Related papers: Improving Long-Range Interactions in Graph Neural …

This work proposes a novel methodology for turbulence modeling in Large Eddy Simulation (LES) based on Graph Neural Networks (GNNs), which embeds the discrete rotational, reflectional and translational symmetries of the Navier-Stokes…

We present a Graph Neural Network (GNN) that accurately simulates a multidisperse suspension of interacting spherical particles. Our machine learning framework is built upon the recent work of Sanchez-Gonzalez et al. ICML, PMLR, 119,…

Despite the immense success of neural networks in modeling system dynamics from data, they often remain physics-agnostic black boxes. In the particular case of physical systems, they might consequently make physically inconsistent…

Gaussian processes (GPs) are powerful but computationally expensive machine learning models, requiring an estimate of the kernel covariance matrix for every prediction. In large and complex domains, such as graphs, sets, or images, the…

This work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochastic modeling of complex dynamical systems. We introduce new…

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

Graph neural networks (GNNs) are vulnerable to adversarial perturbations, including those that affect both node features and graph topology. This paper investigates GNNs derived from diverse neural flows, concentrating on their connection…

Graph Neural Networks (GNNs) achieve an impressive performance on structured graphs by recursively updating the representation vector of each node based on its neighbors, during which parameterized transformation matrices should be learned…

Graph neural networks are powerful architectures for structured datasets. However, current methods struggle to represent long-range dependencies. Scaling the depth or width of GNNs is insufficient to broaden receptive fields as larger GNNs…

Mesh-based graph neural networks (GNNs) have become effective surrogates for PDE simulations, yet their deep message passing incurs high cost and over-smoothing on large, long-range meshes; hierarchical GNNs shorten propagation paths but…

Infrared and visible image fusion aims to extract complementary features to synthesize a single fused image. Many methods employ convolutional neural networks (CNNs) to extract local features due to its translation invariance and locality.…

Graph neural networks (GNNs) have achieved breakthroughs in various real-world downstream tasks due to their powerful expressiveness. As the scale of real-world graphs has been continuously growing, a storage-based approach to GNN training…

While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This…

Recent studies have highlighted the limitations of message-passing based graph neural networks (GNNs), e.g., limited model expressiveness, over-smoothing, over-squashing, etc. To alleviate these issues, Graph Transformers (GTs) have been…

The burgeoning volume of graph data presents significant computational challenges in training graph neural networks (GNNs), critically impeding their efficiency in various applications. To tackle this challenge, graph condensation (GC) has…

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's…

Graph Neural Networks (GNNs) learn from graph-structured data by passing local messages between neighboring nodes along edges on certain topological layouts. Typically, these topological layouts in modern GNNs are deterministically computed…

We consider a Graph Neural Network (GNN) non-Markovian modeling framework to identify coarse-grained dynamical systems on graphs. Our main idea is to systematically determine the GNN architecture by inspecting how the leading term of the…

This paper focuses on representation learning for dynamic graphs with temporal interactions. A fundamental issue is that both the graph structure and the nodes own their own dynamics, and their blending induces intractable complexity in the…

Graph Neural Networks (GNNs) have achieved great success but are often considered to be challenged by varying levels of homophily in graphs. Recent \textit{empirical} studies have surprisingly shown that homophilic GNNs can perform well…