Learning coarse-step dynamics and internal mechanical response with graph networks

2026-09-24

AI Summary

This study addresses the challenge of inferring unobserved forces and mechanical responses from discrete trajectories at coarse time scales. To this end, it proposes the Newmark-beta-DGN framework, which integrates computational mechanics priors with graph neural networks. By leveraging operator-weighted virtual hinge coupling and semi-implicit state updates, the framework enables unsupervised inversion of internal forces and stiffness matrices, thereby overcoming the limitations of explicit simulators. The proposed approach is validated across beam structures, human motion, and protein dynamics tasks. Experimental results demonstrate that the framework achieves high-accuracy long-term predictions while faithfully recovering joint torques and underlying stiffness structures.

Abstract

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.

Problem

• coarse-step dynamics
• mechanical response inference
• unobserved forces
• trajectory-based learning
• long-horizon prediction

Innovation

• Graph Neural Networks
• Newmark-beta method
• Coarse-step dynamics
• Mechanical response inference
• Semi-implicit update