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Graph Convolutional Neural Networks (GCNN) are becoming a preferred model for data processing on irregular domains, yet their analysis and principles of operation are rarely examined due to the black box nature of NNs. To this end, we…
Our proposed framework attempts to break the trade-off between performance and explainability by introducing an explainable-by-design convolutional neural network (CNN) based on the lateral inhibition mechanism. The ExplaiNet model consists…
Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of…
A neural network architecture is presented that exploits the multilevel properties of high-dimensional parameter-dependent partial differential equations, enabling an efficient approximation of parameter-to-solution maps, rivaling…
Owing to flexible architectures of deep convolutional neural networks (CNNs), CNNs are successfully used for image denoising. However, they suffer from the following drawbacks: (i) deep network architecture is very difficult to train. (ii)…
Deep learning techniques have become prominent in modern fault diagnosis for complex processes. In particular, convolutional neural networks (CNNs) have shown an appealing capacity to deal with multivariate time-series data by converting…
In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the…
Convolutional Neural Networks (CNN) have become de fact state-of-the-art for the main computer vision tasks. However, due to the complex underlying structure their decisions are hard to understand which limits their use in some context of…
Convolutional neural networks (CNNs) tend to become a standard approach to solve a wide array of computer vision problems. Besides important theoretical and practical advances in their design, their success is built on the existence of…
Supernovae Ia (SNe) can provide a unique window on the large scale structure (LSS) of the Universe at redshifts where few other observations are available, by solving the inversion problem (IP) consisting in reconstructing the LSS from its…
Convolution Neural Networks is one of the most powerful tools in the present era of science. There has been a lot of research done to improve their performance and robustness while their internal working was left unexplored to much extent.…
This paper introduces a generalization of Convolutional Neural Networks (CNNs) to graphs with irregular linkage structures, especially heterogeneous graphs with typed nodes and schemas. We propose a novel spatial convolution operation to…
Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…
This work presents and analyzes three convolutional neural network (CNN) models for efficient pixelwise classification of images. When using convolutional neural networks to classify single pixels in patches of a whole image, a lot of…
Motivated by the problem of learning with small sample sizes, this paper shows how to incorporate into support-vector machines (SVMs) those properties that have made convolutional neural networks (CNNs) successful. Particularly important is…
Training convolutional neural networks (CNNs) with back-propagation (BP) is time-consuming and resource-intensive particularly in view of the need to visit the dataset multiple times. In contrast, analytic learning attempts to obtain the…
Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some…
Low Dose CT Denoising research aims to reduce the risks of radiation exposure to patients. Recently researchers have used deep learning to denoise low dose CT images with promising results. However, approaches that use mean-squared-error…
Recent work in machine learning shows that deep neural networks can be used to solve a wide variety of inverse problems arising in computational imaging. We explore the central prevailing themes of this emerging area and present a taxonomy…
Deep convolutional neural networks (CNNs) have been widely applied for low-level vision over the past five years. According to nature of different applications, designing appropriate CNN architectures is developed. However, customized…