EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutions

Huayu Deng, Xiangming Zhu, Yunbo Wang, Xiaokang Yang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:13327-13346, 2025.

Abstract

Graph neural networks have been a powerful tool for mesh-based physical simulation. To efficiently model large-scale systems, existing methods mainly employ hierarchical graph structures to capture multi-scale node relations. However, these graph hierarchies are typically manually designed and fixed, limiting their ability to adapt to the evolving dynamics of complex physical systems. We propose EvoMesh, a fully differentiable framework that jointly learns graph hierarchies and physical dynamics, adaptively guided by physical inputs. EvoMesh introduces anisotropic message passing, which enables direction-specific aggregation of dynamic features between nodes within each hierarchy, while simultaneously learning node selection probabilities for the next hierarchical level based on physical context. This design creates more flexible message shortcuts and enhances the model’s capacity to capture long-range dependencies. Extensive experiments on five benchmark physical simulation datasets show that EvoMesh outperforms recent fixed-hierarchy message passing networks by large margins. The project page is available at https://hbell99.github.io/evo-mesh/.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-deng25j, title = {{E}vo{M}esh: Adaptive Physical Simulation with Hierarchical Graph Evolutions}, author = {Deng, Huayu and Zhu, Xiangming and Wang, Yunbo and Yang, Xiaokang}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {13327--13346}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/deng25j/deng25j.pdf}, url = {https://proceedings.mlr.press/v267/deng25j.html}, abstract = {Graph neural networks have been a powerful tool for mesh-based physical simulation. To efficiently model large-scale systems, existing methods mainly employ hierarchical graph structures to capture multi-scale node relations. However, these graph hierarchies are typically manually designed and fixed, limiting their ability to adapt to the evolving dynamics of complex physical systems. We propose EvoMesh, a fully differentiable framework that jointly learns graph hierarchies and physical dynamics, adaptively guided by physical inputs. EvoMesh introduces anisotropic message passing, which enables direction-specific aggregation of dynamic features between nodes within each hierarchy, while simultaneously learning node selection probabilities for the next hierarchical level based on physical context. This design creates more flexible message shortcuts and enhances the model’s capacity to capture long-range dependencies. Extensive experiments on five benchmark physical simulation datasets show that EvoMesh outperforms recent fixed-hierarchy message passing networks by large margins. The project page is available at https://hbell99.github.io/evo-mesh/.} }
Endnote
%0 Conference Paper %T EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutions %A Huayu Deng %A Xiangming Zhu %A Yunbo Wang %A Xiaokang Yang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-deng25j %I PMLR %P 13327--13346 %U https://proceedings.mlr.press/v267/deng25j.html %V 267 %X Graph neural networks have been a powerful tool for mesh-based physical simulation. To efficiently model large-scale systems, existing methods mainly employ hierarchical graph structures to capture multi-scale node relations. However, these graph hierarchies are typically manually designed and fixed, limiting their ability to adapt to the evolving dynamics of complex physical systems. We propose EvoMesh, a fully differentiable framework that jointly learns graph hierarchies and physical dynamics, adaptively guided by physical inputs. EvoMesh introduces anisotropic message passing, which enables direction-specific aggregation of dynamic features between nodes within each hierarchy, while simultaneously learning node selection probabilities for the next hierarchical level based on physical context. This design creates more flexible message shortcuts and enhances the model’s capacity to capture long-range dependencies. Extensive experiments on five benchmark physical simulation datasets show that EvoMesh outperforms recent fixed-hierarchy message passing networks by large margins. The project page is available at https://hbell99.github.io/evo-mesh/.
APA
Deng, H., Zhu, X., Wang, Y. & Yang, X.. (2025). EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutions. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:13327-13346 Available from https://proceedings.mlr.press/v267/deng25j.html.

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