论文标题
量身定制的卷积神经网络，用于使用非结构化空间离散化的计算物理数据的非线性流形学习
A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data using Unstructured Spatial Discretizations
论文作者
论文摘要
我们提出了一种基于深层卷积自动编码器的非线性流形学习技术，该技术适用于复杂几何形状中物理系统的模型订单。事实证明，卷积神经网络对于压缩速度缓慢的kolmogorov n宽度而产生的数据非常有利。但是，这些网络仅限于结构化网格的数据。通常需要非结构化的网格来对具有复杂几何形状的真实系统进行分析。我们的自定义图形卷积运算符基于可用的差分运算符的给定空间离散化有效地将深卷积自动编码器的应用空间扩展到具有任意复杂几何形状的系统，这些系统通常使用非结构化的网格进行离散。我们根据基础空间离散化的空间导数操作员提出了一组卷积操作员，这使该方法特别适合于偏微分方程的解决方案产生的数据。我们使用传热和流体力学的示例演示了该方法，并且比线性方法的准确性提高了数量级更好。
We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly advantageous for compressing data arising from systems demonstrating a slow-decaying Kolmogorov n-width. However, these networks are restricted to data on structured meshes. Unstructured meshes are often required for performing analyses of real systems with complex geometry. Our custom graph convolution operators based on the available differential operators for a given spatial discretization effectively extend the application space of deep convolutional autoencoders to systems with arbitrarily complex geometry that are typically discretized using unstructured meshes. We propose sets of convolution operators based on the spatial derivative operators for the underlying spatial discretization, making the method particularly well suited to data arising from the solution of partial differential equations. We demonstrate the method using examples from heat transfer and fluid mechanics and show better than an order of magnitude improvement in accuracy over linear methods.
