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REVIEW 4 major objections 5 minor 36 references

Learning Deformable Body Interactions With Adaptive Spatial Tokenization

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that Adaptive Spatial Tokenization (AST), which maps deformable-body meshes into octree cells and compresses them into fixed-length tokens via cross-attention, predicts deformation dynamics more accurately than…

desk verdict A plausible tokenization method for deformable-body simulation, but the empirical claims overreach because the baselines are handicapped and the large-scale result has no comparator. read the letter →

arxiv 2507.13707 v1 pith:SL3Y4ZPF submitted 2025-07-18 cs.LG

Hao Wang , Yu Liu , Daniel Biggs , Haoru Wang , Jiandong Yu , Ping Huang This is my paper · ORCID
classification cs.LG
keywords AdaptiveSpatialTokenizationdeformablebodysimulationmesh-basedphysicslearninggraphneuralnetworkscalabilityoctreequantizationcross-attentionlarge-scalefiniteelementcontactdynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper proposes Adaptive Spatial Tokenization (AST), a way to encode the state of deformable-body simulations as a compact set of latent tokens instead of a graph with dynamically computed pairwise edges. The idea is to bin mesh nodes into octree cells each frame, average node features per cell, and use cross-attention to compress the cells into a fixed-length token set that a transformer updates to predict the next state. If the reported results hold, AST removes the O($n^{2}$) world-edge bottleneck that makes graph-based simulators impractical on dense meshes, and extends learned simulation to meshes above 100,000 nodes. The paper also introduces ABCD and ABCD-XL datasets for benchmarking large-scale deformable contact.

What carries the argument

The load-bearing object is the adaptive spatial token: a per-frame octree cell that groups nearby mesh nodes, whose averaged features are compressed through cross-attention into a fixed number of latent tokens. The octree gives O(n) spatial grouping and supports sparse convolution; farthest-point sampling selects a spatially distributed subset of cells as queries; cross-attention compresses those cells into a fixed-length token set; self-attention propagates global information across tokens; and the decoder mirrors the process back to the original mesh. This machinery replaces explicitly constructed pairwise world edges with cell-based interaction grouping.

What would settle it

Take a dense mesh with a thin feature or a narrow contact interface whose thickness is smaller than the octree cell size, run AST with a cell depth coarse enough that the feature falls inside one cell, and compare rollout error against a finer cell depth. If the error does not grow sharply, the averaging assumption survives; if it does, cell quantization is erasing decisive local information.

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Extended reading notes

Core claim

AST's central claim is that spatial quantization plus attention-based tokenization is a better representation for contact-rich deformable simulation than node-level graphs. At each frame, mesh node positions define an octree; non-empty cells aggregate the embedded node features by averaging, and a cross-attention layer with farthest-point-sampled queries condenses the cells into 256 or 512 fixed tokens. Self-attention layers then predict the next state in latent space, and the decoder reverses the process back to mesh and element nodes. In the paper's experiments, AST reports the lowest rollout RMSE on DEFORMINGPLATE, SPHERESIMPLE, and ABCD, and is the only method that runs on ABCD-XL, whose meshes exceed 100,000 nodes, where MGN, BSMS, and HCMT run out of memory.

Load-bearing premise

The load-bearing premise is that averaging the mesh nodes inside each octree cell, and then compressing the cells into a fixed number of tokens, keeps enough local strain, stress, and contact information to make accurate long rollout predictions.

Editorial extensions

If this is right

  • Dynamic pairwise world edges are no longer needed, so the O(n^2) memory bottleneck becomes O(n) cell aggregation, which is what allows 100K-node runs.
  • On DEFORMINGPLATE, AST reports displacement RMSE of 1.1e-3 versus 2.9e-3 for HCMT and stress RMSE of 842 versus 7272, showing the tokenized representation does not sacrifice contact accuracy.
  • On ABCD-XL, AST is the only method that avoids out-of-memory and reports displacement RMSE 0.480e-3, demonstrating stable long rollouts at large scale.
  • The same tokenizer, processor, and decoder transfer across quasi-static compression, cloth-sphere interaction, and CAD part squishing, suggesting the representation generalizes across material and contact regimes.
  • The new ABCD and ABCD-XL datasets give future methods a common benchmark for large-scale deformable interactions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • One implication the paper leaves implicit is that the fixed token budget decouples memory from mesh size, so the same architecture is a candidate for even larger industrial meshes once the cell count saturates.
  • Because the octree is rebuilt every frame, the cell depth Lcell is a continuous accuracy-versus-speed dial; a coarser grid trades contact fidelity for cost, which could be exploited for adaptive simulation.
  • The averaging step is the likeliest failure point; a testable extension would replace mean pooling with attention pooling or per-cell moment features and check whether thin-feature contacts improve.
  • Treating the state as vector fields over cells suggests the tokenization could transfer to other grid-based physical fields such as fluids or thermal fields, but the paper only demonstrates solid mechanics.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes Adaptive Spatial Tokenization (AST), a learned simulator for deformable body interactions. AST maps an unstructured mesh onto a per-frame octree of spatial cells, aggregates mesh-node features into cell features via message passing, compresses the sparse cells into a fixed-length set of latent tokens using farthest-point sampling and cross-attention, processes the tokens with stacked self-attention layers, and decodes the result back to the mesh. The authors introduce two new datasets, ABCD and ABCD-XL, built from CAD geometries with Abaqus simulations, and compare AST against MGN, BSMS, and HCMT on DEFORMINGPLATE, SPHERESIMPLE, ABCD, and ABCD-XL. Reported rollout RMSEs favor AST on DEFORMINGPLATE and ABCD, are comparable on SPHERESIMPLE, and are unopposed on ABCD-XL because the baselines run out of memory.

Significance. The idea of replacing explicit dynamic world edges with adaptive spatial tokenization is a genuine and potentially impactful contribution for learned deformable-body simulation. The method is clearly described, the octree-plus-cross-attention architecture is well motivated, and the new ABCD/ABCD-XL datasets address a real gap in large-scale deformable-contact benchmarks. The DEFORMINGPLATE result (displacement RMSE 1.1 vs 2.9 for HCMT) and the reported runtime scaling are valuable. However, the paper's central claims of 'significant improvement over state-of-the-art' and effectiveness at 100,000 nodes rest on comparisons that are not fully controlled, and the new dataset is not released. The significance is therefore conditional: the architecture is promising, but the quantitative claims need to be re-established under a fair baseline protocol.

major comments (4)
  1. [A.1, Table 1] The ABCD comparison is not controlled. The world-edge construction is modified for MGN, BSMS, and HCMT by retaining only the 1000 world edges with the smallest pairwise distances per frame, while AST uses no world edges and is therefore not subject to this cap. For a 4k-node tetrahedral mesh in ABCD, the deformable-deformable contact interface can contain thousands of close node pairs, and truncating to 1000 edges can remove exactly the edges that encode contact. No sensitivity sweep over the cap is reported, and no justification is given for the value 1000. The reported ABCD gains (0.505 vs 0.541 for HCMT) therefore cannot be attributed to the method rather than to the baseline handicap; the claim of significant improvement on this dataset is not established.
  2. [§5.2, Table 1, Figures 10-11] The large-scale claim is not supported by a controlled comparison. On ABCD-XL, all three baselines run out of memory, so Table 1 reports only AST's absolute RMSE (0.480) with no baseline accuracy. Figures 10 and 11 show runtime scaling only up to roughly 20k elements, not accuracy at 100k elements. The statement that AST 'remains effective' on meshes exceeding 100,000 nodes requires at least an accuracy comparison against a memory-reduced or approximate version of a baseline (e.g., a subsampled MGN or a baseline with restricted edges), or a clearly framed scalability study without the comparative claim.
  3. [§5.2, Table 1] The claim of consistent significant improvement over state-of-the-art is overstated on SPHERESIMPLE. AST reports 14.4 ± 0.8 versus BSMS 15.0 ± 0.8; the difference is within one standard error, and MGN's 19.0 ± 4.9 overlaps. Only DEFORMINGPLATE shows a clearly separated improvement (1.1 vs 2.9). The abstract and conclusion should be qualified to reflect the actual pattern of results.
  4. [§1, §5.1] The paper introduces ABCD and ABCD-XL as novel datasets and claims them as a contribution, but provides no download URL, license, or code release, and the supplementary material contains no artifact. Without the dataset and code, the empirical results cannot be reproduced or audited; at minimum the dataset construction pipeline should be released or a clear availability statement added.
minor comments (5)
  1. [Table 1] The units for stress are not specified; the header says ×10^-3 for displacement only, but stress values appear on very different scales (e.g., 6891 for DEFORMINGPLATE vs 2.11 for ABCD-XL).
  2. [Equation (3)] The notation is inconsistent: c_l^i is used both for the cell and for its feature, and the definition of v'c_t = [c_L^1, ..., c_L^{N_L}] introduces a symbol that is not defined elsewhere.
  3. [B.1] The statement 'When Lcell = 7, all mesh nodes are assigned to a single cell at the initial frame' is inconsistent with the octree definition in Section 3.2, where larger L gives smaller cells; please clarify or correct this sentence.
  4. [A.3] The claim that HCMT 'performs well during the initial 50 frames but gradually diverges' on SPHERESIMPLE would benefit from a quantitative rollout curve, since the table only reports divergence.
  5. [Abstract and Introduction] The phrase 'significantly outperforms' is used before presenting the statistical uncertainty; please align the wording with the standard errors in Table 1, particularly for SPHERESIMPLE.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: AST is an empirical architecture evaluated on rollout prediction; no claim reduces to its own inputs or to a self-citation chain.

full rationale

The paper's central claim—that Adaptive Spatial Tokenization accurately predicts next-frame mesh states—is an empirical result. The encoder maps mesh features to spatial cells by averaging, then to fixed tokens via FPS and cross-attention; the processor runs self-attention; the decoder maps back. Every stage is defined in terms of the input state and trained parameters, and the target quantities (displacement/stress at t+1) are separate from the inputs (positions, node type, material, stress/t). There is no fitted constant or calibration curve being renamed as a prediction. The method is benchmarked against external baselines (MGN, BSMS, HCMT) with published implementations, and the new ABCD/ABCD-XL datasets are simulated with Abaqus/COMSOL/ArcSim, external solvers that do not depend on AST. The only flagged weaknesses are baseline-fairness concerns—the 1000-world-edge cap in Section A.1 and the absence of a baseline that runs on ABCD-XL (Table 5.2)—and these affect the strength of the comparative claim, not the internal circularity of the derivation. The paper contains no load-bearing self-citation (references are all external), no imported uniqueness theorem, and no ansatz smuggled in via citation. Per the scoring rules, a comparative-evaluation concern is a correctness risk, not circularity; the derivation chain is self-contained.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim rests on design hyperparameters chosen by validation, on domain assumptions about the sufficiency of cell averaging and short history, and on the fairness of the adapted baseline protocol. There are no invented physical entities and no free physics parameters; the listed free parameters are network design choices.

free parameters (6)
  • octree depth Lcell = 5 (SPHERESIMPLE, DEFORMINGPLATE), 8 (ABCD), 12 (ABCD-XL)
    Chosen by validation rather than derived; controls cell size and how many mesh nodes share a cell. Figure 9 shows validation loss varies with Lcell.
  • latent token dimension dtoken = 256 (small datasets), 512 (ABCD, ABCD-XL)
    Sets the fixed-length bottleneck; chosen by hand per dataset.
  • number of self-attention layers LSA = 12 for all datasets
    Capacity and compute tradeoff; chosen by hand.
  • OCNN downscale layers locnn = 0 (small), 4 (ABCD-XL)
    Hierarchical compression depth; chosen per dataset.
  • loss weight for stress output = 0.01 on DEFORMINGPLATE and ABCD-XL
    Hand-set weight balancing displacement and stress losses.
  • number of tokens after FPS = not reported
    The paper specifies fixed-length tokens but does not state the token count selected by FPS; an unstated design choice affecting the bottleneck.
assumptions (4)
  • domain assumption The next simulation state is determined by the current state plus boundary conditions within a short history h (0 or 1 steps), as used in Equation 7 and Table 3.
    The model ignores long-range temporal dependencies; if history matters, the Markov assumption could limit accuracy.
  • domain assumption FEA solver outputs (Abaqus, COMSOL, ArcSim) are treated as exact ground truth, with no label noise or solver error modeled.
    Dataset construction in Section A.1 relies on solver-generated stress and displacement as targets.
  • ad hoc to paper Averaging mesh node features into spatial cells and compressing to fixed tokens preserves information needed for prediction.
    This is the central modeling bet of AST; Sections 4.2.3 and 4.2.4 make this compression without an information-loss analysis.
  • domain assumption The modified world-edge construction (retaining only the 1000 closest pairs) does not unfairly handicap MGN, BSMS, and HCMT on ABCD.
    Section A.1 states this modification; no sensitivity analysis shows how baseline performance changes with edge count.

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Cite this review

Pith. "Pith review of Learning Deformable Body Interactions With Adaptive Spatial Tokenization." pith.science (2026). https://pith.science/paper/SL3Y4ZPF

@misc{pith2026250713707,
  author       = {Pith},
  title        = {Pith review of: Learning Deformable Body Interactions With Adaptive Spatial Tokenization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SL3Y4ZPF}},
  note         = {Machine review of arXiv:2507.13707}
}
read the original abstract

Simulating interactions between deformable bodies is vital in fields like material science, mechanical design, and robotics. While learning-based methods with Graph Neural Networks (GNNs) are effective at solving complex physical systems, they encounter scalability issues when modeling deformable body interactions. To model interactions between objects, pairwise global edges have to be created dynamically, which is computationally intensive and impractical for large-scale meshes. To overcome these challenges, drawing on insights from geometric representations, we propose an Adaptive Spatial Tokenization (AST) method for efficient representation of physical states. By dividing the simulation space into a grid of cells and mapping unstructured meshes onto this structured grid, our approach naturally groups adjacent mesh nodes. We then apply a cross-attention module to map the sparse cells into a compact, fixed-length embedding, serving as tokens for the entire physical state. Self-attention modules are employed to predict the next state over these tokens in latent space. This framework leverages the efficiency of tokenization and the expressive power of attention mechanisms to achieve accurate and scalable simulation results. Extensive experiments demonstrate that our method significantly outperforms state-of-the-art approaches in modeling deformable body interactions. Notably, it remains effective on large-scale simulations with meshes exceeding 100,000 nodes, where existing methods are hindered by computational limitations. Additionally, we contribute a novel large-scale dataset encompassing a wide range of deformable body interactions to support future research in this area.

Figures

Figures reproduced from arXiv: 2507.13707 by the authors.

Figure 1
Figure 1. Spatial Cells for interactions. including virtual edges, graph pooling, and U-Net structures to improve computational efficiency and handle long-range interactions. To simulate interactions between objects, these methods typically construct dynamic world edges by connecting spatially close mesh nodes across objects at each time step. FIGNet [1] extends this idea by defining multiple edge types (face-to-face, mesh-to… view at source ↗
Figure 3
Figure 3. The encoder (left) and decoder (right) cross-attention blocks. We use v to denote fea￾ture vectors on the sparse grid (i.e., the previ￾ously defined sparse cells), and h to denote the compact latent tokens. PosEmb and FPS are in￾troduced in Section A.4. We apply cross-attention mechanisms to transform features embedded in spatial cells CL into com￾pact latent tokens ht with a selected dimension dtoken, as illustrate… view at source ↗
Figure 4
Figure 4. We visualize the spatial cells on the ABCD dataset (left) and DEFORMINGPLATE dataset (right). The figure displays one representative feature channel across the cells. Warmer colors indicate higher feature norms. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figures from the paper (9 more)
Figure 5
Figure 5. Figure 5: Visualization results on the ABCD dataset. Displacement is visualized using color warmth, with warmer tones indicating greater displacement magnitude. [11] Ben Graham. Sparse 3d convolutional neural networks, 2015. [12] Omar M Hafez and Mark M Rashid. A robust workflow…
Figure 6
Figure 6. Figure 6: Randomized FEA simulation dataset using geometry from ABC dataset. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 8
Figure 8. Figure 8: Transformer blocks. The CrossAttn is displayed on the left, while the SelfAttn is displayed on the right. FFN stands for Feed-Forward Network. In all our CrossAttn and SelfAttn blocks, we use an FFN module with GEGLU activation as described in [25]. A.5 Model Details M…
Figure 10
Figure 10. Figure 10: Training time per epoch across different mesh sizes. MGN, BSMS, and HCMT run out of [PITH_FULL_IMAGE:figures/full_fig_p017_10.png]
Figure 11
Figure 11. Figure 11: Inference time per epoch across different mesh sizes. [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]
Figure 12
Figure 12. Figure 12: Visualization results on the DEFORMINGPLATE dataset. Stress is visualized using color warmth, with warmer tones indicating greater stress magnitude. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_12.png]
Figure 13
Figure 13. Figure 13: Rollout visualization results on the DEFORMINGPLATE dataset. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_13.png]
Figure 14
Figure 14. Figure 14: Rollout visualization results on the SPHERESIMPLE dataset. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_14.png]
Figure 15
Figure 15. Figure 15: Rollout visualization results on the ABCD dataset. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_15.png]

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Reference graph

Works this paper leans on

36 extracted references · 23 canonical work pages

  1. [1]

    Allen, Yulia Rubanova, Tatiana Lopez-Guevara, William Whitney, Alvaro Sanchez- Gonzalez, Peter W

    Kelsey R. Allen, Yulia Rubanova, Tatiana Lopez-Guevara, William Whitney, Alvaro Sanchez- Gonzalez, Peter W. Battaglia, and Tobias Pfaff. Learning rigid dynamics with face interaction graph networks. InInternational Conference on Learning Representations (ICLR), 2023

    work page 2023

  2. [2]

    CRC press, 2023

    Ever J Barbero.Finite element analysis of composite materials using Abaqus®. CRC press, 2023

    work page 2023

  3. [3]

    Efficient learning of mesh-based physical simulation with bi-stride multi-scale graph neural network

    Yadi Cao, Menglei Chai, Minchen Li, and Chenfanfu Jiang. Efficient learning of mesh-based physical simulation with bi-stride multi-scale graph neural network. InInternational conference on machine learning, pages 3541–3558. PMLR, 2023

    2023

  4. [4]

    A review of physics simulators for robotic applications.IEEE Access, 9:51416–51431, 2021

    Jack Collins, Shelvin Chand, Anthony Vanderkop, and David Howard. A review of physics simulators for robotic applications.IEEE Access, 9:51416–51431, 2021

    work page 2021

  5. [5]

    Variational methods for the solution of problems of equilibrium and vibrations.Lecture notes in pure and applied mathematics, pages 1–1, 1994

    Richard Courant et al. Variational methods for the solution of problems of equilibrium and vibrations.Lecture notes in pure and applied mathematics, pages 1–1, 1994

    work page 1994

  6. [6]

    Application of the finite element method in the analysis of composite materials: A review

    Sarah David Müzel, Eduardo Pires Bonhin, Nara Miranda Guimarães, and Erick Siqueira Guidi. Application of the finite element method in the analysis of composite materials: A review. Polymers, 12(4):818, 2020

    work page 2020

  7. [7]

    Bordas, and Jakub Lengiewicz

    Saurabh Deshpande, Stéphane P.A. Bordas, and Jakub Lengiewicz. Magnet: A graph u-net architecture for mesh-based simulations.Engineering Applications of Artificial Intelligence, 133:108055, 2024

    work page 2024

  8. [8]

    An image is worth 16x16 words: Transformers for image recognition at scale.arXiv preprint arXiv:2010.11929, 2020

    Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al. An image is worth 16x16 words: Transformers for image recognition at scale.arXiv preprint arXiv:2010.11929, 2020

    arXiv 2010

Show all 36 references
  1. [9]

    Multiscale MeshGraphNets

    Meire Fortunato, Tobias Pfaff, Peter Wirnsberger, Alexander Pritzel, and Peter Battaglia. Multiscale MeshGraphNets. InICML 2022 2nd AI for Science Workshop, 2022

    2022

  2. [10]

    Gnn-based physics solver for time-independent pdes.arXiv preprint arXiv:2303.15681, 2023

    Rini Jasmine Gladstone, Helia Rahmani, Vishvas Suryakumar, Hadi Meidani, Marta D’Elia, and Ahmad Zareei. Gnn-based physics solver for time-independent pdes.arXiv preprint arXiv:2303.15681, 2023. Figure 4: We visualize the spatial cells on the ABCDdataset (left) and DEFORMINGPL...

    2023 arXiv

  3. [11]

    Sparse 3d convolutional neural networks, 2015

    Ben Graham. Sparse 3d convolutional neural networks, 2015

    2015

  4. [12]

    A robust workflow for b-rep generation from image masks

    Omar M Hafez and Mark M Rashid. A robust workflow for b-rep generation from image masks. Graphical Models, 128:101174, 2023

    2023

  5. [13]

    Abc: A big cad model dataset for geometric deep learning

    Sebastian Koch, Albert Matveev, Zhongshi Jiang, Francis Williams, Alexey Artemov, Evgeny Burnaev, Marc Alexa, Denis Zorin, and Daniele Panozzo. Abc: A big cad model dataset for geometric deep learning. InProceedings of the IEEE/CVF conference on computer vision and pattern rec...

    2019

  6. [14]

    Learning skillful medium-range global weather forecasting.Science, 382(6677):1416–1421, 2023

    Remi Lam, Alvaro Sanchez-Gonzalez, Matthew Willson, Peter Wirnsberger, Meire Fortunato, Ferran Alet, Suman Ravuri, Timo Ewalds, Zach Eaton-Rosen, Weihua Hu, et al. Learning skillful medium-range global weather forecasting.Science, 382(6677):1416–1421, 2023

    2023

  7. [15]

    Mage: Masked Generative Encoder to Unify Representation Learning and Image Synthesis

    Tianhong Li, Huiwen Chang, Shlok Kumar Mishra, Han Zhang, Dina Katabi, and Dilip Krishnan. Mage: Masked Generative Encoder to Unify Representation Learning and Image Synthesis. In Computer Vision and Pattern Recognition (CVPR), pages 2142–2152, 2023

    2023

  8. [16]

    Triposg: High-Fidelity 3d Shape Synthesis using Large-Scale Rectified Flow Models.arXiv.org, abs/2502.06608, 2025

    Yangguang Li, Zi-Xin Zou, Zexiang Liu, Dehu Wang, Yuan Liang, Zhipeng Yu, Xingchao Liu, Yuan-Chen Guo, Ding Liang, Wanli Ouyang, and Yan-Pei Cao. Triposg: High-Fidelity 3d Shape Synthesis using Large-Scale Rectified Flow Models.arXiv.org, abs/2502.06608, 2025

    2025 arXiv

  9. [17]

    Simulating continuum mechanics with multi-scale graph neural networks.arXiv preprint arXiv:2106.04900, 2021

    Mario Lino, Chris Cantwell, Anil A Bharath, and Stathi Fotiadis. Simulating continuum mechanics with multi-scale graph neural networks.arXiv preprint arXiv:2106.04900, 2021

    2021 arXiv

  10. [18]

    Geometric modeling using octree encoding.Computer graphics and image processing, 19(2):129–147, 1982

    Donald Meagher. Geometric modeling using octree encoding.Computer graphics and image processing, 19(2):129–147, 1982

    1982

  11. [19]

    Neural Discrete Representation Learning

    Aäron van den Oord, Oriol Vinyals, and Koray Kavukcuoglu. Neural Discrete Representation Learning. InConference on Neural Information Processing Systems (NeurIPS), pages 6306– 6315, 2017

    2017

  12. [20]

    Learning mesh- based simulation with graph networks

    Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, and Peter Battaglia. Learning mesh- based simulation with graph networks. InInternational conference on learning representations, 2020

    2020

  13. [21]

    Pointnet++: Deep hierarchical feature learning on point sets in a metric space.Advances in neural information processing systems, 30, 2017

    Charles Ruizhongtai Qi, Li Yi, Hao Su, and Leonidas J Guibas. Pointnet++: Deep hierarchical feature learning on point sets in a metric space.Advances in neural information processing systems, 30, 2017. 10

    2017

  14. [22]

    Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and I

    Alec Radford, Jong Wook Kim, Chris Hallacy, A. Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and I. Sutskever. Learning Transferable Visual Models From Natural Language Supervision. InInternational Conference...

    2021

  15. [23]

    Learning rigid-body simulators over implicit shapes for large-scale scenes and vision.Advances in Neural Information Processing Systems, 37:125809–125838, 2024

    Yulia Rubanova, Tatiana Lopez-Guevara, Kelsey Allen, Will Whitney, Kimberly L Stachenfeld, and Tobias Pfaff. Learning rigid-body simulators over implicit shapes for large-scale scenes and vision.Advances in Neural Information Processing Systems, 37:125809–125838, 2024

    2024

  16. [24]

    Battaglia

    Alvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying, Jure Leskovec, and Pe- ter W. Battaglia. Learning to Simulate Complex Physics with Graph Networks. InInternational Conference on Machine Learning (ICML), pages 8459–8468, 2020

    2020

  17. [25]

    Glu variants improve transformer.arXiv preprint arXiv:2002.05202, 2020

    Noam Shazeer. Glu variants improve transformer.arXiv preprint arXiv:2002.05202, 2020

    2002 arXiv

  18. [26]

    A survey of finite element techniques for mechanism design

    BS Thompson and CK Sung. A survey of finite element techniques for mechanism design. Mechanism and Machine Theory, 21(4):351–359, 1986

    1986

  19. [27]

    Attention is all you need.Advances in neural information processing systems, 30, 2017

    Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need.Advances in neural information processing systems, 30, 2017

    2017

  20. [28]

    Octformer: Octree-based Transformers for 3d Point Clouds.ACM Transac- tions on Graphics, 42(4):1–11, 2023

    Peng-Shuai Wang. Octformer: Octree-based Transformers for 3d Point Clouds.ACM Transac- tions on Graphics, 42(4):1–11, 2023

    2023

  21. [29]

    O-cnn: Octree-based convolutional neural networks for 3d shape analysis.ACM Transactions On Graphics (TOG), 36(4):1–11, 2017

    Peng-Shuai Wang, Yang Liu, Yu-Xiao Guo, Chun-Yu Sun, and Xin Tong. O-cnn: Octree-based convolutional neural networks for 3d shape analysis.ACM Transactions On Graphics (TOG), 36(4):1–11, 2017

    2017

  22. [30]

    Random weight factorization improves the training of continuous neural representations.arXiv preprint arXiv:2210.01274, 2022

    Sifan Wang, Hanwen Wang, Jacob H Seidman, and Paris Perdikaris. Random weight factorization improves the training of continuous neural representations.arXiv preprint arXiv:2210.01274, 2022

    2022 arXiv

  23. [31]

    Second: Sparsely embedded convolutional detection.Sensors, 18(10), 2018

    Yan Yan, Yuxing Mao, and Bo Li. Second: Sparsely embedded convolutional detection.Sensors, 18(10), 2018

    2018

  24. [32]

    Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer

    Youn-Yeol Yu, Jeongwhan Choi, Woojin Cho, Kookjin Lee, Nayong Kim, Kiseok Chang, ChangSeung Woo, Ilho Kim, SeokWoo Lee, Joon-Young Yang, Sooyoung Yoon, and Noseong Park. Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer. InInternational Confe...

    2024

  25. [33]

    3dshape2vecset: A 3d Shape Representation for Neural Fields and Generative Diffusion Models.ACM Transactions on Graphics (TOG), 42(4):92:1–92:16, 2023

    Biao Zhang, Jiapeng Tang, Matthias Nießner, and Peter Wonka. 3dshape2vecset: A 3d Shape Representation for Neural Fields and Generative Diffusion Models.ACM Transactions on Graphics (TOG), 42(4):92:1–92:16, 2023

    2023

  26. [34]

    3dshape2vecset: A 3d shape representation for neural fields and generative diffusion models.ACM Transactions On Graphics (TOG), 42(4):1–16, 2023

    Biao Zhang, Jiapeng Tang, Matthias Niessner, and Peter Wonka. 3dshape2vecset: A 3d shape representation for neural fields and generative diffusion models.ACM Transactions On Graphics (TOG), 42(4):1–16, 2023

    2023

  27. [35]

    Elsevier, 2005

    Olgierd Cecil Zienkiewicz and Robert Leroy Taylor.The finite element method for solid and structural mechanics. Elsevier, 2005. A Technical Appendices and Supplementary Material A.1 Dataset Details The ABCD DatasetWe constructed a larger and more generalized dataset. The goal ...

    2005

  28. [36]

    We note that in the BSMS paper, the authors included velocity as an input feature for DEFORMINGPLATE

    on SPHERESIMPLEand DEFORMINGPLATE. We note that in the BSMS paper, the authors included velocity as an input feature for DEFORMINGPLATE. In contrast, we follow the original MeshGraphNets (MGN) implementation, which uses node type and (relative) positions as input. On ABCD, the...

    2000

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.