Convolutional neural networks are now seeing widespread use in a variety of fields, including image classification, facial and object recognition, medical imaging analysis, and many more. In addition, there are applications such as physics-informed simulators in which accurate forecasts in real time with a minimal lag are required. The present neural network designs include millions of parameters, which makes it difficult to install such complex models on devices that have limited memory. Compression techniques might be able to resolve these issues by decreasing the size of CNN models that are created by reducing the number of parameters that contribute to the complexity of the models. We propose a compressed tensor format of convolutional layer, a priori, before the training of the neural network. 3-way kernels or 2-way kernels in convolutional layers are replaced by one-way fiters. The overfitting phenomena will be reduced also. The time needed to make predictions or time required for training using the original Convolutional Neural Networks model would be cut significantly if there were fewer parameters to deal with. In this paper we present a method of a priori compressing convolutional neural networks for finite element (FE) predictions of physical data. Afterwards we validate our a priori compressed models on physical data from a FE model solving a 2D wave equation. We show that the proposed convolutinal compression technique achieves equivalent performance as classical convolutional layers with fewer trainable parameters and lower memory footprint.

翻译：卷积神经网络现已广泛应用于图像分类、人脸与物体识别、医学影像分析等多个领域。此外，在物理信息模拟器等应用中，需要以最小延迟实现实时精准预测。现有神经网络设计包含数百万个参数，这使得在内存有限的设备上部署此类复杂模型面临困难。压缩技术可通过减少导致模型复杂度的参数数量来缩小CNN模型规模，从而解决这些问题。我们提出了一种在神经网络训练之前对卷积层进行先验压缩的张量格式。将卷积层中的三阶核或二阶核替换为一阶滤波器。同时，过拟合现象也将得到缓解。若减少需处理的参数数量，使用原始卷积神经网络模型进行预测或训练所需的时间将显著缩短。本文提出了一种对卷积神经网络进行先验压缩的方法，用于对物理数据进行有限元预测。随后，我们基于求解二维波动方程的有限元模型生成的物理数据，验证了所提出的先验压缩模型。结果表明，所提出的卷积压缩技术在可训练参数更少、内存占用更低的条件下，实现了与经典卷积层等效的性能。