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:卷积神经网络现在被广泛应用于各种领域,包括图像分类、人脸和物体识别、医学图像分析等等。此外,还有需要在实时进行准确预测的物理模拟应用。目前的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安装这些复杂模型变得困难。压缩技术可以通过减少贡献于模型复杂性的参数数量来解决这些问题。我们提议在神经网络训练之前,先实现卷积层的压缩张量格式。将卷积层中的三维卷积核或二维卷积核替换为一维滤波器,有助于减少过拟合现象。如果参数较少,那么用原始卷积神经网络模型进行预测所需的时间,以及训练所需的时间都会显著减少。在本文中,我们提出了一种卷积神经网络的先验压缩方法,用于有限元预测物理数据。然后我们在二维波动方程的有限元模型上对我们的先验压缩模型进行了验证。我们证明了所提出的卷积压缩技术在可训练参数数量较少和内存占用较低的情况下,具有与传统卷积层相同的性能。