Related papers: Graph-Instructed Neural Networks for Sparse Grid-B…

Physics-informed neural networks (PINNs) have been applied to simulate multiphase flows, yet they are limited in modeling phase changes and sharp interfaces due to optimization conflicts in the strongly coupled Allen-Cahn, Cahn-Hilliard,…

We present a method to detect discontinuity curves, usually called faults, from a set of scattered data. The scheme first extracts from the data set a subset of points close to the faults. This selection is based on an indicator obtained by…

We present GERN, a novel scalable framework for training GNNs in node classification tasks, based on effective resistance, a standard tool in spectral graph theory. Our method progressively refines the GNN weights on a sequence of random…

We address the efficiency issue for the construction of a deep graph neural network (GNN). The approach exploits the idea of representing each input graph as a fixed point of a dynamical system (implemented through a recurrent neural…

In this paper, we present a discontinuity and cusp capturing physics-informed neural network (PINN) to solve Stokes equations with a piecewise-constant viscosity and singular force along an interface. We first reformulate the governing…

Graph neural networks (GNNs) have exhibited superior performance in various classification tasks on graph-structured data. However, they encounter the potential vulnerability from the link stealing attacks, which can infer the presence of a…

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…

This article examines the application of a popular measure of sparsity, Gini Index, on network graphs. A wide variety of network graphs happen to be sparse. But the index with which sparsity is commonly measured in network graphs is edge…

In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…

Graph neural networks (GNNs) have achieved great success in many scenarios with graph-structured data. However, in many real applications, there are three issues when applying GNNs: graphs are unknown, nodes have noisy features, and graphs…

Graph neural networks (GNNs) are typically applied to static graphs that are assumed to be known upfront. This static input structure is often informed purely by insight of the machine learning practitioner, and might not be optimal for the…

Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…

In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve discontinuous-coefficient elliptic interface problems whose solution is continuous but has discontinuous first derivatives on the interface. To find…

Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…

Identifying critical nodes and links in graphs is a crucial task. These nodes/links typically represent critical elements/communication links that play a key role in a system's performance. However, a majority of the methods available in…

Deep neural networks (DNNs) are vulnerable to adversarial examples and other data perturbations. Especially in safety critical applications of DNNs, it is therefore crucial to detect misclassified samples. The current state-of-the-art…

In this paper, we propose an end-to-end graph learning framework, namely Deep Iterative and Adaptive Learning for Graph Neural Networks (DIAL-GNN), for jointly learning the graph structure and graph embeddings simultaneously. We first cast…

This paper addresses the challenging problem of retrieval and matching of graph structured objects, and makes two key contributions. First, we demonstrate how Graph Neural Networks (GNN), which have emerged as an effective model for various…

The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many…

Graph neural networks (GNNs) are widely used for modelling graph-structured data in numerous applications. However, with their inherently finite aggregation layers, existing GNN models may not be able to effectively capture long-range…