Pith. sign in

REVIEW 3 major objections 5 minor 26 references

A Structural Dynamics Graph World Model: Unified Modeling, Constrained Rollout, and Interpretable Calibration

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read A structural graph world model can keep predictions accurate when free neural models collapse.

desk verdict A genuinely useful framework for auditable hybrid modeling, but the headline robustness gain in Table 15 is confounded by a changing test set, so the paper's own evidence undercuts its most striking claim. read the letter →

arxiv 2608.08689 v1 pith:JHWY27R6 submitted 2026-08-09 cs.AI

Wei Wang , Yaosen Chen , Han Yang , Yuegen Liu , Mingli Luo , Xinxin Jiao , Xuming Wen , Ming Liu This is my paper · ORCID
classification cs.AI
keywords graphworldmodelstructuraldynamicsexecutablecontractboundedresidualconstraintprojectionfloodforecastingdistributionshiftauditability
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

SD-GWM, a structural dynamics graph world model, tries to establish that state evolution in complex systems can be organized as an executable contract: nodes declare their own dynamics, edges declare graph-coupled dynamics, an optional bounded residual absorbs learnable error, and a global projection enforces hard constraints. The paper's wager is that this division of labor yields a world model that is semantically faithful to existing domain solvers, auditable through execution traces, and safer under distribution shift than models that learn everything in one black box. A sympathetic reader should care because the claim is concrete: on real USGS streamflow during a 254-day extreme-flood shift, persistence and all neural baselines collapse to 892–3007 cfs RMSE at 90 minutes while SD-GWM holds at 108 cfs, an 8–28x gain. The paper is careful to say this is not universal accuracy superiority: persistence ties or beats SD-GWM on calm data, and the bounded residual helps only when the declared backbone has systematic bias.

What carries the argument

The load-bearing object is the executable structural contract: a dynamic world is a typed property graph whose state update is composed as $x_{t+\Delta t} = \Pi_{\Omega_{t+\Delta t}} T_{\Delta t}(x_t, G_t, c_t; F)$, where $F$ is the weighted composition of a declarative self-dynamics operator $f_S$, a declarative graph-coupled operator $f_N$, and a dimension-wise soft-clipped bounded residual $B_\varepsilon(f_R)$. The composition operator $C$, the one-step transition $T$, and the global projection $\Pi_\Omega$ each have default implementations and admissible families, so domain solvers plug in without being dismantled. The projection finishes every step by mapping the candidate state back into the feasible set, which guarantees constraint preservation rather than accuracy; the bound $\varepsilon$ on the residual fixes how much the learnable part may change the state; and component-level execution traces are retained so that fault localization is done by counterfactually repairing each candidate and comparing error reduction rather than by post-hoc explanation.

What would settle it

Run the same USGS comparison on a 254-day training set drawn entirely from calm, in-distribution flow, keeping the test blocks identical: if neural baselines then match or beat SD-GWM, the 8–28x gain is largely a data-volume effect, not structural robustness. Alternatively, hold training volume at 18 days and test on a shifted 254-day set; if SD-GWM's margin shrinks, the mechanism depends on seeing the shift regime.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that separating the dynamics field into declared mechanism terms (self-dynamics S and neighbor graph-coupled N), an optional bounded residual R, and a feasibility projection Π_Ω turns a graph world model into a compilable, constrainable, auditable loop while preserving, under stated assumptions, the semantics of the source models it embeds. The paper proves four theory properties with explicit boundaries: exact computational embedding of System Dynamics when R is off, invariance of the feasible set under correct projection, a conditional recursive error inequality under local Lipschitz assumptions, and a single-step upper bound on the residual's contribution. Empirically, on eight frozen research questions, it reports bit-for-bit semantic preservation in compilation, zero constraint violation in semi-synthetic and real-data rollouts, perfect counterfactual fault localization, and the 8–28x robustness gain under the 254-day extreme-flood shift, while also reporting the honest counter-results: persistence and linear win on the calm 29-day period, and the bounded residual is neutral or slightly harmful when the backbone has little bias.

Load-bearing premise

The central claim rests on treating the 254-day USGS comparison as evidence of robustness under distribution shift, even though it confounds a 14x increase in training data with the onset of extreme floods.

Editorial extensions

If this is right

  • Rule-based, stock-flow, ODE, and solver models can coexist in one prediction loop with learned components, with each mechanism's responsibility auditable from step-level traces.
  • Deployed predictions satisfy declared hard constraints (non-negativity, conservation, capacity) over long horizons, by construction of the projection, even when candidate states are illegal.
  • The bounded residual improves accuracy by about half under backbone bias and neither helps nor hurts materially when bias is small, so adding the residual is a conditional design choice, not a free accuracy win.
  • Under distribution shift containing extremes, the declarative backbone degrades far more gracefully than persistence, linear, and neural baselines, with an 8–28x smaller 90-minute RMSE on the USGS flood data.
  • The same declared operator family, with domain-specific graph-coupled dynamics and feasible region, transfers across mass-conservation and charge-conservation systems, preserving conservation where neural baselines violate it in 96–100% of steps.

Reading between the lines

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

  • The headline 8–28x gain mixes a 14x increase in training data with the onset of extreme floods; a controlled comparison varying data volume while holding distribution fixed would isolate whether the robustness is structural or partly due to sample size, and the paper explicitly does not claim that control.
  • If the mechanism is right, its value should show most in small-sample, high-regime-shift operational settings; in large homogeneous datasets free networks may catch up in accuracy, but the structural contract would still retain constraint guarantees and auditability.
  • A testable extension would run the same S/N/R contract on more conservation laws (momentum, energy) and on full networks rather than subgraphs; the paper's RQ8 framework makes that a matter of declaring N and Ω per domain.
  • The perfect top-1 fault localization may be an artifact of the six preset fault classes and the repair budget; probing with mixed or unseen fault types would reveal whether trace counterfactuals hold beyond the tested suite.
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

3 major / 5 minor

Summary. The paper proposes SD-GWM, a Structural Dynamics Graph World Model, which decomposes the one-step transition into self-dynamics S, neighbor graph-coupled dynamics N, an optional bounded residual R, and a global feasibility projection ΠΩ. The framework is formalized through Definitions 1–12 and four theory propositions (computational embedding of System Dynamics, feasible-set invariance, conditional error recursion, residual amplitude bound), each with explicit assumptions and declared proof levels. The experimental section tests eight research questions on synthetic, semi-synthetic, real USGS streamflow, and two conservation-law domains (water distribution and power transmission). The headline empirical claim is that on a 254-day extreme-flood evaluation, persistence and neural baselines collapse while SD-GWM maintains 108 cfs RMSE, an 8–28× gain. The paper repeatedly stresses that it claims feasibility and auditability rather than universal accuracy superiority.

Significance. The manuscript's main contribution is a design pattern: an executable structural contract that lets heterogeneous mechanism assets (rules, ODEs, solvers, learned residuals) compose in a fixed order with a bounded learnable residual and a projection finish, providing auditability and hard-constraint preservation. Strengths include the explicit assumption boundaries on the four propositions, honest reporting of negative results (local residual weaker than global, bounded and unbounded residuals performing comparably, persistence beating SD-GWM in calm periods), a reproducible artifact manifest with SHA-256 hashes, bit-for-bit RQ1 results, and counterfactual fault localization with top-1 accuracy 1.0. If the empirical robustness claims were supported by cleaner experiments, the framework would be a useful reference architecture for auditable hybrid modeling. However, the most striking empirical result, the 8–28× gain under flood shift, is confounded as the paper itself concedes, and the RQ6 and RQ8 testbeds contain substantial circularity. The formal framework is valuable; the empirical assertions of distribution-shift robustness need re-analysis.

major comments (3)
  1. [§6.7, Table 15] The 8–28× gain claimed in the abstract and Section 1 is not supported as an out-of-distribution robustness result because the comparison changes training data volume and test blocks simultaneously. Persistence is a training-free model, yet its 90-min RMSE changes from 22.8 cfs in the 18-day train column to 892.0 cfs in the 254-day train column, and its 15-min RMSE changes from 13.0 to 869.2. Such a change can only occur if the 254-day column is evaluated on different test blocks from the 18-day column (the paper confirms the 254-day data contain extreme-flood segments). Consequently, the baseline collapse is explained at least in part by the presence of flood peaks in the new test set, and SD-GWM's advantage may reflect that it was trained on 254 days that include flood segments. The manuscript concedes this in Section 6.7 ('cannot be directly attributed to data-volume increase alone') and Section 8 ('confounds data volume and distribution'), yet the abstract and Section 1 still present the 8–28× gain as headline evidence of robustness under distribution shift. Please hold the test blocks fixed across training-set sizes—for example, evaluate both 18-day and 254-day trained models on the same calm and the same flood blocks—or relegate the 254-day comparison to a clearly labeled confounded pilot and run a controlled same-test comparison before claiming robustness.
  2. [§6.6 and Appendix B] RQ6's semi-synthetic flood testbed is generated from mechanisms that match the declarative backbone by design: the testbed implements rainfall–runoff–confluence–pump–backwater dynamics using fill_gated_flow and threshold_overflow, and the SD-GWM contract declares exactly these operator families for S and N. The calibration then fits the backbone's continuous parameters to data generated by the same functional forms, so the comparison is a self-consistency check. The paper acknowledges this (Section 6.6: 'SD-GWM's advantage comes partly from its mechanism structure correctly reflecting the testbed's ... dynamics'), but RQ6 is still presented as evidence that declarative fixed mechanisms compete with neural baselines in a realistic setting. To make this load-bearing, generate the testbed with a genuinely different simulator (e.g., SWMM or a higher-fidelity process model) than the declared S/N operators, or explicitly restrict the RQ6 claim to integration and compilation rather than forecasting competitiveness.
  3. [§6.8, Table 16 and 'Circularity and the grid reference solution'] The RQ8 power-transmission result is circular on the RMSE dimension: the reference phase angles are generated by DC power flow (Bθ=P), and SD-GWM's declared N is conservative_flow with P_ij=(θ_i-θ_j)/x_ij, which is the same DC-power-flow coupling. The paper discloses this in the 'Circularity and the grid reference solution' paragraph and labels the series a reference solution, which is honest. However, the cross-conservation-law generalization claim in Section 8 states that 'the same declared operator family is no worse than baselines in multi-step prediction under two conservation laws' using both domains. Since the grid RMSE comparison is circular, the only non-circular support for generalization is the water domain (EPANET mass conservation vs. linear storage routing) plus the KCL-violation rate, which is a deterministic structural property. Please separate the grid RMSE from the generalization claim: present the grid result as a conservation-consistency check only, and base the 'no worse in prediction' generalization claim on the water domain or on an independent grid truth (e.g., AC power flow or a different linearization).
minor comments (5)
  1. [Section 1, Table 5, Appendix A] The experiments are described as 'pre-registered' in several places, but Appendix A explains that the freezing is self-attested and not archived with a third party; consider using 'pre-frozen' or 'pre-declared' consistently to avoid implying OSF-style registration.
  2. [Table 15] The column headers '18-day train' and '254-day train' do not indicate that the evaluation test blocks differ between the two columns; add a note that the test blocks change, or better, report per-block RMSEs so the confound between data volume and test composition is immediately visible.
  3. [Section 5.2] The phrase 'absolutely monotone ℓ2 norm' is non-standard; since the intended meaning is the usual ℓ2 norm with monotonicity under componentwise absolute values, consider restating it in those terms for readability.
  4. [Section 8] The phrase 'A key counter-evidence' is misleading because the 254-day comparison is offered in support of robustness, not against it; consider 'A key observation' or 'Supporting evidence, with an admitted confound'.
  5. [Section 6.6] The text says SD-GWM is 'significantly better than free neural baselines' for RQ6 without reporting a paired statistical test for that table; given that RQ7's comparable comparisons have Holm-corrected p=0.053, please ensure any use of 'significantly' is backed by the reported statistics.

Circularity Check

1 steps flagged · score 4.0 of 10

One self-definitional validation on the ACTIVSg2000 grid is explicitly disclosed but remains a same-family construction; the central structural-contract claims otherwise rest on independent evidence, so circularity is partial, not pervasive.

  1. self definitional [Section 6.8, 'Circularity and the grid reference solution' (RQ8, ACTIVSg2000)]
    "The grid phase-angle series is generated by DC power flow (Bθ=P), and the SD-GWM backboneNis the DC-power-flow coupling conservative_flow; the backbone and the reference-solution generator are therefore of the same family. We disclose this openly and note three mitigations."

    The RQ8 grid validation is not an independent test of the declarative mechanism: the reference truth is produced by DC power flow, and SD-GWM's declared edge operator is the same DC-power-flow coupling. Consequently, SD-GWM's zero KCL violation on the grid is guaranteed by construction rather than discovered empirically. The paper acknowledges this and labels the grid result a consistency check, with mitigations (the bounded residual does not help on the grid; the water domain has a genuine fidelity gap; 'reference solution' rather than 'ground truth'). Those mitigations reduce the overclaiming but do not remove the identity between the declared N and the data generator, so the grid half of the cross-conservation-law generalization claim reduces to the paper's own construction.

full rationale

The strongest circularity is confined to the ACTIVSg2000 half of RQ8: the reference series is generated by DC power flow and the SD-GWM backbone is the same DC-power-flow coupling, so zero KCL violation for SD-GWM is a self-definitional outcome. The paper explicitly discloses this in the subsection titled 'Circularity and the grid reference solution,' lists three mitigations, and asks the reader to read the grid result as a conservation-consistency check rather than an accuracy claim; this disclosure is genuine and keeps the issue partial rather than concealed. I do not count the RQ7 254-day comparison as circularity: the abrupt change in persistence RMSE (22.8 to 892.0 cfs at 90 min) shows that the test blocks changed between the 18-day and 254-day columns, but that is a confounding of data volume with distribution shift, not a reduction of a predicted quantity to an equation that defined it. The paper itself admits this confound in Section 6.7 and again in Section 8, so it is a correctly flagged validity limitation rather than a circular derivation. RQ1-RQ3 and Propositions 1-4 are implementation-consistency checks or conditional proofs with stated assumptions; they are not presented as independent predictions, so their near-tautological form is not a circularity problem. No load-bearing self-citation chain appears, and no uniqueness theorem is imported from the authors' prior work. The water-domain RQ8 result and the RQ6/RQ7 comparisons provide independent content, so the paper's central framework claim remains non-circular. Overall, the circularity score is 4: one self-definitional validation exists and is admitted, but it does not force the central derivation.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The paper's guarantees are conditional on unmeasured local Lipschitz constants, the completeness of the declared constraint set, and the validity of synthetic references. The empirical headline results depend on hand-chosen residual budgets, calibration procedures, and deliberate backbone bias levels, so the contribution is an engineering contract rather than a parameter-free derivation.

free parameters (5)
  • composition weights alpha_S, alpha_N, alpha_R = default 1; calibrated in some experiments
    Eq. (4) weights the three generative terms; the paper allows empirical-risk-minimization calibration, so these are tunable and affect the balance of mechanisms.
  • residual budget epsilon = 0.05 (RQ5), 5% node capacity (RQ6), 10% training std (RQ7/RQ8)
    Dimension-wise bound of B_epsilon is a design parameter chosen by hand; the RQ5 result depends on epsilon=0.05 not being binding, and the RQ7 improvement depends on the 10% budget.
  • per-station/per-node decay, baseflow bias, propagation weights = fitted by L-BFGS-B from training transitions
    RQ7/RQ8 calibrate these continuous parameters to data; they are fitted values, not derived.
  • integer routing delays = grid-searched over {1,2,4,8,16,32,64} on training MSE
    RQ7/RQ8 select delays per edge by fitting to training-period single-step error, an additional fitted discrete parameter.
  • RQ5 backbone spring error and regime coefficients = e.g., spring weight -1.5 vs truth -2.0; alpha per regime
    The systematic bias magnitude is chosen by the authors to make the residual useful; the 50% RMSE reduction result is specific to this design.
assumptions (6)
  • standard math Euclidean projection onto a non-empty closed convex set is non-expansive
    Used in Proposition 3 proof sketch and for the interval-clipping projections in RQ1-RQ8.
  • domain assumption The reference truth trajectory lies within the feasible set, so projection does not move it
    Assumption of Proposition 3; if the truth violates undeclared constraints, the error recursion loses its anchor.
  • domain assumption Local Lipschitz continuity of the one-step mapping, composition, and projection on the examined trajectory
    Propositions 3 and 4 rely on local Lipschitz gains Lk, a_R, L_R, K_Pi that are not measured or verified in experiments.
  • domain assumption The declared constraint set Omega captures all real-world legality requirements
    Proposition 2 and Section 7.3 state that projection only guarantees legality within the declared set; omitted constraints are not discovered.
  • domain assumption The grid DC power flow (B theta = P) is an acceptable reference solution
    Section 6.8 uses DC-PF to generate the reference phase angles; the paper labels it a reference solution rather than ground truth, acknowledging the same-family circularity.
  • ad hoc to paper Injected fault classes and their counterfactual repairs are complete and exact
    RQ4 defines six faults and repairs them by the inverse operation; the top-1=1.0 result depends on this exact reversibility.

how reviews work

0 comments
Cite this review

Pith. "Pith review of A Structural Dynamics Graph World Model: Unified Modeling, Constrained Rollout, and Interpretable Calibration." pith.science (2026). https://pith.science/paper/JHWY27R6

@misc{pith2026260808689,
  author       = {Pith},
  title        = {Pith review of: A Structural Dynamics Graph World Model: Unified Modeling, Constrained Rollout, and Interpretable Calibration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JHWY27R6}},
  note         = {Machine review of arXiv:2608.08689}
}
read the original abstract

The state evolution of a complex system arises jointly from object laws, relational propagation, domain conservation, and unmodeled error. Forcing all sources into one black box makes mechanism attribution and constraint preservation unauditable; forcing every mechanism into one equation family discards mature domain solvers. We propose SD-GWM, a Structural Dynamics Graph World Model as an executable structural contract: nodes declare self-dynamics S, edges declare neighbor graph-coupled dynamics N---both fixed-form mechanism assets (rules, ODEs, solvers) calibrating only authorized parameters. An optional bounded residual R concentrates learnability, while a global projection maps states to feasibility, enforcing constraints without guaranteeing accuracy gains. On eight pre-registered research questions, SD-GWM delivers (i) heterogeneous integration: rules and solvers plug in natively; (ii) semantic fidelity: disabling R preserves source semantics bit-for-bit, with four theory properties under explicit proof/empirical boundaries; (iii) auditable governance: stepwise traces enable counterfactual fault localization (top-1 = 1.0) without post-hoc approximations. On a semi-synthetic flood testbed and USGS streamflow, SD-GWM reduces constraint violations to floating-point tolerance in analytical tests and to zero in semi-synthetic and real-data cases. Persistence matches SD-GWM in calm periods, but during a 254-day extreme-flood shift persistence and all neural baselines collapse (90-min RMSE 892-3007 cfs) while SD-GWM holds at 108 cfs (8-28x gain). The bounded residual cuts RMSE ~50% only under backbone bias. We position SD-GWM not as a universally superior forecaster, but as a verifiable substrate for auditable, constraint-safe spatiotemporal mining.

Figures

Figures reproduced from arXiv: 2608.08689 by the authors.

Figure 1
Figure 1. The two-layer unified framework of SD-GWM. The upper layer retains heterogeneous [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. The computational mapping of System Dynamics constructs into [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Summary of RQ1–RQ5 results. RQ1 compilation error and RQ2 composition violation [PITH_FULL_IMAGE:figures/full_fig_p021_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Semi-synthetic flood testbed. The latent oracle state and the noisy observation are [PITH_FULL_IMAGE:figures/full_fig_p035_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

26 extracted references · 17 canonical work pages

  1. [1]

    World Models

    David Ha and Jürgen Schmidhuber. World Models. arXiv preprint, 2018. arXiv:1803.10122

    arXiv 2018

  2. [2]

    Learning Latent Dynamics for Planning from Pixels

    Danijar Hafner, Timothy Lillicrap, Ian Fischer, Ruben Villegas, David Ha, Honglak Lee, and James Davidson. Learning Latent Dynamics for Planning from Pixels. Proceedings of the 36th International Conference on Machine Learning, PMLR 97:2555–2565, 2019

    work page 2019

  3. [3]

    Battaglia, Razvan Pascanu, Matthew Lai, Danilo Jimenez Rezende, and Koray Kavukcuoglu

    Peter W. Battaglia, Razvan Pascanu, Matthew Lai, Danilo Jimenez Rezende, and Koray Kavukcuoglu. Interaction Networks for Learning about Objects, Relations and Physics. Advances in Neural Information Processing Systems 29:4502–4510, 2016

    work page 2016

  4. [4]

    Battaglia, Jessica B

    Peter W. Battaglia, Jessica B. Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, et al. Relational Inductive Biases, Deep Learning, and Graph Networks. arXiv preprint, 2018. arXiv:1806.01261

    arXiv 2018

  5. [5]

    Schoenholz, Patrick F

    Justin Gilmer, Samuel S. Schoenholz, Patrick F. Riley, Oriol Vinyals, and George E. Dahl. Neural Message Passing for Quantum Chemistry. Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1263–1272, 2017

    work page 2017

  6. [6]

    Kipf and Max Welling

    Thomas N. Kipf and Max Welling. Semi-Supervised Classification with Graph Con- volutional Networks. 5th International Conference on Learning Representations, 2017. arXiv:1609.02907

    arXiv 2017

  7. [7]

    Proceedings of the 35th International Conference on Machine Learning, PMLR 80:4470–4479, 2018

    Alvaro Sanchez-Gonzalez, Nicolas Heess, Jost Tobias Springenberg, Josh Merel, Martin Riedmiller, RaiaHadsell, andPeterBattaglia.GraphNetworksasLearnablePhysicsEngines for Inference and Control. Proceedings of the 35th International Conference on Machine Learning, PMLR 80:4470–4479, 2018

    work page 2018

  8. [8]

    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. Proceedings of the 37th International Conference on Machine Learning, PMLR 119:8459–8468, 2020

    work page 2020

Show all 26 references
  1. [9]

    Temporal Graph Networks for Deep Learning on Dynamic Graphs

    Emanuele Rossi, Ben Chamberlain, Fabrizio Frasca, Davide Eynard, Federico Monti, and Michael Bronstein. Temporal Graph Networks for Deep Learning on Dynamic Graphs. arXiv preprint, 2020. arXiv:2006.10637

    2020 arXiv

  2. [10]

    Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints

    Marc Finzi, Ke Alexander Wang, and Andrew Gordon Wilson. Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints. Advances in Neural Information Processing Systems 33:13880–13889, 2020

    2020

  3. [11]

    Forrester

    Jay W. Forrester. Industrial Dynamics. MIT Press, 1961

    1961

  4. [12]

    Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks

    Samy Bengio, Oriol Vinyals, Navdeep Jaitly, and Noam Shazeer. Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks. Advances in Neural Information Pro- cessing Systems 28:1171–1179, 2015

    2015

  5. [13]

    Graph World Model

    Tao Feng, Yexin Wu, Guanyu Lin, and Jiaxuan You. Graph World Model. Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:16931–16955, 2025

    2025

  6. [14]

    Graph World Models: Concepts, Taxonomy, and Future Directions

    Jiawei Liu, Senqiao Yang, Mingjun Wang, Yu Wang, and Bei Yu. Graph World Models: Concepts, Taxonomy, and Future Directions. arXiv preprint, 2026. arXiv:2604.27895

    2026 arXiv

  7. [15]

    Understanding Rollout Error in Graph World Models

    Xinyuan Song and Zekun Cai. Understanding Rollout Error in Graph World Models. arXiv preprint, 2026. arXiv:2606.27780

    2026 arXiv

  8. [16]

    Learning Physical Constraints with Neural Projec- tions

    Shuqi Yang, Xingzhe He, and Bo Zhu. Learning Physical Constraints with Neural Projec- tions. Advances in Neural Information Processing Systems 33:5178–5189, 2020. 36

    2020

  9. [17]

    Spatio-Temporal Graph Convolutional Net- works: A Deep Learning Framework for Traffic Forecasting

    Bing Yu, Haoteng Yin, and Zhanxing Zhu. Spatio-Temporal Graph Convolutional Net- works: A Deep Learning Framework for Traffic Forecasting. Proceedings of the 27th In- ternational Joint Conference on Artificial Intelligence (IJCAI), pages 3634–3640, 2018. arXiv:1709.04875

    2018 arXiv

  10. [18]

    Long Short-Term Memory

    Sepp Hochreiter and Jürgen Schmidhuber. Long Short-Term Memory. Neural Computation, 9(8):1735–1780, 1997

    1997

  11. [19]

    T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction

    Ling Zhao, Yujiao Song, Chao Zhang, Yu Liu, Pu Wang, Tao Lin, Min Deng, and Haifeng Li. T-GCN: A Temporal Graph Convolutional Network for Traffic Prediction. IEEE Trans- actions on Intelligent Transportation Systems, 21(9):3848–3858, 2020. arXiv:1811.05320

    2020 arXiv

  12. [20]

    Physics-informed neural net- works: A deep learning framework for solving forward and inverse problems involving non- linear partial differential equations

    Maziar Raissi, Paris Perdikaris, and George Em Karniadakis. Physics-informed neural net- works: A deep learning framework for solving forward and inverse problems involving non- linear partial differential equations. Journal of Computational Physics, 378:686–707, 2019

    2019

  13. [21]

    Lagrangian Neural Networks

    Miles Cranmer, Sam Greydanus, Stephan Hoyer, Peter Battaglia, David Spergel, and Shirley Ho. Lagrangian Neural Networks. arXiv preprint, 2020. arXiv:2003.04630. (ICLR 2020 Deep Differential Equations Workshop.)

    2020 arXiv

  14. [22]

    GNNEx- plainer: Generating Explanations for Graph Neural Networks

    Rex Ying, Dylan Bourgeois, Jiaxuan You, Marinka Zitnik, and Jure Leskovec. GNNEx- plainer: Generating Explanations for Graph Neural Networks. Advances in Neural Informa- tion Processing Systems 32:9240–9251, 2019

    2019

  15. [23]

    Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR

    Sandra Wachter, Brent Mittelstadt, and Chris Russell. Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR. Harvard Journal of Law & Technology, 31(2):841–887, 2018

    2018

  16. [24]

    Vrachimis, Demetrios G

    Stelios G. Vrachimis, Demetrios G. Eliades, and Marios M. Polycarpou. Benchmark Leakage Detection Dataset (BattLeDIM) for Water Distribution Networks. In Proceedings of the 1st International WDSA/CCWI 2018 Joint Conference, Kingston, Ontario, Canada, 2018. (L- TOWN network, KI...

    2018

  17. [25]

    Lewis A. Rossman. EPANET 2 Users Manual. Water Supply and Water Resources Division, National Risk Management Research Laboratory, U.S. Environmental Protection Agency, Cincinnati, OH, EPA/600/R-00/057, 2000

    2000

  18. [26]

    Birchfield, Ti Xu, Kathleen M

    Adam B. Birchfield, Ti Xu, Kathleen M. Gegner, Komal S. Shetye, and Thomas J. Overbye. Grid Structural Characteristics as Validation Targets for Synthetic Transmission Networks. IEEE Transactions on Power Systems, 33(6):7211–7217, 2018. (ACTIVSg synthetic Texas grids, Texas A&...

    2018

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.