Related papers: Learning the Solution Operator of Boundary Value P…

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 introduce Graph Neural Processes (GNP), inspired by the recent work in conditional and latent neural processes. A Graph Neural Process is defined as a Conditional Neural Process that operates on arbitrary graph data. It takes features of…

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…

We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spaces to represent the (partial) unknowns. The framework…

By recursively summing node features over entire neighborhoods, spatial graph convolution operators have been heralded as key to the success of Graph Neural Networks (GNNs). Yet, despite the multiplication of GNN methods across tasks and…

The significant increase in world population and urbanisation has brought several important challenges, in particular regarding the sustainability, maintenance and planning of urban mobility. At the same time, the exponential increase of…

Graph Neural Networks (GNNs) have achieved notable success in learning from graph-structured data, owing to their ability to capture intricate dependencies and relationships between nodes. They excel in various applications, including…

Deep learning has recently emerged as a disruptive technology to solve challenging radio resource management problems in wireless networks. However, the neural network architectures adopted by existing works suffer from poor scalability,…

Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical…

Graph neural networks (GNNs) are often trained on individual datasets, requiring specialized models and significant hyperparameter tuning due to the unique structures and features of each dataset. This approach limits the scalability and…

Physics-informed neural operators offer a powerful framework for learning solution operators of partial differential equations (PDEs) by combining data and physics losses. However, these physics losses rely on derivatives. Computing these…

We study the generalization capabilities of Message Passing Neural Networks (MPNNs), a prevalent class of Graph Neural Networks (GNN). We derive generalization bounds specifically for MPNNs with normalized sum aggregation and mean…

In this paper, we introduce a generalized value iteration network (GVIN), which is an end-to-end neural network planning module. GVIN emulates the value iteration algorithm by using a novel graph convolution operator, which enables GVIN to…

Graph neural networks (GNNs) are designed to process data associated with graphs. They are finding an increasing range of applications; however, as with other modern machine learning techniques, their theoretical understanding is limited.…

Graph Neural Networks (GNN) have shown a strong potential to be integrated into commercial products for network control and management. Early works using GNN have demonstrated an unprecedented capability to learn from different network…

This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…

Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…

Earth Observation (EO) data analysis has been significantly revolutionized by deep learning (DL), with applications typically limited to grid-like data structures. Graph Neural Networks (GNNs) emerge as an important innovation, propelling…

In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…

Graph neural networks (GNNs) have become the standard learning architectures for graphs. GNNs have been applied to numerous domains ranging from quantum chemistry, recommender systems to knowledge graphs and natural language processing. A…