Equi-Euler GraphNet: An Equivariant, Temporal-Dynamics Informed Graph Neural Network for Dual Force and Trajectory Prediction in Multi-Body Systems
This work addresses the problem of real-time modeling for digital twin applications in industries like predictive maintenance, though it is incremental as it builds on existing GNN methods with specific inductive biases.
The paper tackled the challenge of jointly predicting internal forces and trajectories in multi-body dynamical systems, such as cylindrical roller bearings, by proposing Equi-Euler GraphNet, a physics-informed graph neural network. It achieved up to a 200x speedup over conventional solvers while maintaining accuracy and outperformed state-of-the-art GNNs in stable rollouts over thousands of time steps.
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 especially important for fault detection and predictive maintenance, where internal loads-such as contact forces-act as early indicators of faults, reflecting wear or misalignment before affecting motion. These forces also serve as inputs to degradation models (e.g., crack growth), enabling damage prediction and remaining useful life estimation. We propose Equi-Euler GraphNet, a physics-informed graph neural network (GNN) that simultaneously predicts internal forces and global trajectories in multi-body systems. In this mesh-free framework, nodes represent system components and edges encode interactions. Equi-Euler GraphNet introduces two inductive biases: (1) an equivariant message-passing scheme, interpreting edge messages as interaction forces consistent under Euclidean transformations; and (2) a temporal-aware iterative node update mechanism, based on Euler integration, to capture influence of distant interactions over time. Tailored for cylindrical roller bearings, it decouples ring dynamics from constrained motion of rolling elements. Trained on high-fidelity multiphysics simulations, Equi-Euler GraphNet generalizes beyond the training distribution, accurately predicting loads and trajectories under unseen speeds, loads, and configurations. It outperforms state-of-the-art GNNs focused on trajectory prediction, delivering stable rollouts over thousands of time steps with minimal error accumulation. Achieving up to a 200x speedup over conventional solvers while maintaining comparable accuracy, it serves as an efficient reduced-order model for digital twins, design, and maintenance.