Related papers: Pad\'e Neurons for Efficient Neural Models
Classical image denoising methods utilize the non-local self-similarity principle to effectively recover image content from noisy images. Current state-of-the-art methods use deep convolutional neural networks (CNNs) to effectively learn…
In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
The widespread use of Multi-layer perceptrons (MLPs) often relies on a fixed activation function (e.g., ReLU, Sigmoid, Tanh) for all nodes within the hidden layers. While effective in many scenarios, this uniformity may limit the networks…
Improving the efficiency of current neural networks and modeling them in biological neural systems have become popular research directions in recent years. Pulse-coupled neural network (PCNN) is a well applicated model for imitating the…
In this era of artificial intelligence, deep neural networks like Convolutional Neural Networks (CNNs) have emerged as front-runners, often surpassing human capabilities. These deep networks are often perceived as the panacea for all…
We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…
This work demonstrates how increasing the number of neurons in a network without increasing its number of non-zero parameters improves performance. We show that this gain corresponds with a decrease in interference between multiple features…
Machine learning and neural networks have advanced numerous research domains, but challenges such as large training data requirements and inconsistent model performance hinder their application in certain scientific problems. To overcome…
Convolutional layers are a fundamental component of most image-related models. These layers often implement by default a static padding policy (\eg zero padding), to control the scale of the internal representations, and to allow kernel…
Motivated by the celebrated discrete-time model of nervous activity outlined by McCulloch and Pitts in 1943, we propose a novel continuous-time model, the McCulloch-Pitts network (MPN), for sequence learning in spiking neural networks. Our…
Thanks to their ease of implementation, multilayer perceptrons (MLPs) have become ubiquitous in deep learning applications. The graph underlying an MLP is indeed multipartite, i.e. each layer of neurons only connects to neurons belonging to…
Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…
Artificial Neural Networks are computational network models inspired by signal processing in the brain. These models have dramatically improved the performance of many learning tasks, including speech and object recognition. However,…
This paper deals with the following important research question. Traditionally, the neural network employs non-linear activation functions concatenated with linear operators to approximate a given physical phenomenon. They "fill the space"…
The traditional limitations of neural networks in reliably generalizing beyond the convex hulls of their training data present a significant problem for computational physics, in which one often wishes to solve PDEs in regimes far beyond…
Neural Networks (NNs) are the method of choice for building learning algorithms. Their popularity stems from their empirical success on several challenging learning problems. However, most scholars agree that a convincing theoretical…
Physics-informed Neural Networks (PINNs) have recently emerged as a principled way to include prior physical knowledge in form of partial differential equations (PDEs) into neural networks. Although PINNs are generally viewed as mesh-free,…
Operational Neural Networks (ONNs) have recently been proposed as a special class of artificial neural networks for grid structured data. They enable heterogenous non-linear operations to generalize the widely adopted convolution-based…
Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…