Related papers: Fourier Neural Networks as Function Approximators …

A tensor network is a type of decomposition used to express and approximate large arrays of data. A given data-set, quantum state or higher dimensional multi-linear map is factored and approximated by a composition of smaller multi-linear…

Neural networks allow Q-learning reinforcement learning agents such as deep Q-networks (DQN) to approximate complex mappings from state spaces to value functions. However, this also brings drawbacks when compared to other function…

If the training dataset is not very large, image recognition is usually implemented with the transfer learning methods. In these methods the features are extracted using a deep convolutional neural network, which was preliminarily trained…

Deep Convolutional Neural Networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful…

Neural networks are a convenient way to automatically fit functions that are too complex to be described by hand. The downside of this approach is that it leads to build a black-box without understanding what happened inside. Finding the…

This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of…

Physics-informed neural networks are developed to characterize the state of dynamical systems in a random environment. The neural network approximates the probability density function (pdf) or the characteristic function (chf) of the state…

Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a…

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and…

We show how the success of deep learning could depend not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of…

We address the problem of decomposing an image into albedo and shading. We propose the Fast Fourier Intrinsic Network, FFI-Net in short, that operates in the spectral domain, splitting the input into several spectral bands. Weights in…

Ultrasound (US) image segmentation is an active research area that requires real-time and highly accurate analysis in many scenarios. The detect-to-segment (DTS) frameworks have been recently proposed to balance accuracy and efficiency.…

We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…

Downward continuation is a critical task in potential field processing, including gravity and magnetic fields, which aims to transfer data from one observation surface to another that is closer to the source of the field. Its effectiveness…

Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions. Recently, the Fourier Neural Operator (FNO) has emerged as…

Despite broad interest in applying deep learning techniques to scientific discovery, learning interpretable formulas that accurately describe scientific data is very challenging because of the vast landscape of possible functions and the…

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these…

In this paper we introduce activation functions that move the entire computation of Convolutional Networks into the frequency domain, where they are actually Hadamard Networks. To achieve this result we employ the properties of Discrete…

Large-scale numerical simulations are capable of generating data up to terabytes or even petabytes. As a promising method of data reduction, super-resolution (SR) has been widely studied in the scientific visualization community. However,…