Equi-Euler GraphNet: An Equivariant, Temporal-Dynamics Informed Graph Neural Network for Dual Force and Trajectory Prediction in Multi-Body Systems
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 16 of its 50 references that are in the map. First posted on arXiv 18 Apr 2025.
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16 of 50 references.
References · 16
- 2021E(n) Equivariant Graph Neural Networkscited by 965
- 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
- 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
- 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
- 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 509
- 2022Message Passing Neural PDE Solverscited by 386
- 2021Geometric Deep Learning on Molecular Representationscited by 113
- 2018Flexible Neural Representation for Physics Predictioncited by 91
- 2022Equivariant Graph Mechanics Networks with Constraintscited by 68
- 2022Learning Physical Dynamics with Subequivariant Graph Neural Networkscited by 39
- 2022Equivariant Graph Hierarchy-Based Neural Networkscited by 24
- 2022Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systemscited by 23
4 more
- 2023Graph Neural Network-based surrogate model for granular flowscited by 16
- 2019Data-driven simulation for general purpose multibody dynamics using deep neural networkscited by 7
- 2024Graph Neural Networks for Virtual Sensing in Complex Systems: Addressing Heterogeneous Temporal Dynamicscited by 7
- 2022Tunable Complexity Benchmarks for Evaluating Physics-Informed Neural Networks on Coupled Ordinary Differential Equationscited by 4
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Citing papers per year: 2026: 1.
1 paper.