提出MomentumGNN，让图神经网络模拟变形物体时自动守恒动量。
Momentum-Conserving Graph Neural Networks for Deformable Objects
- 通过预测边的拉伸和弯曲冲量来保证动量守恒
- 在多个场景中比基线方法更准确地追踪线动量和角动量
- 适合需要物理真实性模拟的机器人、动画等领域
图神经网络（GNN）已成为建模可变形材料动态行为的高效通用方法。尽管现有GNN能适应任意形状、网格拓扑和材料参数，但在预测线动量和角动量等关键物理量的时间演化上表现不佳。本文提出MomentumGNN——一种通过设计确保动量守恒的新架构。与传统输出无约束节点加速度的GNN不同，本模型预测每条边的拉伸和弯曲冲量，从而严格保证线动量与角动量守恒。采用基于物理的无监督损失进行训练，在多个动量起关键作用的典型场景中，该方法显著优于基线模型。
原文摘要 · Abstract (English)
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.
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