Equi-Euler GraphNet: An equivariant, temporal-dynamics informed graph neural network for dual force and trajectory prediction in multi-body systems

Accurate real-time modeling of multi-body dynamical systems is essential for enabling digital twin applications across industries. While many data-driven approaches aim to learn system dynamics, jointly predicting internal loads and system trajectories remains a key challenge. This dual prediction is particularly important for fault detection and predictive maintenance in continuously operating systems. Internal loads – such as contact forces – serve as early indicators of faults, reflecting changes due to wear, misalignment, or material degradation before these affect system motion. These forces also serve as inputs to physics-based degradation models (e.g., crack growth or wear propagation), enabling damage prediction and remaining useful life estimation, with the system state updated through predicted trajectories for continuous monitoring. In this research, we propose Equi-Euler GraphNet, a physics-informed graph neural network (GNN) framework that simultaneously predicts internal forces and global trajectories in multi-body dynamical systems. In this mesh-free framework, nodes represent discrete components of the multi-body system and edges encode their interactions. Equi-Euler GraphNet introduces two novel inductive biases: (1) an equivariant message-passing scheme interpreting edge messages as interaction forces that remain consistent under Euclidean transformations; and (2) a temporal-aware iterative node update mechanism based on Euler integration that updates node states to capture the influence of distant interactions over time. Tailored for cylindrical roller bearings, the framework introduces a structural bias that decouples the dynamics of the inner and outer rings from the constrained dynamics of the rolling elements. Trained on high fidelity multiphysics simulations and complementary lumped–parameter dynamics, Equi–Euler GraphNet operates consistently across fidelities and extrapolates well beyond the training distribution, accurately predicting internal loads and system trajectories under extrapolated rotational speeds, loads, and bearing configurations. It outperforms state-of-the-art GNN baselines focused solely on trajectory prediction, delivering stable rollouts over thousands of time steps with minimal error accumulation. Remarkably, it achieves up to a 200x speedup over conventional multiphysics solvers while maintaining comparable accuracy. Moreover, transfer learning experiments demonstrate that the surrogate can be adapted across different dynamics fidelities using only ground reaction force, thereby demonstrating a proof-of-concept pathway towards practical deployment using measurable signals. Finally, the Equi–Euler GraphNet surrogate serves as a proxy for healthy dynamics, supporting fault detection by scaling healthy variability across operating conditions. These results position Equi-Euler GraphNet as an efficient reduced-order model for digital twins, design, and maintenance tasks.