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

arXiv: https://arxiv.org/abs/2504.13768 · HTML: https://mlsanity.com/paper/2504.13768/

## Key facts

- Cited by 1 papers 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.

## Builds on (most cited first, 16 of 16)

- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Equivariant Graph Mechanics Networks with Constraints](https://mlsanity.com/paper/2203.06442/) (2022)
- [Learning Physical Dynamics with Subequivariant Graph Neural Networks](https://mlsanity.com/paper/2210.06876/) (2022)
- [Equivariant Graph Hierarchy-Based Neural Networks](https://mlsanity.com/paper/2202.10643/) (2022)
- [Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systems](https://mlsanity.com/paper/2211.05520/) (2022)
- [Graph Neural Network-based surrogate model for granular flows](https://mlsanity.com/paper/2305.05218/) (2023)
- [Data-driven simulation for general purpose multibody dynamics using deep neural networks](https://mlsanity.com/paper/1909.02391/) (2019)
- [Graph Neural Networks for Virtual Sensing in Complex Systems: Addressing Heterogeneous Temporal Dynamics](https://mlsanity.com/paper/2407.18691/) (2024)
- [Tunable Complexity Benchmarks for Evaluating Physics-Informed Neural Networks on Coupled Ordinary Differential Equations](https://mlsanity.com/paper/2210.07880/) (2022)

## Built on by (most cited first, 1 of 1)

- [PiGGO: Physics-Guided Learnable Graph Kalman Filters for Virtual Sensing of Nonlinear Dynamic Structures under Uncertainty](https://mlsanity.com/paper/2604.26593/) (2026)

## 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.