# Momentum-Conserving Graph Neural Networks for Deformable Objects

arXiv: https://arxiv.org/abs/2604.26097 · HTML: https://mlsanity.com/paper/2604.26097/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 50 references that are in the map.
- First posted on arXiv 28 Apr 2026.

## Builds on (most cited first, 25 of 25)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows](https://mlsanity.com/paper/1810.08217/) (2018)
- [TailorNet: Predicting Clothing in 3D as a Function of Human Pose, Shape and Garment Style](https://mlsanity.com/paper/2003.04583/) (2020)
- [CLOTH3D: Clothed 3D Humans](https://mlsanity.com/paper/1912.02792/) (2019)
- [Hamiltonian Graph Networks with ODE Integrators](https://mlsanity.com/paper/1909.12790/) (2019)
- [DeepWrinkles: Accurate and Realistic Clothing Modeling](https://mlsanity.com/paper/1808.03417/) (2018)
- [SNUG: Self-Supervised Neural Dynamic Garments](https://mlsanity.com/paper/2204.02219/) (2022)
- [PBNS: Physically Based Neural Simulator for Unsupervised Garment Pose Space Deformation](https://mlsanity.com/paper/2012.11310/) (2020)
- [Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics](https://mlsanity.com/paper/2304.14369/) (2023)
- [Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separately](https://mlsanity.com/paper/2201.10085/) (2022)
- [DeePSD: Automatic Deep Skinning And Pose Space Deformation For 3D Garment Animation](https://mlsanity.com/paper/2009.02715/) (2020)
- [DrapeNet: Garment Generation and Self-Supervised Draping](https://mlsanity.com/paper/2211.11277/) (2022)
- [CFDNet: a deep learning-based accelerator for fluid simulations](https://mlsanity.com/paper/2005.04485/) (2020)
- [Neural Cloth Simulation](https://mlsanity.com/paper/2212.11220/) (2022)
- [High-order Differentiable Autoencoder for Nonlinear Model Reduction](https://mlsanity.com/paper/2102.11026/) (2021)
- [Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics](https://mlsanity.com/paper/2210.06036/) (2022)
- [ContourCraft: Learning to Resolve Intersections in Neural Multi-Garment Simulations](https://mlsanity.com/paper/2405.09522/) (2024)
- [Data-Free Learning of Reduced-Order Kinematics](https://mlsanity.com/paper/2305.03846/) (2023)
- [A Deep Emulator for Secondary Motion of 3D Characters](https://mlsanity.com/paper/2103.01261/) (2021)
- [Neural Modes: Self-supervised Learning of Nonlinear Modal Subspaces](https://mlsanity.com/paper/2404.17620/) (2024)

## Abstract (arXiv)

Graph neural networks (GNNs) have emerged as a versatile and efficient option for modeling the dynamic behavior of deformable materials. While GNNs generalize readily to arbitrary shapes, mesh topologies, and material parameters, existing architectures struggle to correctly predict the temporal evolution of key physical quantities such as linear and angular momentum. In this work, we propose MomentumGNN -- a novel architecture designed to accurately track momentum by construction. Unlike existing GNNs that output unconstrained nodal accelerations, our model predicts per-edge stretching and bending impulses which guarantee the preservation of linear and angular momentum. We train our network in an unsupervised fashion using a physics-based loss, and we show that our method outperforms baselines in a number of common scenarios where momentum plays a pivotal role.