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.

翻译：图神经网络（GNNs）已成为模拟可变形材料动态行为的一种通用且高效的选择。虽然GNNs能够轻松泛化至任意形状、网格拓扑和材料参数，但现有架构难以正确预测线动量与角动量等关键物理量的时间演化。在这项工作中，我们提出MomentumGNN——一种通过构造设计以精准追踪动量的新型架构。不同于输出无约束节点加速度的现有GNNs，我们的模型预测每条边的拉伸与弯曲冲量，从而保证线动量与角动量的守恒。我们采用基于物理的损失函数以无监督方式训练网络，并在动量起关键作用的多个常见场景中证明，我们的方法优于基线模型。