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- Learning Mesh-Based Simulation with Graph Networks
Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation
- PIORF: Physics-Informed Ollivier-Ricci Flow for Long–Range. . .
This paper introduces an enhancement in mesh-based graph network simulators by addressing the over-squashing problem using a novel physics-informed rewiring approach
- L M -BASED SIMULATION WITH G N - OpenReview
Here we intro- duce MESHGRAPHNETS, a framework for learning mesh-based simulations us- ing graph neural networks Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation
- Learning Distributions of Complex Fluid Simulations with Diffusion . . .
The graph-based structure enables operations on unstructured meshes, which is critical for representing complex geometries with spatially localized high gradients, while latent-space diffusion modeling with a multi-scale GNN allows for efficient learning and inference of entire distributions of solutions
- Discovering Message Passing Hierarchies for Mesh-Based Physics Simulation
Graph neural networks have emerged as a powerful tool for large-scale mesh-based physics simulation Existing approaches primarily employ hierarchical, multi-scale message passing to capture long-range dependencies within the graph
- Bi-Stride Multi-Scale Graph Neural Network for Mesh-Based Physical . . .
On regular grids, the convolutional neural networks (CNNs) with a U-net structure can resolve this challenge by efficient stride, pooling, and upsampling operations Nonetheless, these tools are much less developed for graph neural networks (GNNs), especially when GNNs are employed for learning large-scale mesh-based physics
- MMGP: a Mesh Morphing Gaussian Process-based machine learning. . .
Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches
- EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutions
Abstract Graph neural networks have been a powerful tool for mesh-based physical simulation To efi-ciently model large-scale systems, existing meth-ods mainly employ hierarchical graph structures to capture multi-scale node relations However, these graph hierarchies are typically manually de-signed and fixed, limiting their ability to adapt to the evolving dynamics of complex physical sys
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