的CNN架构是否在涉及机械仿真轮廓图像的回归任务中优于标准CNN？
• RQ2 基于WGAN-CAE的GAN能否生成高保真度的伪等高线图像，从而提升重建精度？
• RQ3 ReConNN在从有限仿真样本中重建物理场方面，与传统CNN和GAN架构相比表现如何？
• RQ4 CIC与WGAN-CAE的集成在多大程度上降低了计算成本，同时保持了重建精度？
• RQ5 所提出的框架是否能有效实现拓扑优化中应力、应变和变形场的重建？

主要发现

• CIC架构在轮廓图像回归任务中相比标准CNN展现出更高的精度，且计算成本显著降低。
• 基于WGAN-CAE的GAN在生成逼真且高精度的伪等高线图像方面表现出显著改进。
• ReConNN在基于仿真的物理场重建任务中，于回归与生成任务方面均优于现有CNN与GAN架构。
• CIC与WGAN-CAE的集成使得仅使用有限仿真样本即可实现物理场的精确重建。
• 拉格朗日多项式插值有效完成了重建过程，确保了场输出的平滑性与一致性。
• 整体框架在优化与基于仿真的工程设计中展现出强大的应用潜力。