Momentum-Conserving Graph Neural Networks for Deformable Objects
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918472869478400 |
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| author | Wang, Jiahong Numerow, Logan Coros, Stelian Theobalt, Christian Babaei, Vahid Thomaszewski, Bernhard |
| author_facet | Wang, Jiahong Numerow, Logan Coros, Stelian Theobalt, Christian Babaei, Vahid Thomaszewski, Bernhard |
| contents | Graph neural networks (GNNs) have emerged as a versatile and efficient option for modeling the dynamic behavior of deformable materials. While GNNs generalize readily to arbitrary shapes, mesh topologies, and material parameters, existing architectures struggle to correctly predict the temporal evolution of key physical quantities such as linear and angular momentum. In this work, we propose MomentumGNN -- a novel architecture designed to accurately track momentum by construction. Unlike existing GNNs that output unconstrained nodal accelerations, our model predicts per-edge stretching and bending impulses which guarantee the preservation of linear and angular momentum. We train our network in an unsupervised fashion using a physics-based loss, and we show that our method outperforms baselines in a number of common scenarios where momentum plays a pivotal role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26097 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Momentum-Conserving Graph Neural Networks for Deformable Objects Wang, Jiahong Numerow, Logan Coros, Stelian Theobalt, Christian Babaei, Vahid Thomaszewski, Bernhard Machine Learning Artificial Intelligence Graphics Graph neural networks (GNNs) have emerged as a versatile and efficient option for modeling the dynamic behavior of deformable materials. While GNNs generalize readily to arbitrary shapes, mesh topologies, and material parameters, existing architectures struggle to correctly predict the temporal evolution of key physical quantities such as linear and angular momentum. In this work, we propose MomentumGNN -- a novel architecture designed to accurately track momentum by construction. Unlike existing GNNs that output unconstrained nodal accelerations, our model predicts per-edge stretching and bending impulses which guarantee the preservation of linear and angular momentum. We train our network in an unsupervised fashion using a physics-based loss, and we show that our method outperforms baselines in a number of common scenarios where momentum plays a pivotal role. |
| title | Momentum-Conserving Graph Neural Networks for Deformable Objects |
| topic | Machine Learning Artificial Intelligence Graphics |
| url | https://arxiv.org/abs/2604.26097 |