Equi-Euler GraphNet: An Equivariant, Temporal-Dynamics Informed Graph Neural Network for Dual Force and Trajectory Prediction in Multi-Body Systems

2025-04-18

AI Summary

Real-time, joint prediction of internal contact forces and global trajectories is critical for early fault detection and remaining useful life estimation in digital twins of multibody systems—but remains challenging due to stringent accuracy, speed, and generalization requirements. Method: We propose a physics-informed Euclidean-equivariant graph neural network (PI-Equivariant GNN). It employs an equivariant message-passing mechanism and Euler-integration-based temporal node updates to decouple ring–roller dynamics on mesh-free graphs; further enhanced by domain-specific cylindrical roller bearing topology and joint training on multiphysics simulation data. Results: The model achieves minimal cumulative rollout error over 1,000 steps under unseen operating conditions, matching the accuracy of conventional solvers while accelerating inference by 200×. To our knowledge, it is the first method enabling high-fidelity, real-time, joint reduced-order modeling of internal forces and trajectories for multibody digital twins.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Graph-based Machine Learning
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Predict internal forces and trajectories in multi-body systems
• Enable fault detection and predictive maintenance via load prediction
• Develop efficient reduced-order model for digital twin applications

Innovation

• Equivariant GNN for force and trajectory prediction
• Physics-informed graph neural network with Euler integration
• Mesh-free framework with component nodes and interaction edges