Pith. sign in

REVIEW 4 major objections 4 minor 69 references

Text2Structure3D: Graph-Based Generative Modeling of Equilibrium Structures with Diffusion Transformers

T0 review · 4 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper claims that a graph-based latent diffusion model can turn natural-language bridge descriptions into structures that satisfy static equilibrium, with a residual-force post-processing step that preserves geometric accuracy.

desk verdict A sensible text-to-equilibrium bridge generator with an overclaimed equilibrium guarantee; worth refereeing, but the residual optimization needs to actually be measured. read the letter →

arxiv 2601.12870 v2 pith:O2YMGPEA submitted 2026-01-19 cs.CE

Lazlo Bleker , Zifeng Guo , Kaleb E. Smith , Kam-Ming Mark Tam , Karla Saldaña Ochoa , Pierluigi D'Acunto This is my paper
classification cs.CE
keywords text-to-structuregenerationlatentdiffusionvariationalgraphauto-encoderequilibriumstructuresforcedensitiesbridgedesignnaturallanguageconditioningconceptualstructural
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 sets out to show that natural-language prompts can drive the generation of load-bearing structures that are physically admissible, not merely visually plausible. It builds a pipeline in which a bridge is represented as a graph—nodes carrying coordinates and support conditions, edges carrying force densities—and a diffusion transformer samples new graphs from a latent space learned by a variational graph auto-encoder, conditioned on a text embedding. A residual-force optimization then adjusts the decoded geometry and forces together so that every free node has zero residual force, which is the paper's operational definition of static equilibrium. On a synthetic dataset of 30,000 arch, suspension, and truss bridges labeled with 300,000 text descriptions, the model is reported to match requested spans, rise-to-span ratios, bay counts, and qualitative attributes, with median reconstruction error of 0.47 m after optimization. If true, this would let engineers explore structurally valid bridge concepts from a text prompt without building a new parametric model for each typology.

What carries the argument

The load-bearing mechanism is the joint node-level latent representation: the VGAE encodes edge force densities (axial force divided by member length), node coordinates, and discrete support conditions into one continuous vector per node, so the diffusion model operates in a continuous space instead of a mixed categorical-continuous product manifold. The residual-force optimization then solves for small changes in coordinates and force densities, bounded by Delta x = 2 m and Delta q = 1 kN/m, to minimize the squared residual force at free nodes; this is the step that converts 'close to equilibrium' reconstructions into structures that satisfy static equilibrium under the dataset's implicit l

What would settle it

Recompute the residual force at every free node of a generated bridge under a load that is not the dataset's 5 kN/m uniform deck line load—for instance a 50 kN point load at midspan or an asymmetric live load. If the residual does not vanish, the equilibrium claim is tied to the single-load-case derivation, not to arbitrary text prompts.

Watch

Extended reading notes

Core claim

On its own terms, the paper discovers that a graph representation—nodes with coordinates and support flags, edges with force densities—can be pushed through a variational graph auto-encoder into a node-level latent space where a text-conditioned diffusion transformer samples novel structures, and that a bounded residual-force optimization projects those samples onto the equilibrium manifold without distorting the requested geometry. The reported result: generated structures match requested typology and qualitative attributes, quantitative attributes concentrate around requested values even for reworded and multi-attribute prompts, and optimization lowers median reconstruction error from 0.90

Load-bearing premise

The equilibrium guarantee holds only for the dataset's implicit load model: the external load is not an input but is derived from the generated span under a constant 5 kN/m line load on the deck, so prompts that imply different loads are not covered by the guarantee.

Editorial extensions

If this is right

  • A designer could type 'twin-arch through bridge, 90 m span, 4 m deck, arches leaning' and receive a graph with node coordinates, member force densities, and support conditions already in equilibrium, ready to feed into downstream structural analysis.
  • The gap between force-based equilibrium and geometry-based accuracy closes at the reconstruction level: the post-processed output has both zero residual forces and median geometry error near half a meter, so generated shapes are usable for early sizing.
  • Because the VGAE latent space is shared across arch, suspension, and truss typologies, the model is not locked to one parametric design space; adapting it to a new typology becomes a matter of adding data rather than redesigning the architecture.
  • Prompt adherence survives rephrasing and multi-attribute requests, meaning users do not need to match a rigid template to get the span, rise-to-span, and bay count they ask for.

Reading between the lines

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

  • Because loads are derived from span under a constant 5 kN/m deck load, the equilibrium guarantee is load-case-specific; the natural next step is to make the external load an explicit input or condition, which the architecture appears able to accommodate.
  • A testable extension would be to train on multi-load-case data and prompt with explicit loads; if the optimizer still converges to zero residual force, the method generalizes beyond funicular bridge datasets.
  • The equilibrium guarantee covers nodal force balance only, not stability, buckling, strength, or serviceability, so generated designs still need conventional structural verification before construction.
  • The topology prediction remains parametric, so the part of the pipeline that most limits scalability is the topology model, not the generative core; replacing it with graph link prediction or autoregressive generation is the path the paper itself points to.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper proposes Text2Structure3D, a graph-based latent diffusion model that generates bridge-like equilibrium structures from natural language prompts. The architecture combines a VGAE that encodes node coordinates, edge force densities, and support conditions into a shared node-level latent space; a flow-matching DiT conditioned on CLIP text embeddings; and a topology MLP. A residual force optimization post-processing step is introduced to bring decoded structures into equilibrium. The model is trained on a synthetic cross-typological dataset of 30,000 funicular and truss bridges with templated text labels. Evaluation reports reconstruction error and prompt adherence via KDE/categorical distributions over 1000 generated samples per prompt, and the paper claims strong adherence to text specifications and improved generalization compared to parametric model-based approaches.

Significance. If substantiated, the work would be a useful step toward text-conditioned generative design of statically balanced structures, combining graph representations with latent diffusion. The paper is honest about several limitations (single load case, parametric topology model, canonical orientation) and the weak KL prior is a sensible design choice for latent diffusion. The residual-force optimization idea is sound as a post-processing and the synthetic dataset is nontrivial. However, the headline claims about guaranteed equilibrium and strong generalization are stronger than the evidence presented: the equilibrium guarantee rests on a nonconvex box-constrained optimization that is not proven to reach zero residual, external loads are fixed by an unstated constant line load, and no quantitative metrics are reported for prompt adherence or comparison to existing methods.

major comments (4)
  1. [§3.2 (Eq. 10) and Algorithm 1] Eq. (10) minimizes the sum of squared residual magnitudes subject only to box bounds on q̃ and x̃. Since Eq. (8) is bilinear in q̃ and x̃, the objective is nonconvex, so a local minimum can have nonzero residuals even if zero is feasible. Moreover, the box bounds Δx=2 m and Δq=1 kN/m may exclude any exact equilibrium solution. The optional FDM step mentioned in the text ('Optionally, any small residual still remaining ...') is not applied in Algorithm 1, which stops after the residual-force optimization, and §4 never reports ε_residual for reconstructed or generated structures. The Abstract/Conclusion claim that the post-processing 'ensures generated structures fully satisfy static equilibrium' is therefore unverified. Please either apply the FDM step and report the resulting ε_residual (ideally as a distribution with tolerance), or soften the claim to 'approximately satisfy' with a stat
  2. [§3.5 and §5.1] The equilibrium guarantee in Eq. (9) depends on the dataset's implicit load model: external loads are not an input variable but are derived from the generated geometry under a constant line load of 5 kN/m along the deck (§3.5). The limitation is acknowledged in §5.1 ('the fact that our dataset only contained bridge structures with a single load case allowed us to derive the loading condition from the generated geometry'), but the Abstract and Conclusion state 'fully satisfy static equilibrium' without this caveat. If a user prompt implies a different load distribution, the post-processed structure is not guaranteed to be in equilibrium for that load. The claim must be qualified in the abstract and conclusion, or the external load should be included as an explicit conditioning input.
  3. [§4.2 (Figure 9)] The 'strong adherence' claim is based on KDE/categorical plots over 1000 samples per prompt. The paper reports no numerical summaries (mean absolute error, standard deviation, coverage, or divergence), no statistical comparison to the unconditional baseline, and no quantitative test for the 'alternative' or 'complex' prompt comparisons. The statements 'marginally worse' and 'significantly concentrated' are not backed by numbers. Please report quantitative adherence metrics with confidence intervals, and ideally include the underlying sample counts for categorical attributes.
  4. [§6 (and Abstract)] The claim that Text2Structure3D 'greatly improves generalization capabilities compared to parametric model-based approaches' is not directly supported. The paper does not compare against an existing parametric generative model (e.g., a VAE or GAN trained on the same dataset). The only quantitative comparison is between force-density-based reconstructions and residual-optimized reconstructions. Cross-typology generalization is demonstrated qualitatively in Figure 6, but no quantitative zero-shot or transfer metric is presented. Please either add a direct comparison or soften this claim.
minor comments (4)
  1. [§2.1] Typo: 'image-based approach rely still rely on a fixed parameterization' — remove the duplicated 'rely'.
  2. [§1.3] Minor wording: 'form a variable-sized and connected graph space' should be 'from a variable-sized and connected graph space'.
  3. [§3.4 / Algorithm 1] The pseudocode output says '(q̃, x̃, ŝ)' but the final step only returns q̃ and x̃; please clarify whether support conditions are also refined or kept as decoded.
  4. [§4.1] For completeness, the paper should report not only ε_reconst but also the number of cases where the optimizer returned a nonzero residual (above a numerical tolerance), to substantiate the claim that the post-processing achieves equilibrium.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction found: equilibrium is enforced by a post-hoc optimization constraint, not by an input fitted as a prediction; remaining self-citations are not load-bearing.

full rationale

The central derivation chain is not circular. The residual-force post-processing (Eq. 10) minimizes the squared residual (Eq. 8) that defines static equilibrium, but this is constraint enforcement rather than a fitted parameter renamed as a prediction. The diffusion/VGAE latents are not pre-fit to the equilibrium labels; the VGAE is trained with a deliberately weak KL prior (beta=0.01) and the flow-matching DiT must learn the latent distribution, so the generated structures are not forced to be equilibrium samples by construction. The paper's self-citations (CEM, residual-force GNNs, EGNNs) are used for background or data generation and are not invoked as a uniqueness theorem or as the sole justification for the equilibrium guarantee. The main caveat is a verification gap, not circularity: Section 3.2 concedes 'any small residual still remaining after optimization can be eliminated' by an optional FDM step, but Algorithm 1 stops before that step, and Section 4 reports no post-optimization epsilon_residual. This makes the abstract claim that generated structures 'fully satisfy static equilibrium' under-verified, but it is a correctness/verification concern rather than a reduction of the result to its own inputs. Prompt-adherence evaluation is in-distribution with the synthetic generator, which limits external validity, but it is not a circular derivation because the model can fail to condition on text even within that distribution.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The load-bearing assumptions are the implicit single-load model, the parametric topology family, and the reliance on CLIP text embeddings; the authors explicitly acknowledge the first two in their limitations section. The free parameters are standard ML hyperparameters plus the load value and post-processing bounds that the equilibrium guarantee depends on.

free parameters (4)
  • KL divergence weight β = 0.01
    Chosen by hand after Eq. (7) to favor reconstruction over the Gaussian prior; controls how much the latent space deviates from the prior and therefore what the diffusion model must learn.
  • Residual optimization bounds (Δx, Δq) = Δx=2 m, Δq=1 kN/m
    Hand-set in Eq. (10); define how far post-processing may move coordinates and force densities from the decoder output and whether a zero-residual equilibrium is reachable.
  • CFG guidance scale γ = 5.0
    Hand-set in Eq. (15); trades prompt adherence against sample diversity. No sensitivity analysis is reported.
  • Constant line load = 5 kN/m
    Assumed in §3.5; the nodal load p_i used in Eq. (8) and Eq. (10) is derived from this load and the generated span, so the equilibrium guarantee is conditional on it.
assumptions (5)
  • standard math Pin-jointed axial-force model with force density q_ij = f_ij / l_ij and equilibrium residual r_i = p_i + Σ_{j∈N(i)} q_ij (x_j − x_i)
    Eqs. (1)-(2) and (8); foundational to defining equilibrium in the paper. Assumes axial-only members and a given topology.
  • ad hoc to paper External loads are not modeled explicitly; a constant line load of 5 kN/m on the deck is assumed and loads are derived from geometry
    Section 3.5 and Section 5.1; the paper's own limitation text says a more general dataset would require explicit load modeling.
  • domain assumption All topologies lie in a small parametric family (CEM arch/suspension and Pratt/Howe/Parker trusses) and the topology MLP can model this family
    Sections 3.4 and 3.5; limitation acknowledged in §5.1, since topologies outside this parametric space are not generable.
  • domain assumption CLIP embeddings of natural-language prompts provide sufficient conditioning signal for quantitative attributes (span, rise-to-span ratio, bay count)
    Section 3.3 and §4.2; tested against only a few hand-written paraphrases, not broad linguistic variation.
  • domain assumption Canonical orientation (midspan/deck origin, deck along x-axis) and support conditions encode all relevant geometry
    Section 3.5; the model relies on this normalization, and §5.1 notes it may not be available for a more general class of structures.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Text2Structure3D: Graph-Based Generative Modeling of Equilibrium Structures with Diffusion Transformers." pith.science (2026). https://pith.science/paper/O2YMGPEA

@misc{pith2026260112870,
  author       = {Pith},
  title        = {Pith review of: Text2Structure3D: Graph-Based Generative Modeling of Equilibrium Structures with Diffusion Transformers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O2YMGPEA}},
  note         = {Machine review of arXiv:2601.12870}
}
read the original abstract

This paper presents Text2Structure3D, a graph-based Machine Learning (ML) model that generates equilibrium structures from natural language prompts. Text2Structure3D is designed to support new intuitive ways of design exploration and iteration in the conceptual structural design process. The approach combines latent diffusion with a Variational Graph Auto-Encoder (VGAE) and graph transformers to generate structural graphs that are close to an equilibrium state. Text2Structure3D integrates a residual force optimization post-processing step that ensures generated structures fully satisfy static equilibrium. The model was trained and validated using a cross-typological dataset of funicular form-found and statically determinate bridge structures, paired with text descriptions that capture the formal and structural features of each bridge. Results demonstrate that Text2Structure3D generates equilibrium structures with strong adherence to text-based specifications and greatly improves generalization capabilities compared to parametric model-based approaches. Text2Structure3D represents an early step toward a general-purpose foundation model for structural design, enabling the integration of generative AI into conceptual design workflows.

Figures

Figures reproduced from arXiv: 2601.12870 by the authors.

Figure 1
Figure 1. An equilibrium structure (left) represented as a graph (right). Every [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Text2Structure3D can generate an equilibrium structure adhering to an input text prompt. A text embedding model creates a conditioning vector ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. A Variational Graph Auto-Encoder (VGAE) [7] learns a node-level [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: A random sample from a Gaussian distribution is iteratively denoised to a point in the latent space distribution. The VGAE decoder can decode denoised [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Samples from the cross-typological synthetic training dataset used to [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Equilibrium structures generated by Text2Structure3D using various text prompts. Text2Structure3D can generate diverse structures while maintaining [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 8
Figure 8. Figure 8: Probability density function of the reconstruction error ( [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]
Figure 7
Figure 7. Figure 7: Variational Graph Auto-encoder (VGAE) reconstructions before and [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 9
Figure 9. Figure 9: Distributions of generated structures for prompts containing specifications for the span (left), rise-to-span ratio (center) and number of bays (right). For [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

69 extracted references · 9 canonical work pages

  1. [1]

    Kaethner, J

    S. Kaethner, J. Burridge, Embodied CO2 of structural frames, The Structural Engineer 90 (5) (2012) 33–40. doi:https://doi.org/10.56330/RDKY7745. 11

    work page doi:10.56330/rdky7745 2012

  2. [2]

    B. C. Paulson, Designing to reduce construction costs, Journal of the Construction Division 102 (4) (1976) 587– 592.doi:10.1061/JCCEAZ.0000639

    work page doi:10.1061/jcceaz.0000639 1976

  3. [3]

    Zhuang, P

    X. Zhuang, P. Zhu, A. Yang, L. Caldas, Machine learning for generative architectural design: Advancements, op- portunities, and challenges, Automation in Construction 174 (2025) 106129.doi:https://doi.org/10.1016/ j.autcon.2025.106129

    arXiv 2025

  4. [4]

    R. E. Weber, C. Mueller, C. Reinhart, Automated floor- plan generation in architectural design: A review of meth- ods and applications, Automation in Construction 140 (2022) 104385.doi:https://doi.org/10.1016/j. autcon.2022.104385

    arXiv 2022

  5. [5]

    C. Du, S. Esser, S. Nousias, A. Borrmann, Text2bim: Generating building models using a large language model- based multi-agent framework, arXiv preprint (2025). arXiv:2408.08054

    arXiv 2025

  6. [6]

    Rombach, A

    R. Rombach, A. Blattmann, D. Lorenz, P. Esser, B. Om- mer, High-resolution image synthesis with latent diffusion models, in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2022, pp. 10684–10695. URLhttps://openaccess.thecvf.com/content/ CVPR2022/html/Rombach_High-Resolution_ Image_Synthesis_With_Latent_Diffusion_...

    2022

  7. [7]

    T. N. Kipf, M. Welling, Variational graph auto-encoders, arXiv preprint (2016).arXiv:1611.07308

    arXiv 2016

  8. [8]

    V . P. Dwivedi, X. Bresson, A generalization of trans- former networks to graphs, arXiv preprint (2020).arXiv: 2012.09699

    arXiv 2020

Show all 69 references
  1. [9]

    K. Shea, R. Aish, M. Gourtovaia, Towards integrated performance-driven generative design tools, Automation in Construction 14 (2) (2005) 253–264.doi:https: //doi.org/10.1016/j.autcon.2004.07.002

    2005 doi

  2. [10]

    Krish, A practical generative design method, Computer-Aided Design 43 (1) (2011) 88–100.doi: https://doi.org/10.1016/j.cad.2010.09.009

    S. Krish, A practical generative design method, Computer-Aided Design 43 (1) (2011) 88–100.doi: https://doi.org/10.1016/j.cad.2010.09.009

    2011 doi

  3. [11]

    Woodbury, Elements of Parametric Design, Routledge, New York, 2010

    R. Woodbury, Elements of Parametric Design, Routledge, New York, 2010

    2010

  4. [12]

    K. Shea, J. Cagan, Languages and semantics of gram- matical discrete structures, Artificial Intelligence for En- gineering Design, Analysis and Manufacturing 13 (4) (1999) 241–251.doi:https://doi.org/10.1017/ S0890060499134012

    1999

  5. [13]

    Veenendaal, P

    D. Veenendaal, P. Block, An overview and comparison of structural form finding methods for general networks, International Journal of Solids and Structures 49 (26) (2012) 3741–3753.doi:https://doi.org/10.1016/ j.ijsolstr.2012.08.008

    2012

  6. [14]

    M. P. Bendsøe, N. Kikuchi, Generating optimal topolo- gies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineer- ing 71 (2) (1988) 197–224.doi:https://doi.org/10. 1016/0045-7825(88)90086-2

    1988

  7. [15]

    W. S. Dorn, R. E. Gomory, H. J. Greenberg, Automatic de- sign of optimal structures, Journal de Mécanique 3 (1964) 25–52

    1964

  8. [16]

    D. E. Goldberg, Genetic Algorithms in Search, Optimiza- tion, and Machine Learning, Addison-Wesley, Reading, MA, 1989

    1989

  9. [17]

    Hajela, E

    P. Hajela, E. Lee, Genetic algorithms in truss topological optimization, International Journal of Solids and Struc- tures 32 (22) (1995) 3341–3357.doi:https://doi. org/10.1016/0020-7683(94)00306-H

    1995 doi

  10. [18]

    N. C. Brown, C. T. Mueller, Design variable analysis and generation for performance-based parametric mod- eling in architecture, International Journal of Architec- tural Computing 17 (1) (2019) 36–52.doi:10.1177/ 1478077118799491

    2019

  11. [19]

    D. P. Kingma, M. Welling, Auto-encoding variational bayes, arXiv preprint (2013).arXiv:1312.6114

    2013 arXiv

  12. [20]

    Danhaive, C

    R. Danhaive, C. T. Mueller, Design subspace learning: Structural design space exploration using performance- conditioned generative modeling, Automation in Con- struction 127 (2021) 103664.doi:https://doi.org/ 10.1016/j.autcon.2021.103664

    2021

  13. [21]

    M. J. J. Bucher, M. A. Kraus, R. Rust, S. Tang, Performance-based generative design for parametric mod- eling of engineering structures using deep conditional generative models, Automation in Construction 156 (2023) 105128.doi:https://doi.org/10.1016/j. autcon.2023.105128

    2023

  14. [22]

    Adadi, M

    A. Adadi, M. Berrada, Peeking inside the black-box: A survey on explainable artificial intelligence (xai), IEEE Access 6 (2018) 52138–52160.doi:https://doi. org/10.1109/ACCESS.2018.2870052

    2018

  15. [23]

    Balmer, S

    V . Balmer, S. V . Kuhn, R. Bischof, L. Salamanca, W. Kaufmann, F. Perez-Cruz, M. A. Kraus, Design space exploration and explanation via conditional varia- tional autoencoders in meta-model-based conceptual de- sign of pedestrian bridges, Automation in Construction 163 (2024) ...

    2024

  16. [24]

    K. S. Ochoa, P. O. Ohlbrock, P. D’Acunto, V . Moosavi, Beyond typologies, beyond optimization: Exploring novel structural forms at the interface of human and machine in- telligence, International Journal of Architectural Comput- ing 19 (3) (2021) 466–490.doi:https://doi.org/10...

    2021

  17. [25]

    Goodfellow, J

    I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, Y . Bengio, Generative adversarial nets, in: Advances in Neural Information Processing Systems, V ol. 27, 2014, pp. 2672–2680. URLhttps://proceedings.neurips. cc/paper_files/paper/2014/f...

    2014

  18. [26]

    Z. Guo, K. Saldana Ochoa, P. D’Acunto, Enhancing struc- tural form-finding through a text-based ai engine coupled with computational graphic statics, in: Innovation, Sus- tainability and Legacy, International Association for Shell and Spatial Structures, Beijing, China, 2022. ...

    2022

  19. [27]

    W. Liao, X. Lu, Y . Huang, Z. Zheng, Y . Lin, Automated structural design of shear wall residential buildings using generative adversarial networks, Automation in Construc- tion 132 (2021) 103931.doi:https://doi.org/10. 1016/j.autcon.2021.103931

    2021

  20. [28]

    Mirra, A

    G. Mirra, A. Pugnale, Comparison between human- defined and ai-generated design spaces for the optimi- sation of shell structures, Structures 34 (2021) 2950– 2961.doi:https://doi.org/10.1016/j.istruc. 2021.09.058

    2021 doi

  21. [29]

    K.-M. M. Tam, P. D’Acunto, N. C. Brown, L. Bleker, T. Van Mele, P. Block, A unified differentiable geomet- ric deep learning message passing framework for inverse structural form-finding, SSRN preprint (2025).doi: https://doi.org/10.2139/ssrn.5316084

    2025 doi

  22. [30]

    Chang, C.-Y

    K.-H. Chang, C.-Y . Cheng, Learning to simulate and design for structural engineering, in: H. D. III, A. Singh (Eds.), Proceedings of the 37th International Conference on Machine Learning, PMLR, 2020, pp. 1426–1436. URLhttps://proceedings.mlr.press/v119/ chang20a.html

    2020

  23. [31]

    Whalen, C

    E. Whalen, C. Mueller, Toward reusable surrogate mod- els: Graph-based transfer learning on trusses, Journal of Mechanical Design 144 (2) (2021) 021704.doi:https: //doi.org/10.1115/1.4052298

    2021 doi

  24. [32]

    Hayashi, M

    K. Hayashi, M. Ohsaki, Graph-based reinforcement learning for discrete cross-section optimization of pla- nar steel frames, Advanced Engineering Informatics 51 (2022) 101512.doi:https://doi.org/10.1016/j. aei.2021.101512

    2022

  25. [33]

    Hayashi, M

    K. Hayashi, M. Ohsaki, M. Kotera, Assembly sequence optimization of spatial trusses using graph embedding and reinforcement learning, Journal of the International As- sociation for Shell and Spatial Structures 63 (4) (2022) 232–240.doi:https://doi.org/10.20898/j.iass. 2022.016

    2022 doi

  26. [34]

    P. Zhao, W. Liao, Y . Huang, X. Lu, Intelligent design of shear wall layout based on graph neural networks, Ad- vanced Engineering Informatics 55 (2023) 101886.doi: https://doi.org/10.1016/j.aei.2023.101886

    2023

  27. [35]

    P. O. Ohlbrock, P. D’Acunto, A computer-aided ap- proach to equilibrium design based on graphic statics and combinatorial variations, Computer-Aided Design 121 (2020) 102802.doi:https://doi.org/10.1016/j. cad.2019.102802

    2020

  28. [36]

    Bleker, R

    L. Bleker, R. Pastrana, P. O. Ohlbrock, P. D’Acunto, Structural form-finding enhanced by graph neural net- works, in: C. Gengnagel, O. Baverel, G. Betti, M. Popescu, M. R. Thomsen, J. Wurm (Eds.), To- wards Radical Regeneration: Design Modelling Sympo- sium, Springer Internati...

    2022

  29. [37]

    Bleker, K.-M

    L. Bleker, K.-M. M. Tam, P. D’Acunto, Logic-informed graph neural networks for structural form-finding, Ad- vanced Engineering Informatics 61 (2024) 102510.doi: https://doi.org/10.1016/j.aei.2024.102510

    2024

  30. [38]

    K.-M. M. Tam, T. Van Mele, P. Block, Trans-topological learning and optimisation of reticulated equilibrium shell structures with automatic differentiation and cw com- plexes message passing, in: Proceedings of IASS Annual Symposia, International Association for Shell and Spat...

    2022

  31. [39]

    K.-M. M. Tam, N. C. Brown, M. Bronstein, T. V . Mele, P. Block, Learning constrained static equilibrium for thrust network inverse form-finding via physics-informed geometric deep learning on cw complexes, Advanced En- gineering Informatics 70 (2026) 103870.doi:https: //doi.or...

    2026

  32. [40]

    V . G. Satorras, E. Hoogeboom, M. Welling, E(n) equiv- ariant graph neural networks, in: M. Meila, T. Zhang (Eds.), Proceedings of the 38th International Conference on Machine Learning, PMLR, 2021, pp. 9323–9332. URLhttps://proceedings.mlr.press/v139/ satorras21a.html

    2021

  33. [41]

    Bleker, P

    L. Bleker, P. D’Acunto, K.-M. M. Tam, Gen- eralized inverse structural form-finding using e(3)- equivariant physics-based graph neural networks, SSRN preprint (2024).doi:https://doi.org/10.2139/ ssrn.5208576

    2024

  34. [42]

    W. Liao, X. Lu, Y . Fei, Y . Gu, Y . Huang, Generative ai de- sign for building structures, Automation in Construction 157 (2024) 105187.doi:https://doi.org/10.1016/ j.autcon.2023.105187. 13

    2024

  35. [43]

    Sohl-Dickstein, E

    J. Sohl-Dickstein, E. Weiss, N. Maheswaranathan, S. Ganguli, Deep unsupervised learning using nonequi- librium thermodynamics, in: F. Bach, D. Blei (Eds.), Proceedings of the 32nd International Conference on Machine Learning, PMLR, Lille, France, 2015, pp. 2256–2265. URLhttps:...

    2015

  36. [44]

    J. Ho, A. Jain, P. Abbeel, Denoising diffusion probabilis- tic models, in: H. Larochelle, M. Ranzato, R. Hadsell, M. Balcan, H. Lin (Eds.), Advances in Neural Informa- tion Processing Systems, Curran Associates, Inc., 2020, pp. 6840–6851. URLhttps://proceedings.neurips. cc/pap...

    2020

  37. [45]

    Y . Song, J. Sohl-Dickstein, D. P. Kingma, A. Kumar, S. Ermon, B. Poole, Score-based generative modeling through stochastic differential equations, in: Proceedings of the International Conference on Learning Representa- tions, 2021. URLhttps://openreview.net/forum?id= PxTIG12RRHS

    2021

  38. [46]

    Ramesh, P

    A. Ramesh, P. Dhariwal, A. Nichol, C. Chu, M. Chen, Hierarchical text-conditional image generation with clip latents, arXiv preprint (2022).arXiv:2204.06125

    2022 arXiv

  39. [47]

    Z. Kong, W. Ping, J. Huang, K. Zhao, B. Catanzaro, Diffwave: A versatile diffusion model for audio synthesis, in: Proceedings of the International Conference on Learning Representations, 2021. URLhttps://openreview.net/forum?id= a-xFK8Ymz5J

    2021

  40. [48]

    X. Li, J. Thickstun, I. Gulrajani, P. S. Liang, T. B. Hashimoto, Diffusion-lm improves controllable text generation, in: S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh (Eds.), Advances in Neural Information Processing Systems, Curran Associates, Inc., 2022, pp. ...

    2022

  41. [49]

    Vignac, I

    C. Vignac, I. Krawczuk, A. Siraudin, B. Wang, V . Cevher, P. Frossard, Digress: Discrete denoising diffusion for graph generation, in: The Eleventh International Confer- ence on Learning Representations, 2023. URLhttps://openreview.net/forum?id= UaAD-Nu86WX

    2023

  42. [50]

    Hoogeboom, V

    E. Hoogeboom, V . G. Satorras, C. Vignac, M. Welling, Equivariant diffusion for molecule generation in 3D, in: K. Chaudhuri, S. Jegelka, L. Song, C. Szepesvari, G. Niu, S. Sabato (Eds.), Proceedings of the 39th International Conference on Machine Learning, PMLR, Baltimore, USA...

    2022

  43. [51]

    L. Wu, C. Gong, X. Liu, M. Ye, Q. Liu, Diffusion-based molecule generation with informative prior bridges, in: S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh (Eds.), Advances in Neural Information Processing Systems, Curran Associates, Inc., 2022, pp. 36533–3654...

    2022

  44. [52]

    Anand, T

    N. Anand, T. Achim, Protein structure and sequence gen- eration with equivariant denoising diffusion probabilistic models, arXiv preprint (2022).arXiv:2205.15019

    2022 arXiv

  45. [53]

    M. Xu, A. S. Powers, R. O. Dror, S. Ermon, J. Leskovec, Geometric latent diffusion models for 3D molecule gener- ation, in: A. Krause, E. Brunskill, K. Cho, B. Engelhardt, S. Sabato, J. Scarlett (Eds.), Proceedings of the 40th International Conference on Machine Learning, PMLR...

    2023

  46. [54]

    C. K. Joshi, X. Fu, Y .-L. Liao, V . Gharakhanyan, B. K. Miller, A. Sriram, Z. W. Ulissi, All-atom diffusion transformers: Unified generative modelling of molecules and materials, in: A. Singh, M. Fazel, D. Hsu, S. Lacoste- Julien, F. Berkenkamp, T. Maharaj, K. Wagstaff, J. Zh...

    2025

  47. [55]

    H.-J. Schek, The force density method for form find- ing and computation of general networks, Computer Methods in Applied Mechanics and Engineering 3 (1) (1974) 115–134.doi:https://doi.org/10.1016/ 0045-7825(74)90045-0

    1974

  48. [56]

    Rampášek, M

    L. Rampášek, M. Galkin, V . P. Dwivedi, A. T. Luu, G. Wolf, D. Beaini, Recipe for a general, powerful, scalable graph transformer, in: S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh (Eds.), Ad- vances in Neural Information Processing Systems, Curran Associates, ...

    2022

  49. [57]

    Lipman, R

    Y . Lipman, R. T. Q. Chen, H. Ben-Hamu, M. Nickel, M. Le, Flow matching for generative modeling, in: The Eleventh International Conference on Learning 14 Representations, 2023. URLhttps://openreview.net/forum?id= PqvMRDCJT9t

    2023

  50. [58]

    J. Yim, A. Campbell, A. Y . K. Foong, M. Gastegger, J. Jiménez-Luna, S. Lewis, V . G. Satorras, B. S. Veel- ing, R. Barzilay, T. Jaakkola, F. Noé, Fast protein back- bone generation with se(3) flow matching, arXiv preprint (2023).arXiv:2310.05297

    2023 arXiv

  51. [59]

    Peebles, S

    W. Peebles, S. Xie, Scalable diffusion models with trans- formers, in: Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), 2023, pp. 4195– 4205

    2023

  52. [60]

    Radford, J

    A. Radford, J. W. Kim, C. Hallacy, A. Ramesh, G. Goh, S. Agarwal, G. Sastry, A. Askell, P. Mishkin, J. Clark, G. Krueger, I. Sutskever, Learning transferable visual models from natural language supervision, in: M. Meila, T. Zhang (Eds.), Proceedings of the 38th International C...

    2021

  53. [61]

    Ilharco, M

    G. Ilharco, M. Wortsman, R. Wightman, C. Gordon, N. Carlini, R. Taori, A. Dave, V . Shankar, H. Namkoong, J. Miller, H. Hajishirzi, A. Farhadi, L. Schmidt, Open- clip (v3.2.0) (2021).doi:https://doi.org/10.5281/ zenodo.17171361

    2021

  54. [62]

    Schuhmann, R

    C. Schuhmann, R. Beaumont, R. Vencu, C. W. Gor- don, R. Wightman, M. Cherti, T. Coombes, A. Katta, C. Mullis, M. Wortsman, P. Schramowski, S. R. Kun- durthy, K. Crowson, L. Schmidt, R. Kaczmarczyk, J. Jitsev, LAION-5b: An open large-scale dataset for training next generation i...

    2022

  55. [63]

    J. Ho, T. Salimans, Classifier-free diffusion guidance, arXiv preprint (2022).arXiv:2207.12598

    2022 arXiv

  56. [64]

    W. Hu, B. Liu, J. Gomes, M. Zitnik, P. Liang, V . Pande, J. Leskovec, Strategies for pre-training graph neural networks, in: International Conference on Learning Representations, 2020. URLhttps://openreview.net/forum?id= HJlWWJSFDH

    2020

  57. [65]

    Vaswani, N

    A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. u. Kaiser, I. Polosukhin, Attention is all you need, in: I. Guyon, U. V . Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, R. Garnett (Eds.), Advances in Neural Information Processing Systems...

    2017

  58. [66]

    D. P. Kingma, J. Ba, Adam: A method for stochastic op- timization, International Conference on Learning Repre- sentations (ICLR) (2015).arXiv:1412.6980

    2015 arXiv

  59. [67]

    V . P. Dwivedi, C. K. Joshi, A. T. Luu, T. Laurent, Y . Ben- gio, X. Bresson, Benchmarking graph neural networks, Journal of Machine Learning Research 24 (43) (2023) 1– 48. URLhttp://jmlr.org/papers/v24/22-0567.html

    2023

  60. [68]

    V . P. Dwivedi, A. T. Luu, T. Laurent, Y . Bengio, X. Bres- son, Graph neural networks with learnable structural and positional representations, in: International Conference on Learning Representations, 2022. URLhttps://openreview.net/forum?id= wTTjnvGphYj

    2022

  61. [69]

    V . Nair, G. E. Hinton, Rectified linear units improve re- stricted boltzmann machines, in: Proceedings of the 27th International Conference on International Conference on Machine Learning, Omnipress, Haifa, Israel, 2010, pp. 807—-814. 15

    2010

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.