发表机构
EPFL（洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出Newmark-β-DGN图网络框架，结合半隐式更新与虚拟枢纽，在粗时间步长下预测物理系统运动并推断内部力学响应，无需力或本构监督。
AI 中文摘要
现代传感技术记录了物理系统的运动，但往往无法观测到控制该运动的力与力学响应。在粗时间尺度下，力学响应在观测之间演化且相互作用在系统中传播，此时从离散采样轨迹推断这些量尤为困难。本文提出了Newmark-β-DGN，一种基于图神经网络的框架，结合了计算力学启发的两种结构。首先，受Newmark-β方法启发的半隐式更新利用学习到的动量通量和矩阵值响应算子，在每个观测区间内推进状态。其次，一个算子加权的虚拟枢纽通过稀疏连接集提供系统级耦合。学习到的量因此决定预测运动，并保持可访问以进行力学分析。在可变形梁、人体运动和蛋白质动力学中，Newmark-β-DGN支持在显式学习模拟器失效的时间步长上进行长时程预测。在没有力、力矩或本构关系监督的情况下，从步行运动学推断出的力与独立推导的髋关节和膝关节力矩相吻合，而在梁上学习到的响应算子恢复了其有限元刚度切线的相对空间和方向结构。因此，Newmark-β-DGN将粗步预测与训练期间从未观测到的力学量的推断联系起来。
英文摘要
Modern sensing records the motion of physical systems, but often leaves the forces and mechanical response governing that motion unobserved. Inferring these quantities from discretely sampled trajectories is especially difficult at coarse time scales, when mechanical response evolves between observations and interactions propagate across the system. Here we introduce Newmark-\b{eta}-DGN, a graph neural network-based framework that combines two structures inspired by computational mechanics. First, a semi-implicit update inspired by the Newmark-\b{eta} method uses learned momentum fluxes and matrix-valued response operators to advance the state over each observed interval. Second, an operator-weighted virtual hub provides system-wide coupling through a sparse set of connections. The learned quantities thus determine the predicted motion and remain accessible for mechanical analysis. Across a deformable beam, human motion and protein dynamics, Newmark-\b{eta}-DGN supports long-horizon prediction at time steps for which explicit learned simulators deteriorate. Without force, moment or constitutive relation supervision, forces inferred from walking kinematics track independently derived hip and knee joint moments, while response operators learned on the beam recover the relative spatial and directional structure of its finite-element stiffness tangent. Newmark-\b{eta}-DGN therefore links coarse-step prediction to the inference of mechanical quantities that were never observed during training.
