Related papers: Graph-Based Operator Learning from Limited Data on…

Graph neural networks (GNNs) learn representations from network data with naturally distributed architectures, rendering them well-suited candidates for decentralized learning. Oftentimes, this decentralized graph support changes with time…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

Data-efficient learning on graphs (GEL) is essential in real-world applications. Existing GEL methods focus on learning useful representations for nodes, edges, or entire graphs with ``small'' labeled data. But the problem of data-efficient…

Recently, graph neural networks (GNNs) have proved to be suitable in tasks on unstructured data. Particularly in tasks as community detection, node classification, and link prediction. However, most GNN models still operate with static…

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from…

Neural combinatorial optimization (NCO) solvers, implemented with graph neural networks (GNNs), have introduced new approaches for solving routing problems. Trained with reinforcement learning (RL), the state-of-the-art graph attention…

Regularization plays a pivotal role in integrating prior information into inverse problems. While many deep learning methods have been proposed to solve inverse problems, determining where to apply regularization remains a crucial…

Graph Neural Networks (GNNs) are routinely used in molecular physics, social sciences, and economics to model many-body interactions in graph-like systems. However, GNNs are inherently local and can suffer from information flow bottlenecks.…

Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…

Graph neural networks (GNN) have been successful in many fields, and derived various researches and applications in real industries. However, in some privacy sensitive scenarios (like finance, healthcare), training a GNN model centrally…

Spectral-based graph neural networks (SGNNs) have been attracting increasing attention in graph representation learning. However, existing SGNNs are limited in implementing graph filters with rigid transforms (e.g., graph Fourier or…

Dynamic graph neural networks (DGNNs) are increasingly pervasive in exploiting spatio-temporal patterns on dynamic graphs. However, existing works fail to generalize under distribution shifts, which are common in real-world scenarios. As…

Graph Neural Networks (GNNs) have emerged as a notorious alternative to address learning problems dealing with non-Euclidean datasets. However, although most works assume that the graph is perfectly known, the observed topology is prone to…

We propose a general architecture that combines the coefficient learning scheme with a residual operator layer for learning mappings between continuous functions in the 3D Euclidean space. Our proposed model is guaranteed to achieve…

Graphs model latent variable relationships in many real-world systems, and Message Passing Neural Networks (MPNNs) are widely used to learn such structures for downstream tasks. While edge-based MPNNs effectively capture local interactions,…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

Graph Convolutional Networks (GCNs) have shown to be effective in handling unordered data like point clouds and meshes. In this work we propose novel approaches for graph convolution, pooling and unpooling, inspired from finite differences…

Most compilers for machine learning (ML) frameworks need to solve many correlated optimization problems to generate efficient machine code. Current ML compilers rely on heuristics based algorithms to solve these optimization problems one at…

Graph neural networks (GNNs) have emerged as a powerful tool for learning software engineering tasks including code completion, bug finding, and program repair. They benefit from leveraging program structure like control flow graphs, but…

Graph Domain Adaptation (GDA) aims to bridge distribution shifts between domains by transferring knowledge from well-labeled source graphs to given unlabeled target graphs. One promising recent approach addresses graph transfer by…