Momentum-Conserving Graph Neural Networks for Deformable Objects

2026-04-30 · Source: cs.LG updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Expert, extended

Summary

MomentumGNN is a novel graph neural network (GNN) architecture designed to accurately simulate the dynamic behavior of deformable objects while explicitly conserving linear and angular momentum. Unlike existing GNNs like MeshGraphNets, which output unconstrained nodal accelerations and often exhibit non-physical behaviors such as drift and unnatural spin, MomentumGNN predicts per-edge stretching and bending impulses. This design guarantees momentum preservation by construction. The network is trained in an unsupervised fashion using a physics-based loss function derived from a two-step implicit Euler formulation. MomentumGNN incorporates a layer-by-layer update scheme that sequentially refines vertex positions using momentum-conserving impulses, enhancing its representational capacity. Benchmarking against MeshGraphNets, MomentumGNN demonstrates superior performance in scenarios like falling cloth, cloth draping on a torus, and basket-shooting simulations, maintaining physical plausibility and stability with a modest computational overhead (12 fps vs. 14 fps for MeshGraphNets, significantly faster than implicit Euler's 2 fps).

Key takeaway

For Computer Vision Engineers developing physics-based simulations of deformable objects, MomentumGNN offers a robust solution to overcome the momentum conservation issues prevalent in existing GNN architectures. You should consider integrating its per-edge impulse prediction and layer-by-layer update scheme to achieve more physically accurate and stable simulations, especially for free motion and collision scenarios. This approach ensures realistic dynamics without significant computational overhead, improving the reliability of your models.

Key insights

MomentumGNN is a GNN that conserves momentum in deformable object simulations by predicting per-edge impulses.

Principles

• Decompose momentum changes into external non-conservative and internal momentum-conserving forces.
• Design impulses to affect only quantities invariant to translations and rotations.
• Momentum conservation does not imply energy conservation.

Method

MomentumGNN modifies MeshGraphNets by replacing per-vertex decoders with per-edge decoders that predict momentum-conserving stretching and bending impulses, followed by a layer-by-layer position update and a velocity projection step.

In practice

• Use per-edge decoders for momentum-conserving impulse prediction.
• Implement a layer-by-layer position update for enhanced fidelity.
• Apply velocity projection to ensure angular momentum conservation.

Topics

• Graph Neural Networks
• Deformable Object Simulation
• Momentum Conservation
• MeshGraphNets
• Physics-based Loss

Best for: Computer Vision Engineer, AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.