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

Neural operators have been validated as promising deep surrogate models for solving partial differential equations (PDEs). Despite the critical role of boundary conditions in PDEs, however, only a limited number of neural operators robustly…

Graph neural networks (GNNs) have excelled in various graph learning tasks, particularly node classification. However, their performance is often hampered by noisy measurements in real-world graphs, which can corrupt critical patterns in…

Graph Neural Networks (GNN) rely on graph convolutions to learn features from network data. GNNs are stable to different types of perturbations of the underlying graph, a property that they inherit from graph filters. In this paper we…

The performance of an optimizer on large-scale deep learning models depends critically on fine-tuning the learning rate, often requiring an extensive grid search over base learning rates, schedules, and other hyperparameters. In this paper,…

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to…

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…

Graph Transformers (GTs) have demonstrated great effectiveness across various graph analytical tasks. However, the existing GTs focus on training and testing graph data originated from the same distribution, but fail to generalize under…

Neural operators learn to map initial conditions to the terminal solution of partial differential equations (PDEs), providing a surrogate for the full operator mapping. This enables rapid prediction across different input configurations.…

Graph domain adaptation (GDA) is a fundamental task in graph machine learning, with techniques like shift-robust graph neural networks (GNNs) and specialized training procedures to tackle the distribution shift problem. Although these…

Graph neural networks (GNNs) have achieved impressive performance when testing and training graph data come from identical distribution. However, existing GNNs lack out-of-distribution generalization abilities so that their performance…

Graph Neural Networks (GNNs) have shown impressive performance in graph representation learning, but they face challenges in capturing long-range dependencies due to their limited expressive power. To address this, Graph Transformers (GTs)…

Solving partial differential equations (PDEs) efficiently and accurately remains a cornerstone challenge in science and engineering, especially for problems involving complex geometries and limited labeled data. We introduce a Physics- and…

Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data. We propose a…

This paper develops a Deep Graph Operator Network (DeepGraphONet) framework that learns to approximate the dynamics of a complex system (e.g. the power grid or traffic) with an underlying sub-graph structure. We build our DeepGraphONet by…

Neural operators have emerged as powerful tools for learning mappings between function spaces, enabling efficient solutions to partial differential equations across varying inputs and domains. Despite the success, existing methods often…

Mission planning for a fleet of cooperative autonomous drones in applications that involve serving distributed target points, such as disaster response, environmental monitoring, and surveillance, is challenging, especially under partial…

Graph-level anomaly detection aims to identify anomalous graphs or subgraphs within graph datasets, playing a vital role in various fields such as fraud detection, review classification, and biochemistry. While Graph Neural Networks (GNNs)…

Graph Neural Networks (GNNs) are deep-learning architectures designed for graph-type data, where understanding relationships among individual observations is crucial. However, achieving promising GNN performance, especially on unseen data,…

Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…