arxiv: 2604.26097 · v1 · submitted 2026-04-28 · 💻 cs.LG · cs.AI· cs.GR

Recognition: unknown

Momentum-Conserving Graph Neural Networks for Deformable Objects

Jiahong Wang , Logan Numerow , Stelian Coros , Christian Theobalt , Vahid Babaei , Bernhard Thomaszewski

Authors on Pith no claims yet

Pith reviewed 2026-05-07 16:19 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.GR

keywords graph neural networksdeformable objectsmomentum conservationphysics-based simulationunsupervised learningimpulse dynamicscloth simulation

0 comments

The pith

MomentumGNN predicts per-edge stretching and bending impulses to conserve linear and angular momentum by construction in deformable object simulations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces MomentumGNN, a graph neural network for simulating the dynamic behavior of deformable materials. Standard GNN approaches output nodal accelerations that can violate momentum conservation over time. This architecture instead predicts impulses for stretching and bending along each edge, which are formulated to automatically preserve both linear and angular momentum. Training occurs unsupervised through a physics-based loss that penalizes deviations from physical principles. The resulting model outperforms existing baselines in scenarios such as collisions and free-flight motion where momentum tracking is essential.

Core claim

MomentumGNN predicts per-edge stretching and bending impulses which guarantee the preservation of linear and angular momentum, in contrast to existing GNNs that output unconstrained nodal accelerations. The network is trained in an unsupervised fashion using a physics-based loss, and it outperforms baselines in a number of common scenarios where momentum plays a pivotal role.

What carries the argument

Per-edge stretching and bending impulses that enforce conservation of linear and angular momentum by construction instead of predicting unconstrained nodal accelerations.

If this is right

Simulations of deformable objects can maintain correct momentum without adding explicit post-hoc correction steps.
The architecture generalizes across arbitrary shapes, mesh connectivities, and material parameters while respecting conservation laws.
Unsupervised training with a physics loss produces usable models without requiring ground-truth acceleration data.
Performance gains appear precisely in the scenarios (collisions, free motion) where momentum errors accumulate most visibly in prior GNNs.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same per-edge impulse idea could be applied to other conservation principles such as energy or volume preservation in future GNN simulators.
Long-horizon rollouts in animation or robotics may become more stable because momentum drift is removed at the architecture level.
The method might combine with mesh-adaptation or contact-handling modules to handle more complex scenes without breaking conservation.

Load-bearing premise

That impulses defined only on stretching and bending per edge are sufficient to capture the full dynamics of arbitrary deformable objects and that the unsupervised physics loss can train the network to accurate predictions.

What would settle it

A test simulation in which the predicted impulses cause total linear or angular momentum to change across time steps, or in which the model produces visibly worse results than a baseline on a momentum-critical benchmark such as a free-flying cloth or colliding soft body.

Figures

Figures reproduced from arXiv: 2604.26097 by Bernhard Thomaszewski, Christian Theobalt, Jiahong Wang, Logan Numerow, Stelian Coros, Vahid Babaei.

**Figure 1.** Figure 1: Simulation of a basket-shooting scene, where accurate view at source ↗

**Figure 2.** Figure 2: We visualize MomentumGNN and denote latent edge and node features jointly by view at source ↗

**Figure 3.** Figure 3: Dihedral angle θ defined by two edge-adjacent triangles. Per-vertex gradients ∂θ ∂xi are shown in blue. use the dihedral angle formed by two edgeadjacent triangles. As indicated in the inset figure, the dihedral angle is determined by the four vertex positions of its two adjacent triangles. To obtain momentumconserving impulses that only change the dihedral angle (to first order), we endow each edge wi… view at source ↗

**Figure 4.** Figure 4: A 2D mass-spring chain. While smaller step sizes will alleviate this problem, its root cause is the fact that, while each message passing layer adjusts all impulse magnitudes, the direction of these impulses is kept constant across all steps. A natural way of increasing the space of momentum-conserving impulses is therefore to update the geometry with the current impulses after each message passing step.… view at source ↗

**Figure 5.** Figure 5: MomentumGNN conserves linear and angular momen view at source ↗

**Figure 8.** Figure 8: We drop a cloth onto a torus and simulate the cloth view at source ↗

**Figure 7.** Figure 7: We release the pinned-vertex constraints for the hanging view at source ↗

**Figure 9.** Figure 9: We simulate a basket-shooting scene, where a robotic hand throws a beach ball to the basket. Both MomentumGNN and Implicit view at source ↗

**Figure 10.** Figure 10: We simulate an Armadillo released from a nonlinear view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper builds momentum conservation into a GNN by outputting antisymmetric per-edge impulses rather than free nodal accelerations, which works by construction but the abstract supplies no numbers or test details to show it improves accuracy.

read the letter

The main contribution is the output change: the network predicts stretching and bending impulses on edges instead of accelerations at nodes. Because each impulse is equal and opposite, net force and net torque are zero for any prediction the network makes. This removes the need for the loss function to police momentum and avoids the drift that appears in standard GNN simulators for meshes and deformable bodies.

Referee Report

2 major / 2 minor

Summary. The paper introduces MomentumGNN, a graph neural network architecture for modeling the dynamics of deformable objects. Unlike standard GNNs that predict unconstrained nodal accelerations, MomentumGNN predicts per-edge stretching and bending impulses. This design choice is claimed to guarantee preservation of linear and angular momentum by construction. The network is trained in an unsupervised manner using a physics-based loss, and the authors report that it outperforms baselines in scenarios where momentum conservation is critical.

Significance. If the momentum-conservation property holds as described and the experimental results are robust, the work would represent a meaningful advance in physics-constrained machine learning for deformable-body simulation. The architectural guarantee of conservation (via antisymmetric per-edge impulses) addresses a known limitation of generic GNN simulators and could improve long-term stability without requiring explicit penalty terms. The unsupervised physics-based training is also a positive feature.

major comments (2)

[§3.2] §3.2 (Impulse-to-force mapping): The claim that per-edge impulses 'guarantee' linear and angular momentum preservation requires an explicit statement that the nodal force update is strictly antisymmetric (equal-and-opposite). Without this, the conservation property does not follow automatically from the impulse prediction.
[§4] §4 (Experimental validation): The manuscript states that the method 'outperforms baselines' in momentum-critical scenarios, yet no quantitative error metrics, ablation studies, or statistical significance tests are reported for the conservation property itself (e.g., measured drift in total linear/angular momentum over long rollouts). This leaves the central empirical claim unsupported.

minor comments (2)

[Abstract / §1] The abstract and introduction use the term 'impulses' without clarifying whether these are instantaneous or integrated over a time step; consistent notation with the time-step size Δt would improve clarity.
[Figure 2] Figure 2 (network diagram) would benefit from an explicit arrow or equation showing how the predicted edge impulses are converted into nodal accelerations while preserving antisymmetry.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and positive assessment of the potential impact of MomentumGNN. We address each major comment below, indicating the changes we will make to strengthen the manuscript.

read point-by-point responses

Referee: [§3.2] §3.2 (Impulse-to-force mapping): The claim that per-edge impulses 'guarantee' linear and angular momentum preservation requires an explicit statement that the nodal force update is strictly antisymmetric (equal-and-opposite). Without this, the conservation property does not follow automatically from the impulse prediction.

Authors: We agree that the manuscript would benefit from an explicit statement on antisymmetry. In the revised version of Section 3.2 we will add a short derivation showing that the nodal force update is defined as the negative of the impulse applied to the opposite node (i.e., F_i = -F_j for each edge), which directly implies equal-and-opposite forces and therefore exact conservation of linear and angular momentum by construction. This clarification will be placed immediately after the impulse-prediction equations. revision: yes
Referee: [§4] §4 (Experimental validation): The manuscript states that the method 'outperforms baselines' in momentum-critical scenarios, yet no quantitative error metrics, ablation studies, or statistical significance tests are reported for the conservation property itself (e.g., measured drift in total linear/angular momentum over long rollouts). This leaves the central empirical claim unsupported.

Authors: The referee correctly notes that the current experiments emphasize qualitative long-term stability and visual comparisons rather than direct quantitative tracking of momentum drift. While the existing results demonstrate improved behavior in momentum-sensitive regimes, we acknowledge that explicit drift metrics would provide stronger support. In the revision we will add quantitative plots of linear and angular momentum drift over extended rollouts (with error bars from multiple random seeds), together with an ablation isolating the antisymmetric impulse mechanism. These additions will be included in Section 4 and the supplementary material. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's core claim is that MomentumGNN predicts per-edge stretching and bending impulses whose equal-and-opposite application guarantees linear and angular momentum preservation by construction. This follows directly from the architectural definition of symmetric impulse application to nodes and does not reduce any learned prediction or first-principles derivation to its own inputs. No fitted parameters are relabeled as predictions, no load-bearing self-citations justify uniqueness theorems, and no ansatz is smuggled via prior work. The unsupervised physics-based loss and performance comparisons operate on top of this architectural guarantee rather than defining it. The derivation chain is therefore self-contained and non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated assumption that edge impulses can represent all relevant forces in deformable dynamics.

pith-pipeline@v0.9.0 · 5440 in / 1040 out tokens · 54135 ms · 2026-05-07T16:19:29.380053+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

49 extracted references

[1]

Inverse design for fluid-structure interactions using graph network simulators

Kelsey Allen, Tatiana Lopez-Guevara, Kimberly L Stachen- feld, Alvaro Sanchez Gonzalez, Peter Battaglia, Jessica B Hamrick, and Tobias Pfaff. Inverse design for fluid-structure interactions using graph network simulators. InAdvances in Neural Information Processing Systems, pages 13759– 13774. Curran Associates, Inc., 2022. 2

2022
[2]

Cloth3d: clothed 3d humans

Hugo Bertiche, Meysam Madadi, and Sergio Escalera. Cloth3d: clothed 3d humans. InEuropean Conference on Computer Vision, pages 344–359. Springer, 2020. 2

2020
[3]

Pbns: physically based neural simulation for unsupervised garment pose space deformation.ACM Trans

Hugo Bertiche, Meysam Madadi, and Sergio Escalera. Pbns: physically based neural simulation for unsupervised garment pose space deformation.ACM Trans. Graph., 40(6), 2021. 2

2021
[4]

Deepsd: Automatic deep skinning and pose space deformation for 3d garment animation

Hugo Bertiche, Meysam Madadi, Emilio Tylson, and Sergio Escalera. Deepsd: Automatic deep skinning and pose space deformation for 3d garment animation. InProceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 5471–5480, 2021. 2

2021
[5]

Neu- ral cloth simulation.ACM Trans

Hugo Bertiche, Meysam Madadi, and Sergio Escalera. Neu- ral cloth simulation.ACM Trans. Graph., 41(6), 2022. 2, 6

2022
[6]

Projective dynamics: fusing constraint projections for fast simulation.ACM Trans

Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Ka- van, and Mark Pauly. Projective dynamics: fusing constraint projections for fast simulation.ACM Trans. Graph., 33(4),
[7]

Brown, Matthew Overby, Zahra Forootaninia, and Rahul Narain

George E. Brown, Matthew Overby, Zahra Forootaninia, and Rahul Narain. Accurate dissipative forces in optimization integrators.ACM Trans. Graph., 37(6), 2018. 4

2018
[8]

A procedural approach to au- thoring solid models.ACM Trans

Barbara Cutler, Julie Dorsey, Leonard McMillan, Matthias M¨uller, and Robert Jagnow. A procedural approach to au- thoring solid models.ACM Trans. Graph., 21(3):302–311,
[9]

DrapeNet: Garment Generation and Self- Supervised Draping

Luca De Luigi, Ren Li, Benoit Guillard, Mathieu Salzmann, and Pascal Fua. DrapeNet: Garment Generation and Self- Supervised Draping. InProceedings of the IEEE/CVF Con- ference on Computer Vision and Pattern Recognition, 2023. 2

2023
[10]

Lawson Fulton, Vismay Modi, David Duvenaud, David I. W. Levin, and Alec Jacobson. Latent-space dynamics for re- duced deformable simulation.Computer Graphics Forum,
[11]

T. F. Gast and C. Schroeder. Optimization integrator for large time steps. InProceedings of the ACM SIG- GRAPH/Eurographics Symposium on Computer Animation, page 31–40, Goslar, DEU, 2015. Eurographics Association. 4

2015
[12]

Mesh- based gnn surrogates for time-independent pdes.Scientific reports, 14(1):3394, 2024

Rini Jasmine Gladstone, Helia Rahmani, Vishvas Suryaku- mar, Hadi Meidani, Marta D’Elia, and Ahmad Zareei. Mesh- based gnn surrogates for time-independent pdes.Scientific reports, 14(1):3394, 2024. 2

2024
[13]

Hamiltonian neural networks

Samuel Greydanus, Misko Dzamba, and Jason Yosinski. Hamiltonian neural networks. InAdvances in Neural Infor- mation Processing Systems. Curran Associates, Inc., 2019. 2

2019
[14]

Hood: Hierarchical graphs for general- ized modelling of clothing dynamics.Computer Vision and Pattern Recognition (CVPR), 2023

Artur Grigorev, Bernhard Thomaszewski, Michael J Black, and Otmar Hilliges. Hood: Hierarchical graphs for general- ized modelling of clothing dynamics.Computer Vision and Pattern Recognition (CVPR), 2023. 1, 2, 3, 6

2023
[15]

Contourcraft: Learn- ing to resolve intersections in neural multi-garment simula- tions

Artur Grigorev, Giorgio Becherini, Michael Black, Otmar Hilliges, and Bernhard Thomaszewski. Contourcraft: Learn- ing to resolve intersections in neural multi-garment simula- tions. InACM SIGGRAPH 2024 Conference Papers, New York, NY , USA, 2024. Association for Computing Machin- ery. 1, 2

2024
[16]

Hirani, Mathieu Desbrun, and Peter Schr¨oder

Eitan Grinspun, Anil N. Hirani, Mathieu Desbrun, and Peter Schr¨oder. Discrete shells. InProceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Anima- tion, page 62–67, Goslar, DEU, 2003. Eurographics Associ- ation. 5

2003
[17]

Neuroanimator: Fast neural network emulation and con- trol of physics-based models

Radek Grzeszczuk, Demetri Terzopoulos, and Geoffrey Hin- ton. Neuroanimator: Fast neural network emulation and con- trol of physics-based models. InProceedings of the 25th an- nual conference on Computer graphics and interactive tech- niques, pages 9–20, 1998. 2

1998
[18]

Graph neural net- works for the prediction of aircraft surface pressure distri- butions.Aerospace Science and Technology, 137:108268,

Derrick Hines and Philipp Bekemeyer. Graph neural net- works for the prediction of aircraft surface pressure distri- butions.Aerospace Science and Technology, 137:108268,
[19]

Deepwrin- kles: Accurate and realistic clothing modeling

Zorah Lahner, Daniel Cremers, and Tony Tung. Deepwrin- kles: Accurate and realistic clothing modeling. InPro- ceedings of the European Conference on Computer Vision (ECCV), 2018. 2

2018
[20]

Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, and Danny M. Kaufman. Incremental potential contact: intersection-and inversion-free, large-deformation dynamics. ACM Trans. Graph., 39(4), 2020. 1

2020
[21]

Meshgraphnetrp: Improving generalization of gnn-based cloth simulation

Emmanuel Ian Libao, Myeongjin Lee, Sumin Kim, and Sung-Hee Lee. Meshgraphnetrp: Improving generalization of gnn-based cloth simulation. InProceedings of the 16th ACM SIGGRAPH Conference on Motion, Interaction and Games, New York, NY , USA, 2023. Association for Com- puting Machinery. 1, 2

2023
[22]

Nnwarp: Neural network- based nonlinear deformation.IEEE Transactions on Visu- alization and Computer Graphics, 26(4):1745–1759, 2020

Ran Luo, Tianjia Shao, Huamin Wang, Weiwei Xu, Xiang Chen, Kun Zhou, and Yin Yang. Nnwarp: Neural network- based nonlinear deformation.IEEE Transactions on Visu- alization and Computer Graphics, 26(4):1745–1759, 2020. 2

2020
[23]

Deep la- grangian networks: Using physics as model prior for deep learning

Michael Lutter, Christian Ritter, and Jan Peters. Deep la- grangian networks: Using physics as model prior for deep learning. InInternational Conference on Learning Repre- sentations (ICLR), 2019. 2

2019
[24]

Learning neural constitutive laws from motion observations for generalizable pde dynamics

Pingchuan Ma, Peter Yichen Chen, Bolei Deng, Joshua B Tenenbaum, Tao Du, Chuang Gan, and Wojciech Matusik. Learning neural constitutive laws from motion observations for generalizable pde dynamics. InInternational Conference on Machine Learning, pages 23279–23300. PMLR, 2023. 8

2023
[25]

Xpbd: position-based simulation of compliant constrained dynamics

Miles Macklin, Matthias M ¨uller, and Nuttapong Chentanez. Xpbd: position-based simulation of compliant constrained dynamics. InProceedings of the 9th International Confer- ence on Motion in Games, page 49–54, New York, NY , USA,
[26]

Association for Computing Machinery. 1
[27]

Example-based elastic materials

Sebastian Martin, Bernhard Thomaszewski, Eitan Grinspun, and Markus Gross. Example-based elastic materials. InACM SIGGRAPH 2011 Papers, New York, NY , USA, 2011. Asso- ciation for Computing Machinery. 3

2011
[28]

Cfdnet: a deep learning- based accelerator for fluid simulations

Octavi Obiols-Sales, Abhinav Vishnu, Nicholas Malaya, and Aparna Chandramowliswharan. Cfdnet: a deep learning- based accelerator for fluid simulations. InProceedings of the 34th ACM International Conference on Supercomputing, New York, NY , USA, 2020. Association for Computing Ma- chinery. 2

2020
[29]

Pytorch: An imperative style, high-performance deep learning library

Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zem- ing Lin, Natalia Gimelshein, Luca Antiga, Alban Desmai- son, Andreas Kopf, Edward Yang, Zachary DeVito, Mar- tin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high...

2019
[30]

Tailornet: Predicting clothing in 3d as a function of human pose, shape and garment style

Chaitanya Patel, Zhouyingcheng Liao, and Gerard Pons- Moll. Tailornet: Predicting clothing in 3d as a function of human pose, shape and garment style. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2020. 2

2020
[31]

Battaglia

Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, and Peter W. Battaglia. Learning mesh-based simulation with graph networks. InInternational Conference on Learn- ing Representations (ICLR), 2021. 1, 2, 3

2021
[32]

Guaranteed conservation of momentum for learning particle-based fluid dynamics

Lukas Prantl, Benjamin Ummenhofer, Vladlen Koltun, and Nils Thuerey. Guaranteed conservation of momentum for learning particle-based fluid dynamics. InProceedings of the 36th International Conference on Neural Information Pro- cessing Systems, Red Hook, NY , USA, 2022. Curran Asso- ciates Inc. 2

2022
[33]

Maziar Raissi, Paris Perdikaris, and George E Karniadakis. Physics-informed neural networks: A deep learning frame- work for solving forward and inverse problems involving nonlinear partial differential equations.Journal of Computa- tional physics, 378:686–707, 2019. 2

2019
[34]

Learning contact corrections for handle-based sub- space dynamics.ACM Trans

Cristian Romero, Dan Casas, Jes ´us P ´erez, and Miguel Otaduy. Learning contact corrections for handle-based sub- space dynamics.ACM Trans. Graph., 40(4), 2021. 2

2021
[35]

Graph networks as learnable physics engines for inference and control

Alvaro Sanchez-Gonzalez, Nicolas Heess, Jost Tobias Sprin- genberg, Josh Merel, Martin Riedmiller, Raia Hadsell, and Peter Battaglia. Graph networks as learnable physics engines for inference and control. InProceedings of the 35th Interna- tional Conference on Machine Learning, pages 4470–4479. PMLR, 2018. 2, 3

2018
[36]

Hamiltonian graph networks with ode inte- grators

Alvaro Sanchez-Gonzalez, Victor Bapst, Kyle Cranmer, and Peter Battaglia. Hamiltonian graph networks with ode inte- grators. InProceedings of the NeurIPS 2019 Workshop on Machine Learning and the Physical Sciences, 2019. 2

2019
[37]

Learning to simulate complex physics with graph networks

Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Peter Battaglia. Learning to simulate complex physics with graph networks. InProceed- ings of the 37th International Conference on Machine Learn- ing, pages 8459–8468. PMLR, 2020. 2

2020
[38]

Snug: Self-supervised neural dynamic garments

Igor Santesteban, Miguel A Otaduy, and Dan Casas. Snug: Self-supervised neural dynamic garments. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8140–8150, 2022. 2, 6

2022
[39]

A physics-informed graph neural network conserving linear and angular momentum for dynamical systems.Nature Communications, 2026

Vinay Sharma and Olga Fink. A physics-informed graph neural network conserving linear and angular momentum for dynamical systems.Nature Communications, 2026. 2

2026
[40]

Levin, and Justin Solomon

Nicholas Sharp, Cristian Romero, Alec Jacobson, Etienne V ouga, Paul Kry, David I.W. Levin, and Justin Solomon. Data-free learning of reduced-order kinematics. InACM SIGGRAPH 2023 Conference Proceedings, New York, NY , USA, 2023. Association for Computing Machinery. 2, 6

2023
[41]

High-order differentiable autoencoder for nonlinear model reduction.ACM Trans

Siyuan Shen, Yin Yang, Tianjia Shao, He Wang, Chenfanfu Jiang, Lei Lan, and Kun Zhou. High-order differentiable autoencoder for nonlinear model reduction.ACM Trans. Graph., 40(4), 2021. 2

2021
[42]

Dissipative hamilto- nian neural networks: Learning dissipative and conservative dynamics separately

Andrew Sosanya and Sam Greydanus. Dissipative hamilto- nian neural networks: Learning dissipative and conservative dynamics separately. InInternational Conference on Learn- ing Representations (ICLR), 2022. 2

2022
[43]

Elastically deformable models

Demetri Terzopoulos, John Platt, Alan Barr, and Kurt Fleis- cher. Elastically deformable models. InProceedings of the 14th Annual Conference on Computer Graphics and Interac- tive Techniques, page 205–214, New York, NY , USA, 1987. Association for Computing Machinery. 1

1987
[44]

Deep learning methods for reynolds-averaged navier–stokes simulations of airfoil flows.AIAA Journal, 58 (1):25–36, 2020

Nils Thuerey, Konstantin Weißenow, Lukas Prantl, and Xi- angyu Hu. Deep learning methods for reynolds-averaged navier–stokes simulations of airfoil flows.AIAA Journal, 58 (1):25–36, 2020. 2

2020
[45]

Neural modes: Self-supervised learning of nonlinear modal subspaces

Jiahong Wang, Yinwei Du, Stelian Coros, and Bernhard Thomaszewski. Neural modes: Self-supervised learning of nonlinear modal subspaces. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 23158–23167, 2024. 2

2024
[46]

Discrete quadratic curvature en- ergies.Computer Aided Geometric Design, 24(8):499–518,

Max Wardetzky, Mikl ´os Bergou, David Harmon, Denis Zorin, and Eitan Grinspun. Discrete quadratic curvature en- ergies.Computer Aided Geometric Design, 24(8):499–518,
[47]

Discrete Differential Geometry. 5
[48]

A deep emulator for secondary motion of 3d characters

Mianlun Zheng, Yi Zhou, Duygu Ceylan, and Jernej Bar- bic. A deep emulator for secondary motion of 3d characters. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 5932–5940,
[49]

Completeness of Per-Edge Momentum Basis We show that per-edge momentum basis is complete in the sense that any momentum-preserving impulse can be gener- ated in this way

1, 2 Momentum-Conserving Graph Neural Networks for Deformable Objects Appendix A. Completeness of Per-Edge Momentum Basis We show that per-edge momentum basis is complete in the sense that any momentum-preserving impulse can be gener- ated in this way. To this end, we assume that there exist momentum- conserving impulses impulsesqthat cannot be generated ...