Related papers: Physics-constrained 3D Convolutional Neural Networ…
Homogenization is a technique commonly used in multiscale computational science and engineering for predicting collective response of heterogeneous materials and extracting effective mechanical properties. In this paper, a three-dimensional…
In this paper, using the Newman-Penrose formalism, we find the Maxwell equations in NUT space and after separation into angular and radial components solve them analytically. All the angular equations are solved in terms of Jaccobi…
In this paper we develop a neural network for the numerical simulation of time-dependent linear transport equations with diffusive scaling and uncertainties. The goal of the network is to resolve the computational challenges of…
Phase-field models have been widely used to investigate the phase transformation phenomena. However, it is difficult to solve the problems numerically due to their strong nonlinearities and higher-order terms. This work is devoted to…
Data sparsity is a common issue to train machine learning tools such as neural networks for engineering and scientific applications, where experiments and simulations are expensive. Recently physics-constrained neural networks (PCNNs) were…
Using a covariant embedding formalism, we find the effective field equations for the Electromagnetism that emerge on branes in the context of Dvali-Gabadadze-Porrati (DGP) braneworld scenario. Our treatment is essentially geometrical. We…
Traditional physics-informed neural networks (PINNs) do not always satisfy physics based constraints, especially when the constraints include differential operators. Rather, they minimize the constraint violations in a soft way. Strict…
A deep neural network (DNN) based power control method is proposed, which aims at solving the non-convex optimization problem of maximizing the sum rate of a multi-user interference channel. Towards this end, we first present PCNet, which…
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…
Research in neural models inspired by mammal's visual cortex has led to many spiking neural networks such as pulse-coupled neural networks (PCNNs). These models are oscillating, spatio-temporal models stimulated with images to produce…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
The interaction of condensed phase systems with external electric fields is crucial in myriad processes in nature and technology ranging from the field-directed motion of cells (galvanotaxis), to energy storage and conversion systems…
This paper presents Point Convolutional Neural Networks (PCNN): a novel framework for applying convolutional neural networks to point clouds. The framework consists of two operators: extension and restriction, mapping point cloud functions…
Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…
We employ Physics-Informed Neural Networks (PINNs) to solve the diffusion of heavy quarks within the expanding hot QCD medium generated in relativistic heavy-ion collisions. Due to the strong coupling between heavy quarks and the bulk…
Solving the Schr\"odinger equation is key to many quantum mechanical properties. However, an analytical solution is only tractable for single-electron systems. Recently, neural networks succeeded at modeling wave functions of many-electron…
In recent years, Convolutional Neural Networks (CNN) have proven to be efficient analysis tools for processing point clouds, e.g., for reconstruction, segmentation and classification. In this paper, we focus on the classification of edges…
Physics-informed neural networks have shown promise in solving partial differential equations (PDEs) by integrating physical constraints into neural network training, but their performance is sensitive to the sampling of points. Based on…
This article deals with approximating steady-state particle-resolved fluid flow around a fixed particle of interest under the influence of randomly distributed stationary particles in a dispersed multiphase setup using Convolutional Neural…
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…