Spatiotemporal Learning on Cell-embedded Graphs

• URL: http://arxiv.org/abs/2409.18013v1
• Date: Thu, 26 Sep 2024 16:22:08 GMT
• Title: Spatiotemporal Learning on Cell-embedded Graphs
• Authors: Yuan Mi, Hao Sun,
• Abstract summary: We introduce a learnable cell attribution to the node-edge message passing process, which better captures the spatial dependency of regional features. Experiments on various PDE systems and one real-world dataset demonstrate that CeGNN achieves superior performance compared with other baseline models.
• Score: 6.8090864965073274
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Data-driven simulation of physical systems has recently kindled significant attention, where many neural models have been developed. In particular, mesh-based graph neural networks (GNNs) have demonstrated significant potential in predicting spatiotemporal dynamics across arbitrary geometric domains. However, the existing node-edge message passing mechanism in GNNs limits the model's representation learning ability. In this paper, we proposed a cell-embedded GNN model (aka CeGNN) to learn spatiotemporal dynamics with lifted performance. Specifically, we introduce a learnable cell attribution to the node-edge message passing process, which better captures the spatial dependency of regional features. Such a strategy essentially upgrades the local aggregation scheme from the first order (e.g., from edge to node) to a higher order (e.g., from volume to edge and then to node), which takes advantage of volumetric information in message passing. Meanwhile, a novel feature-enhanced block is designed to further improve the performance of CeGNN and relieve the over-smoothness problem, via treating the latent features as basis functions. The extensive experiments on various PDE systems and one real-world dataset demonstrate that CeGNN achieves superior performance compared with other baseline models, particularly reducing the prediction error with up to 1 orders of magnitude on several PDE systems.

Related papers

• PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems [31.006807854698376]
  We propose a new graph learning approach, namely, Physics-encoded Message Passing Graph Network (PhyMPGN) We incorporate a GNN into a numerical integrator to approximate the temporal marching of partialtemporal dynamics for a given PDE system. PhyMPGN is capable of accurately predicting various types of operatortemporal dynamics on coarse unstructured meshes.
  arXiv  Detail & Related papers  (2024-10-02T08:54:18Z)
• Re-Think and Re-Design Graph Neural Networks in Spaces of Continuous Graph Diffusion Functionals [7.6435511285856865]
  Graph neural networks (GNNs) are widely used in domains like social networks and biological systems. locality assumption of GNNs hampers their ability to capture long-range dependencies and global patterns in graphs. We propose a new inductive bias based on variational analysis, drawing inspiration from the Brachchronistoe problem.
  arXiv  Detail & Related papers  (2023-07-01T04:44:43Z)
• MGNNI: Multiscale Graph Neural Networks with Implicit Layers [53.75421430520501]
  implicit graph neural networks (GNNs) have been proposed to capture long-range dependencies in underlying graphs. We introduce and justify two weaknesses of implicit GNNs: the constrained expressiveness due to their limited effective range for capturing long-range dependencies, and their lack of ability to capture multiscale information on graphs at multiple resolutions. We propose a multiscale graph neural network with implicit layers (MGNNI) which is able to model multiscale structures on graphs and has an expanded effective range for capturing long-range dependencies.
  arXiv  Detail & Related papers  (2022-10-15T18:18:55Z)
• DPGNN: Dual-Perception Graph Neural Network for Representation Learning [21.432960458513826]
  Graph neural networks (GNNs) have drawn increasing attention in recent years and achieved remarkable performance in many graph-based tasks. Most existing GNNs are based on the message-passing paradigm to iteratively aggregate neighborhood information in a single topology space. We present a novel message-passing paradigm, based on the properties of multi-step message source, node-specific message output, and multi-space message interaction.
  arXiv  Detail & Related papers  (2021-10-15T05:47:26Z)
• Exploiting Spiking Dynamics with Spatial-temporal Feature Normalization in Graph Learning [9.88508686848173]
  Biological spiking neurons with intrinsic dynamics underlie the powerful representation and learning capabilities of the brain. Despite recent tremendous progress in spiking neural networks (SNNs) for handling Euclidean-space tasks, it still remains challenging to exploit SNNs in processing non-Euclidean-space data. Here we present a general spike-based modeling framework that enables the direct training of SNNs for graph learning.
  arXiv  Detail & Related papers  (2021-06-30T11:20:16Z)
• Overcoming Catastrophic Forgetting in Graph Neural Networks [50.900153089330175]
  Catastrophic forgetting refers to the tendency that a neural network "forgets" the previous learned knowledge upon learning new tasks. We propose a novel scheme dedicated to overcoming this problem and hence strengthen continual learning in graph neural networks (GNNs) At the heart of our approach is a generic module, termed as topology-aware weight preserving(TWP)
  arXiv  Detail & Related papers  (2020-12-10T22:30:25Z)
• On the spatial attention in Spatio-Temporal Graph Convolutional Networks for skeleton-based human action recognition [97.14064057840089]
  Graphal networks (GCNs) promising performance in skeleton-based human action recognition by modeling a sequence of skeletons as a graph. Most of the recently proposed G-temporal-based methods improve the performance by learning the graph structure at each layer of the network.
  arXiv  Detail & Related papers  (2020-11-07T19:03:04Z)
• A Unified View on Graph Neural Networks as Graph Signal Denoising [49.980783124401555]
  Graph Neural Networks (GNNs) have risen to prominence in learning representations for graph structured data. In this work, we establish mathematically that the aggregation processes in a group of representative GNN models can be regarded as solving a graph denoising problem. We instantiate a novel GNN model, ADA-UGNN, derived from UGNN, to handle graphs with adaptive smoothness across nodes.
  arXiv  Detail & Related papers  (2020-10-05T04:57:18Z)
• Graph Neural Networks for Motion Planning [108.51253840181677]
  We present two techniques, GNNs over dense fixed graphs for low-dimensional problems and sampling-based GNNs for high-dimensional problems. We examine the ability of a GNN to tackle planning problems such as identifying critical nodes or learning the sampling distribution in Rapidly-exploring Random Trees (RRT) Experiments with critical sampling, a pendulum and a six DoF robot arm show GNNs improve on traditional analytic methods as well as learning approaches using fully-connected or convolutional neural networks.
  arXiv  Detail & Related papers  (2020-06-11T08:19:06Z)
• Binarized Graph Neural Network [65.20589262811677]
  We develop a binarized graph neural network to learn the binary representations of the nodes with binary network parameters. Our proposed method can be seamlessly integrated into the existing GNN-based embedding approaches. Experiments indicate that the proposed binarized graph neural network, namely BGN, is orders of magnitude more efficient in terms of both time and space.
  arXiv  Detail & Related papers  (2020-04-19T09:43:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.