  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.
