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Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…

Neural networks (NNs) have gained significant attention across various engineering disciplines, particularly in design optimization, where they are used to build surrogate models for high-dimensional regression problems. Despite their power…

In this paper, we propose an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale structured convex optimization problems. Unlike the exact versions considered in literature,…

A sequential quadratic programming (SQP) algorithm is designed for nonsmooth optimization problems with upper-C^2 objective functions. Upper-C^2 functions are locally equivalent to difference-of-convex (DC) functions with smooth convex…

In recent years, graph neural networks (GNN) have achieved significant developments in a variety of graph analytical tasks. Nevertheless, GNN's superior performance will suffer from serious damage when the collected node features or…

We present a data-parallel software package for fitting Gaussian Approximation Potentials (GAPs) on multiple nodes using the ScaLAPACK library with MPI and OpenMP. Until now the maximum training set size for GAP models has been limited by…

Graph neural networks (GNNs) are widely used for learning node embeddings in graphs, typically adopting a message-passing scheme. This approach, however, leads to the neighbor explosion problem, with exponentially growing computational and…

This paper studies the nucleus decomposition problem, which has been shown to be useful in finding dense substructures in graphs. We present a novel parallel algorithm that is efficient both in theory and in practice. Our algorithm achieves…

Graph Neural Networks (GNNs) have become powerful tools for learning from graph-structured data, finding applications across diverse domains. However, as graph sizes and connectivity increase, standard GNN training methods face significant…

Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…

Overlapping community detection is a key problem in graph mining. Some research has considered applying graph convolutional networks (GCN) to tackle the problem. However, it is still challenging to incorporate deep graph convolutional…

Graphs are omnipresent and GNNs are a powerful family of neural networks for learning over graphs. Despite their popularity, scaling GNNs either by deepening or widening suffers from prevalent issues of unhealthy gradients,…

The Directed Layering Problem (DLP) solves a step of the widely used layer-based approach to automatically draw directed acyclic graphs. To cater for cyclic graphs, usually a preprocessing step is used that solves the Feedback Arc Set…

Real-world graphs, such as social networks, financial transactions, and recommendation systems, often demonstrate dynamic behavior. This phenomenon, known as graph stream, involves the dynamic changes of nodes and the emergence and…

Nonlinear Parametric Optimization Network (NLPOpt-Net) is an unsupervised learning architecture to solve constrained nonlinear programs (NLP). Given the structure of an NLP, it learns the parametric solution maps with guaranteed constraint…

The "exact subgraph" approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…

With the rapid growth of unstructured and semistructured data, parallelizing graph algorithms has become essential for efficiency. However, due to the inherent irregularity in computation, memory access patterns, and communication, graph…

Solutions to the Traveling Salesperson Problem (TSP) have practical applications to processes in transportation, logistics, and automation, yet must be computed with minimal delay to satisfy the real-time nature of the underlying tasks.…

In the last few years, graph convolutional networks (GCN) have become a popular research direction in the machine learning community to tackle NP-hard combinatorial optimization problems (COPs) defined on graphs. While the obtained results…

Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition…