Related papers: Learning Relaxation for Multigrid
Employing equivariance in neural networks leads to greater parameter efficiency and improved generalization performance through the encoding of domain knowledge in the architecture; however, the majority of existing approaches require an a…
We present a method for parametrizing sub-grid processes in the Shallow Water equations. We define coarse variables and local spatial averages and use a feed-forward neural network to learn sub-grid fluxes. Our method results in a local…
This paper is concerned with the approximation of the solution of partial differential equations by means of artificial neural networks. Here a feedforward neural network is used to approximate the solution of the partial differential…
Large-scale deep neural networks (DNN) have been successfully used in a number of tasks from image recognition to natural language processing. They are trained using large training sets on large models, making them computationally and…
Compression of Neural Networks (NN) has become a highly studied topic in recent years. The main reason for this is the demand for industrial scale usage of NNs such as deploying them on mobile devices, storing them efficiently, transmitting…
A recent strategy to circumvent the exploding and vanishing gradient problem in RNNs, and to allow the stable propagation of signals over long time scales, is to constrain recurrent connectivity matrices to be orthogonal or unitary. This…
Graph Neural Networks (GNNs) are a powerful representational tool for solving problems on graph-structured inputs. In almost all cases so far, however, they have been applied to directly recovering a final solution from raw inputs, without…
The highly non-linear nature of deep neural networks causes them to be susceptible to adversarial examples and have unstable gradients which hinders interpretability. However, existing methods to solve these issues, such as adversarial…
Semi-supervised learning (SSL) over graph-structured data emerges in many network science applications. To efficiently manage learning over graphs, variants of graph neural networks (GNNs) have been developed recently. By succinctly…
Machine learning models differ in terms of accuracy, computational/memory complexity, training time, and adaptability among other characteristics. For example, neural networks (NNs) are well-known for their high accuracy due to the quality…
Algebraic multigrid (AMG) methods derive their optimal efficiency from the interplay between a relaxation process and a corresponding coarse grid correction. In many standard formulations, relaxation and coarse-graining are analyzed and…
Large sparse linear algebraic systems can be found in a variety of scientific and engineering fields, and many scientists strive to solve them in an efficient and robust manner. In this paper, we propose an interpretable neural solver, the…
Modern data analysis pipelines are becoming increasingly complex due to the presence of multi-view information sources. While graphs are effective in modeling complex relationships, in many scenarios a single graph is rarely sufficient to…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
Probabilistic graphical models are traditionally known for their successes in generative modeling. In this work, we advocate layered graphical models (LGMs) for probabilistic discriminative learning. To this end, we design LGMs in close…
Deep neural networks (DNNs) have been proven to have many redundancies. Hence, many efforts have been made to compress DNNs. However, the existing model compression methods treat all the input samples equally while ignoring the fact that…
We generalize a graph-based multiclass semi-supervised classification technique based on diffuse interface methods to multilayer graphs. Besides the treatment of various applications with an inherent multilayer structure, we present a very…
An important goal in neural map learning, which can conveniently be accomplished by magnification control, is to achieve information optimal coding in the sense of information theory. In the present contribution we consider the winner…
Recent advances in image data processing through machine learning and especially deep neural networks (DNNs) allow for new optimization and performance-enhancement schemes for radiation detectors and imaging hardware through data-endowed…
In recent years, deep neural networks (DNNs) have known an important rise in popularity. However, although they are state-of-the-art in many machine learning challenges, they still suffer from several limitations. For example, DNNs require…