Related papers: Can Neural Networks learn Finite Elements?

Graph Neural Networks (GNNs), neural network architectures targeted to learning representations of graphs, have become a popular learning model for prediction tasks on nodes, graphs and configurations of points, with wide success in…

We derive upper bounds on the complexity of ReLU neural networks approximating the solution maps of parametric partial differential equations. In particular, without any knowledge of its concrete shape, we use the inherent…

Understanding how the visual cortex of the human brain really works is still an open problem for science today. A better understanding of natural intelligence could also benefit object-recognition algorithms based on convolutional neural…

Neural networks are a promising tool for characterizing intermediate-scale quantum devices from limited amounts of measurement data. A challenging problem in this area is to learn the action of an unknown quantum process on an ensemble of…

We report the possibility of using a simple neural network for effortless restoration of low-light images inspired by the retina model, which mimics the neurophysiological principles and dynamics of various types of optical neurons. The…

Defect detection is a basic and essential task in automatic parts production, especially for automotive engine precision parts. In this paper, we propose a new idea to construct a deep convolutional network combining related knowledge of…

A critical factor in adopting machine learning for time-sensitive financial tasks is computational speed, including model training and inference. This paper demonstrates that a broad class of such problems, especially those previously…

Adversarial attacks are usually expressed in terms of a gradient-based operation on the input data and model, this results in heavy computations every time an attack is generated. In this work, we solidify the idea of representing…

The success of Neural networks in providing miraculous results when applied to a wide variety of tasks is astonishing. Insight in the working can be obtained by studying the universal approximation property of neural networks. It is proved…

Partitioned neural network functions are used to approximate the solution of partial differential equations. The problem domain is partitioned into non-overlapping subdomains and the partitioned neural network functions are defined on the…

It turned out that the set of the fixed points is not necessarily the same as the set of the local minima of the energy functional. It depends on the diagonal elements of the connection matrix. The simple method which allows to cut off…

In this lecture I will present some models of neural networks that have been developed in the recent years. The aim is to construct neural networks which work as associative memories. Different attractors of the network will be identified…

Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with…

Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…

Recent advances in incorporating neural networks into particle filters provide the desired flexibility to apply particle filters in large-scale real-world applications. The dynamic and measurement models in this framework are learnable…

One of the major concerns for neural network training is that the non-convexity of the associated loss functions may cause bad landscape. The recent success of neural networks suggests that their loss landscape is not too bad, but what…

Today artificial neural networks are applied in various fields - engineering, data analysis, robotics. While they represent a successful tool for a variety of relevant applications, mathematically speaking they are still far from being…

We introduce a framework for reasoning about what meaning is captured by the neurons in a trained neural network. We provide a strategy for discovering meaning by training a second model (referred to as an observer model) to classify the…

Training neural networks involves solving large-scale non-convex optimization problems. This task has long been believed to be extremely difficult, with fear of local minima and other obstacles motivating a variety of schemes to improve…

The success of deep neural networks (DNNs) is attributable to three factors: increased compute capacity, more complex models, and more data. These factors, however, are not always present, especially for edge applications such as autonomous…