Related papers: Spatio-spectral graph neural operator for solving …

Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle…

Continuous graph neural networks (CGNNs) have garnered significant attention due to their ability to generalize existing discrete graph neural networks (GNNs) by introducing continuous dynamics. They typically draw inspiration from…

Current Graph Neural Networks (GNNs) suffer from the over-smoothing problem, which results in indistinguishable node representations and low model performance with more GNN layers. Many methods have been put forward to tackle this problem…

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a…

Spatio-temporal graph neural networks (ST-GNNs) have achieved notable success in structured domains such as road traffic and public transportation, where spatial entities can be naturally represented as fixed nodes. In contrast, many…

Operator eigenvalue problems play a critical role in various scientific fields and engineering applications, yet numerical methods are hindered by the curse of dimensionality. Recent deep learning methods provide an efficient approach to…

Graph Convolutional Networks (GCN) is a pioneering model for graph-based semi-supervised learning. However, GCN does not perform well on sparsely-labeled graphs. Its two-layer version cannot effectively propagate the label information to…

We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint…

This study introduces a two-scale Graph Neural Operator (GNO), namely, LatticeGraphNet (LGN), designed as a surrogate model for costly nonlinear finite-element simulations of three-dimensional latticed parts and structures. LGN has two…

Graph Neural Networks (GNNs) are a popular technique for modelling graph-structured data and computing node-level representations via aggregation of information from the neighborhood of each node. However, this aggregation implies an…

In recent years, Graph Neural Networks (GNNs) have been utilized for various applications ranging from drug discovery to network design and social networks. In many applications, it is impossible to observe some properties of the graph…

Many real-world problems can be represented as graph-based learning problems. In this paper, we propose a novel framework for learning spatial and attentional convolution neural networks on arbitrary graphs. Different from previous…

Self-supervised learning (SSL) is a powerful paradigm for learning from unlabeled time-series data. However, popular methods such as masked autoencoders (MAEs) rely on reconstructing inputs from a fixed, predetermined masking ratio. Instead…

Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.…

Stability of graph neural networks (GNNs) characterizes how GNNs react to graph perturbations and provides guarantees for architecture performance in noisy scenarios. This paper develops a self-regularized graph neural network (SR-GNN)…

The understanding of geographical reality is a process of data representation and pattern discovery. Former studies mainly adopted continuous-field models to represent spatial variables and to investigate the underlying spatial…

Combinatorial optimization (CO) problems are challenging as the computation time grows exponentially with the input. Graph Neural Networks (GNNs) show promise for researchers in solving CO problems. This study investigates the effectiveness…

Deep learning has consistently defied state-of-the-art techniques in many fields over the last decade. However, we are just beginning to understand the capabilities of neural learning in symbolic domains. Deep learning architectures that…

Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state configurations, which complicates the task of encompassing all…

Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…