Related papers: The G\^ateaux-Hopfield Neural Network method

The combinations of machine learning with ab initio methods have attracted much attention for their potential to resolve the accuracy-efficiency dilemma and facilitate calculations for large-scale systems. Recently, equivariant message…

Heterogeneous graph neural networks (HeteGNNs) have demonstrated strong abilities to learn node representations by effectively extracting complex structural and semantic information in heterogeneous graphs. Most of the prevailing HeteGNNs…

Various phenomena in biology, physics, and engineering are modeled by differential equations. These differential equations including partial differential equations and ordinary differential equations can be converted and represented as…

Binary Neural Networks are a promising technique for implementing efficient deep models with reduced storage and computational requirements. The training of these is however, still a compute-intensive problem that grows drastically with the…

The first provably efficient algorithm for learning graph neural networks (GNNs) with one hidden layer for node information convolution is provided in this paper. Two types of GNNs are investigated, depending on whether labels are attached…

We develop a new edge detection algorithm that tackles two important issues in this long-standing vision problem: (1) holistic image training and prediction; and (2) multi-scale and multi-level feature learning. Our proposed method,…

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…

Heterogeneous Graphs (HGs) effectively model complex relationships in the real world through multi-type nodes and edges. In recent years, inspired by self-supervised learning (SSL), contrastive learning (CL)-based Heterogeneous Graphs…

We propose Alternating Phase-Field Fourier Neural Networks (APF-FNNs) as a unified and physics-based framework for topology optimization. The approach decouples the design problem by representing the state, adjoint, and topology fields with…

Recently, a Gaussian Process Regression - neural network (GPRNN) hybrid machine learning method was proposed, which is based on additive-kernel GPR in redundant coordinates constructed by rules [J. Phys. Chem. A 127 (2023) 7823]. The method…

Graph Neural Networks (GNNs) are widely used in graph representation learning. However, most GNN methods are designed for either homogeneous or heterogeneous graphs. In this paper, we propose a new model, Hop-Hop Relation-aware Graph Neural…

We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…

Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems.…

Graph Neural Networks (GNNs) are deep learning models that take graph data as inputs, and they are applied to various tasks such as traffic prediction and molecular property prediction. However, owing to the complexity of the GNNs, it has…

Graph Convolution Networks (GCNs) are widely considered state-of-the-art for collaborative filtering. Although several GCN-based methods have been proposed and achieved state-of-the-art performance in various tasks, they can be…

Solving large-scale linear programming (LP) problems is an important task in various areas such as communication networks, power systems, finance and logistics. Recently, two distinct approaches have emerged to expedite LP solving: (i)…

The recent increase in computational resources and data availability has led to a significant rise in the use of Machine Learning (ML) techniques for data analysis in physics. However, the application of ML methods to solve differential…

Edge detection remains a fundamental yet challenging task in computer vision, especially under varying illumination, noise, and complex scene conditions. This paper introduces a Hybrid Multi-Stage Learning Framework that integrates…

Optical Diffraction Neural Networks (DNNs), a subset of Optical Neural Networks (ONNs), show promise in mirroring the prowess of electronic networks. This study introduces the Hybrid Diffraction Neural Network (HDNN), a novel architecture…

Neural ordinary differential equations (NODEs) treat computation of intermediate feature vectors as trajectories of ordinary differential equation parameterized by a neural network. In this paper, we propose a novel model, delay…