论文标题
IAE-NET：离散不变学习的积分自动编码器
IAE-Net: Integral Autoencoders for Discretization-Invariant Learning
论文作者
论文摘要
离散的不变学习旨在在无限维函数空间中学习，其能力将功能的异质离散表示作为学习模型的输入和/或输出。本文提出了一个基于整体自动编码器（IAE-NET）的新型深度学习框架，用于离散不变学习。 IAE-NET的基本构建块由一个编码器和解码器组成，作为与数据驱动的内核的积分转换，以及编码器和解码器之间的完全连接的神经网络。该基本的构建块并行地在宽的多通道结构中应用，该结构反复组成，形成具有IAE-NET的Skip Connections的深度连接的神经网络。 IAE-NET接受了随机数据扩展的培训，该数据增加了具有异质结构的培训数据，以促进离散化不变学习的性能。提出的IAE-NET在预测数据科学中进行了各种应用，解决了科学计算中的前进和反向问题，以及信号/图像处理。与文献中的替代方案相比，IAE-NET在现有应用中实现了最先进的性能，并创建了广泛的新应用程序。
Discretization invariant learning aims at learning in the infinite-dimensional function spaces with the capacity to process heterogeneous discrete representations of functions as inputs and/or outputs of a learning model. This paper proposes a novel deep learning framework based on integral autoencoders (IAE-Net) for discretization invariant learning. The basic building block of IAE-Net consists of an encoder and a decoder as integral transforms with data-driven kernels, and a fully connected neural network between the encoder and decoder. This basic building block is applied in parallel in a wide multi-channel structure, which are repeatedly composed to form a deep and densely connected neural network with skip connections as IAE-Net. IAE-Net is trained with randomized data augmentation that generates training data with heterogeneous structures to facilitate the performance of discretization invariant learning. The proposed IAE-Net is tested with various applications in predictive data science, solving forward and inverse problems in scientific computing, and signal/image processing. Compared with alternatives in the literature, IAE-Net achieves state-of-the-art performance in existing applications and creates a wide range of new applications.
