Related papers: Graph Neural PDE Solvers with Conservation and Sim…

Graph neural network (GNN) is effective to model graphs for distributed representations of nodes and an entire graph. Recently, research on the expressive power of GNN attracted growing attention. A highly-expressive GNN has the ability to…

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…

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…

We propose a novel Stochastic Differential Equation (SDE) framework to address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODEs) have shown…

The integration of Graph Neural Networks (GNNs) and Neural Ordinary and Partial Differential Equations has been extensively studied in recent years. GNN architectures powered by neural differential equations allow us to reason about their…

Heterogeneous graphs offer powerful data representations for traffic, given their ability to model the complex interaction effects among a varying number of traffic participants and the underlying road infrastructure. With the recent advent…

Graph Neural Networks (GNNs) have become a central tool for learning on graph-structured data, yet their applicability to real-world systems remains limited by key challenges such as scalability, temporality, directionality, data…

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…

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…

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…

Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics systems, learning molecular fingerprints, predicting protein interface, and classifying diseases demand a model…

Graph Neural Networks (GNNs) have attracted increasing attention in recent years and have achieved excellent performance in semi-supervised node classification tasks. The success of most GNNs relies on one fundamental assumption, i.e., the…

Graph neural networks (GNNs) are the predominant approach for graph-based machine learning. While neural networks have shown great performance at learning useful representations, they are often criticized for their limited high-level…

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…

Accurate yet efficient surrogate models are essential for large-scale simulations of partial differential equations (PDEs), particularly for uncertainty quantification (UQ) tasks that demand hundreds or thousands of evaluations. We develop…

Graphs are a powerful data structure to represent relational data and are widely used to describe complex real-world data structures. Probabilistic Graphical Models (PGMs) have been well-developed in the past years to mathematically model…

Graph Neural Networks (GNNs) have emerged as a prominent research topic in the field of machine learning. Existing GNN models are commonly categorized into two types: spectral GNNs, which are designed based on polynomial graph filters, and…

The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…

Graph neural networks (GNNs) have emerged as a powerful model to capture critical graph patterns. Instead of treating them as black boxes in an end-to-end fashion, attempts are arising to explain the model behavior. Existing works mainly…

This paper presents $\Psi$-GNN, a novel Graph Neural Network (GNN) approach for solving the ubiquitous Poisson PDE problems with mixed boundary conditions. By leveraging the Implicit Layer Theory, $\Psi$-GNN models an "infinitely" deep…