论文标题
QuadConv：基于正交的卷积，应用于非均匀PDE数据压缩
QuadConv: Quadrature-Based Convolutions with Applications to Non-Uniform PDE Data Compression
论文作者
论文摘要
我们为深度学习体系结构提供了一个新的卷积层，我们称之为Quadconv，这是通过正交持续卷积的近似值。我们的操作员是针对非均匀，基于网格的数据的明确开发的，并通过学习可以在任意位置进行采样的连续内核来实现这一目标。此外，我们的运营商的构建承认了我们详细介绍和构建的有效实施。作为对操作员的实验验证，我们考虑了从固定网格中压缩部分微分方程（PDE）模拟数据的任务。我们表明，QuadConv可以通过将QuadConv自动编码器（QCAE）与标准卷积自动装置（CAE）进行比较，可以使均匀网格数据上的标准离散卷积的性能匹配。此外，我们表明QCAE即使在不均匀的数据上也可以保持这种准确性。在这两种情况下，QuadConv还均优于替代性非结构化卷积方法，例如图形卷积。
We present a new convolution layer for deep learning architectures which we call QuadConv -- an approximation to continuous convolution via quadrature. Our operator is developed explicitly for use on non-uniform, mesh-based data, and accomplishes this by learning a continuous kernel that can be sampled at arbitrary locations. Moreover, the construction of our operator admits an efficient implementation which we detail and construct. As an experimental validation of our operator, we consider the task of compressing partial differential equation (PDE) simulation data from fixed meshes. We show that QuadConv can match the performance of standard discrete convolutions on uniform grid data by comparing a QuadConv autoencoder (QCAE) to a standard convolutional autoencoder (CAE). Further, we show that the QCAE can maintain this accuracy even on non-uniform data. In both cases, QuadConv also outperforms alternative unstructured convolution methods such as graph convolution.
