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arxiv: 2606.31574 · v1 · pith:KHZZROQAnew · submitted 2026-06-30 · 💻 cs.CV · cs.AI· cs.LG

Temperature Field Reconstruction of Tungsten Monoblock Divertor on EAST using Physics-aware Neural Operator Transformer

Zikang Yan , Xiao Wang , Qingquan Yang , Zhendong Yang , Gaoting Chen , Zehua Chen , Bo Jiang , Jin Tang
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Guosheng Xu
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Pith reviewed 2026-07-01 05:42 UTC · model grok-4.3

classification 💻 cs.CV cs.AIcs.LG
keywords temperature field reconstructionphysics-aware neural operatordivertorgraph attentionSobolev regularizationfusion devicesEAST tokamaktungsten monoblock
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The pith

A physics-aware neural operator transformer reconstructs tungsten monoblock divertor temperatures in real time by embedding heat diffusion rules into graph attention and slicing-based aggregation.

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

The paper introduces the Physics-aware Neural Operator Transformer to model how temperature evolves across the divertor surface in the EAST fusion device. Traditional finite element simulations are accurate but too slow for real-time decisions, so the method replaces them with a learned operator that treats boundary heat fluxes as a graph and uses attention to link nearby physical conditions. A slicing aggregation step and a Sobolev loss that penalizes mismatches between predicted values and their gradients are added to keep the output consistent with heat diffusion. Experiments indicate these additions raise accuracy while keeping the solution physically valid. If the approach holds, operators could monitor and adjust plasma conditions without waiting for full numerical solves.

Core claim

The Physics-aware Neural Operator Transformer models boundary heat-flux relations as a structured graph, applies graph attention to capture spatial physical dependencies, uses a physics-aware neural operator module with slicing to aggregate points under similar conditions and model diffusion, and adds gradient-constrained Sobolev regularization; the resulting predictions of the divertor temperature field show higher accuracy and preserved physical consistency on EAST tungsten monoblock data.

What carries the argument

The Physics-aware Neural Operator Transformer (PNOT), which represents heat-flux boundaries as a graph for attention and applies slicing-based aggregation plus Sobolev loss to enforce diffusion physics.

If this is right

  • Real-time temperature field reconstruction becomes possible for active control of fusion devices.
  • Physical consistency is maintained even when the model runs faster than conventional numerical solvers.
  • Prediction errors decrease when the graph attention and Sobolev terms are included versus baseline operators.
  • The same architecture can be applied to other divertor geometries once the graph is redefined for the new shape.

Where Pith is reading between the lines

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

  • The method could be coupled directly to real-time diagnostic streams to trigger protective actions before melting occurs.
  • Retraining the operator on data from different tokamaks might allow transfer without full re-derivation of the mesh.
  • Because the slicing step groups points by physical similarity, the model may generalize to transient events not seen in training.

Load-bearing premise

Boundary heat-flux relations in the monoblock can be captured by a graph whose attention and slicing steps encode the dominant spatiotemporal heat diffusion.

What would settle it

Compare PNOT outputs against independent high-resolution FEM runs or EAST sensor measurements on a set of previously unseen heat-flux boundary conditions; systematic deviation in temperature values or violation of the heat equation would falsify the claim.

Figures

Figures reproduced from arXiv: 2606.31574 by Bo Jiang, Gaoting Chen, Guosheng Xu, Jin Tang, Qingquan Yang, Xiao Wang, Zehua Chen, Zhendong Yang, Zikang Yan.

Figure 1
Figure 1. Figure 1: Divertor system of the EAST device. (a) Infrared-view image of the interior of the EAST device and schematic of the divertor model; (b) Physical model of the EAST divertor and the corresponding boundary conditions; (c) Cross-sectional mod￾eling configuration of a single divertor monoblock. earning fusion devices the name artificial suns. State-of-the-art fusion facilities worldwide consist of DIII-D 6 , EA… view at source ↗
Figure 2
Figure 2. Figure 2: An overview of our proposed Physics-aware Neural Operator Transformer (PNOT) for temperature field reconstruction on EAST divertor. where ϕg(·) is a learnable embedding network. For heat flux boundary conditions, accurately modeling the spatial variation of boundary heat flux is essential for capturing the thermal response. As shown in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overview of the proposed spatial heat graph propagation framework. (a) Con￾struction of a K-nearest neighbor (KNN) graph from temperature sampling points. (b) Spatial heat graph propagation via neighbor gathering, weighted diffusion, message projection, and gated residual fusion. (c) Graph Sobolev loss for preserving local tem￾perature gradients. both geometric proximity and local heat-flux variation, we d… view at source ↗
Figure 4
Figure 4. Figure 4: Representative samples from the heat conduction dataset with a heat source power of 1 MW: (a) finite element discretization mesh, (b) temperature distribution at the final simulation time, and (c) surface heat flux distribution. MAE(ˆu) = 1 N X N n=1 |uˆ(xn, tn) − u(xn, tn)|. (25) where N is the number of test points, u(x, t) is the ground-truth solution, and uˆ(x, t) is the model’s prediction. 4.2 Impleme… view at source ↗
Figure 5
Figure 5. Figure 5: Temporal evolution of temperature under the 5 MW operating condition the number of blocks to 4 or 5 leads to performance degradation, suggesting that excessive blocks may introduce optimization difficulty or redundancy. Therefore, we use 3 PNOT blocks in our experiments. • Influences of the parameter K on KNN Graphs. As shown in [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the reconstructed temperature fields by the proposed model and the finite element method under different yi conditions at 5 MW. To further evaluate the spatial reconstruction performance, [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
read the original abstract

Accurate modeling of the divertor temperature field is essential for preventing material melting and damage and for extending the service life of fusion devices. However, conventional numerical methods, such as the Finite Element Method (FEM), are computationally expensive and therefore unsuitable for real-time applications. Therefore, a fast and generalizable method is required for real-time reconstruction of the divertor temperature field and subsequent real-time control. To address the above issue, we propose a Physics-aware Neural Operator Transformer (PNOT) to characterize the spatiotemporal evolution of the divertor temperature field. It models boundary heat-flux relations as a structured graph and employs graph attention to explicitly capture spatial physical dependencies. Inspired by physics-aware attention, we further develop a physics-aware neural operator module to aggregate query points with similar physical conditions via slicing and model heat diffusion, while a gradient-constrained Sobolev regularization loss enforces consistency between function values and their derivatives. Experimental results show that these physical constraints improve prediction accuracy while preserving physical consistency. The source code of this paper will be released on https://github.com/Event-AHU/OpenFusion

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a Physics-aware Neural Operator Transformer (PNOT) for reconstructing the spatiotemporal temperature field of the tungsten monoblock divertor on EAST. Boundary heat-flux relations are modeled as a structured graph with graph attention to capture spatial dependencies; a physics-aware neural operator module aggregates query points via slicing to model heat diffusion; and a gradient-constrained Sobolev regularization loss enforces consistency between function values and derivatives. The central claim is that these physical constraints improve prediction accuracy while preserving physical consistency, with source code promised for release.

Significance. If the quantitative claims hold, the method could offer a computationally efficient alternative to FEM for real-time divertor monitoring and control in fusion devices, directly addressing material damage risks. The explicit incorporation of physics via graph attention and Sobolev loss, combined with the code-release commitment, strengthens potential impact and verifiability.

major comments (2)
  1. [Abstract] Abstract: the claim that 'Experimental results show that these physical constraints improve prediction accuracy while preserving physical consistency' is presented without any quantitative metrics, baseline comparisons, dataset details, ablation results, or error tables. This absence makes it impossible to evaluate whether the stated improvements are supported or load-bearing for the central claim.
  2. [Method] Method section (physics-aware neural operator module): the assumption that slicing-based aggregation on a graph-attention model of boundary fluxes will capture the dominant spatiotemporal heat diffusion for the specific tungsten monoblock geometry is not accompanied by targeted validation experiments or sensitivity analysis on the geometry; without such tests the modeling choice remains an unverified modeling decision rather than a demonstrated necessity.
minor comments (1)
  1. [Abstract] Abstract: the GitHub link is supplied but the code is not yet released, preventing immediate reproducibility checks.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. We address each major comment point by point below and indicate where revisions will be made to strengthen the paper.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'Experimental results show that these physical constraints improve prediction accuracy while preserving physical consistency' is presented without any quantitative metrics, baseline comparisons, dataset details, ablation results, or error tables. This absence makes it impossible to evaluate whether the stated improvements are supported or load-bearing for the central claim.

    Authors: We agree that the abstract claim would be stronger with explicit quantitative support. In the revised manuscript we will expand the abstract to include key metrics (e.g., error reductions relative to baselines, ablation results on the physics-aware components, and dataset characteristics) drawn from the experimental section, thereby making the claim directly verifiable within the abstract. revision: yes

  2. Referee: [Method] Method section (physics-aware neural operator module): the assumption that slicing-based aggregation on a graph-attention model of boundary fluxes will capture the dominant spatiotemporal heat diffusion for the specific tungsten monoblock geometry is not accompanied by targeted validation experiments or sensitivity analysis on the geometry; without such tests the modeling choice remains an unverified modeling decision rather than a demonstrated necessity.

    Authors: The slicing aggregation is motivated by the need to group query points that share similar physical boundary conditions, consistent with the underlying heat-diffusion physics. The overall PNOT framework is evaluated on EAST tungsten monoblock data. Nevertheless, we acknowledge that dedicated sensitivity analysis on the geometry and slicing parameters would provide stronger justification. We will add targeted experiments and analysis in the revised method section to demonstrate the necessity of this design choice. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents a standard physics-informed neural operator (PNOT) that trains a graph-attention model plus Sobolev regularization against external simulation or measurement targets for the divertor temperature field. No derivation step reduces by construction to a fitted parameter renamed as a prediction, nor does any load-bearing premise rest on a self-citation chain whose cited result is itself unverified within the paper. The central claim—that added physical constraints improve accuracy while preserving consistency—is an empirical statement evaluated on held-out data, not a self-referential definition or ansatz smuggled via prior work by the same authors. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the effectiveness of a newly introduced neural architecture and regularization term whose performance is asserted via experiments whose details are not visible in the abstract.

axioms (2)
  • domain assumption Boundary heat-flux relations can be represented as a structured graph whose attention mechanism captures the essential spatial physical dependencies of heat diffusion.
    Invoked when the authors state that the model 'models boundary heat-flux relations as a structured graph and employs graph attention to explicitly capture spatial physical dependencies.'
  • domain assumption Aggregating query points with similar physical conditions via slicing and enforcing gradient consistency via Sobolev loss will improve both accuracy and physical consistency.
    Stated in the description of the physics-aware neural operator module and the gradient-constrained loss.
invented entities (1)
  • Physics-aware Neural Operator Transformer (PNOT) no independent evidence
    purpose: To characterize the spatiotemporal evolution of the divertor temperature field with explicit physical constraints.
    New model architecture introduced in the paper; no independent evidence outside this work is mentioned.

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discussion (0)

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Reference graph

Works this paper leans on

44 extracted references · 12 canonical work pages · 4 internal anchors

  1. [1]

    In: Fluids engineering division summer meeting

    Cai, S., Wang, Z., Chryssostomidis, C., Karniadakis, G.E.: Heat transfer pre- diction with unknown thermal boundary conditions using physics-informed neu- ral networks. In: Fluids engineering division summer meeting. vol. 83730, p. V003T05A054. American Society of Mechanical Engineers (2020) 18 Zikang Yan et al

    2020

  2. [2]

    Journal of Machine Learning Research26(300), 1–52 (2025)

    Calvello, E., Kovachki, N.B., Levine, M.E., Stuart, A.M.: Continuum attention for neural operators. Journal of Machine Learning Research26(300), 1–52 (2025)

    2025

  3. [3]

    Advances in neural information processing systems34, 24924–24940 (2021)

    Cao, S.: Choose a transformer: Fourier or galerkin. Advances in neural information processing systems34, 24924–24940 (2021)

    2021

  4. [4]

    Book- boon (2010)

    Causon, D., Mingham, C.: Introductory finite difference methods for PDEs. Book- boon (2010)

    2010

  5. [5]

    Progress in Nuclear Energy188, 105895 (2025)

    Cheng, Q., Sahadath, M.H., Yang, H., Pan, S., Ji, W.: Surrogate modeling of heat transferunderflowfluctuation conditionsusing fourierbasis-deep operator network with uncertainty quantification. Progress in Nuclear Energy188, 105895 (2025)

    2025

  6. [6]

    International Journal of Heat and Mass Transfer258, 128335 (2026)

    Ding, S., Tian, Y., Qin, L., Ma, H., Yang, R.: Physics-informed hierarchical neural operator for solving inverse problem of unsteady heat conduction. International Journal of Heat and Mass Transfer258, 128335 (2026)

    2026

  7. [7]

    Handbook of nu- merical analysis7, 713–1018 (2000)

    Eymard, R., Gallouët, T., Herbin, R.: Finite volume methods. Handbook of nu- merical analysis7, 713–1018 (2000)

    2000

  8. [8]

    Advances in neural information processing systems34, 24048–24062 (2021)

    Gupta, G., Xiao, X., Bogdan, P.: Multiwavelet-based operator learning for differen- tial equations. Advances in neural information processing systems34, 24048–24062 (2021)

    2021

  9. [9]

    arXiv preprint arXiv:2403.03542 (2024)

    Hao, Z., Su, C., Liu, S., Berner, J., Ying, C., Su, H., Anandkumar, A., Song, J., Zhu, J.: Dpot: Auto-regressive denoising operator transformer for large-scale pde pre-training. arXiv preprint arXiv:2403.03542 (2024)

    work page arXiv 2024

  10. [10]

    Hao, Z., Wang, Z., Su, H., Ying, C., Dong, Y., Liu, S., Cheng, Z., Song, J., Zhu, J.: Gnot:Ageneralneuraloperatortransformerforoperatorlearning.In:International conference on machine learning. pp. 12556–12569. PMLR (2023)

    2023

  11. [11]

    In: International conference on computational science

    Hennigh, O., Narasimhan, S., Nabian, M.A., Subramaniam, A., Tangsali, K., Fang, Z., Rietmann, M., Byeon, W., Choudhry, S.: Nvidia simnet™: An ai-accelerated multi-physics simulation framework. In: International conference on computational science. pp. 447–461. Springer (2021)

    2021

  12. [12]

    From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

    Jha, P.K.: From theory to application: A practical introduction to neural operators in scientific computing. arXiv preprint arXiv:2503.05598 (2025)

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  13. [13]

    Nature Reviews Physics3(6), 422–440 (2021)

    Karniadakis, G.E., Kevrekidis, I.G., Lu, L., Perdikaris, P., Wang, S., Yang, L.: Physics-informed machine learning. Nature Reviews Physics3(6), 422–440 (2021)

    2021

  14. [14]

    Journal of Machine Learning Research24(89), 1–97 (2023)

    Kovachki, N., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., Anandkumar, A.: Neural operator: Learning maps between function spaces with applications to pdes. Journal of Machine Learning Research24(89), 1–97 (2023)

    2023

  15. [15]

    arXiv preprint arXiv:2507.20065 (2025)

    Li, X., Li, Z., Kovachki, N., Anandkumar, A.: Geometric operator learning with optimal transport. arXiv preprint arXiv:2507.20065 (2025)

    work page arXiv 2025

  16. [16]

    arXiv preprint arXiv:2205.13671 (2022)

    Li, Z., Meidani, K., Farimani, A.B.: Transformer for partial differential equations’ operator learning. arXiv preprint arXiv:2205.13671 (2022)

    work page arXiv 2022

  17. [17]

    Li, Z., Huang, D.Z., Liu, B., Anandkumar, A.: Fourier neural operator with learned deformationsforpdesongeneralgeometries.JournalofMachineLearningResearch 24(388), 1–26 (2023)

    2023

  18. [18]

    Fourier Neural Operator for Parametric Partial Differential Equations

    Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., Anandkumar, A.: Fourier neural operator for parametric partial differential equa- tions. arXiv preprint arXiv:2010.08895 (2020)

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  19. [19]

    Neural Operator: Graph Kernel Network for Partial Differential Equations

    Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., Anandkumar, A.: Neural operator: Graph kernel network for partial differential equations. arXiv preprint arXiv:2003.03485 (2020)

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  20. [20]

    Advances in Neural Information Processing Systems36, 35836–35854 (2023) Title Suppressed Due to Excessive Length 19

    Li, Z., Kovachki, N., Choy, C., Li, B., Kossaifi, J., Otta, S., Nabian, M.A., Stadler, M., Hundt, C., Azizzadenesheli, K., et al.: Geometry-informed neural operator for large-scale 3d pdes. Advances in Neural Information Processing Systems36, 35836–35854 (2023) Title Suppressed Due to Excessive Length 19

    2023

  21. [21]

    ACM/IMS Journal of Data Science1(3), 1–27 (2024)

    Li, Z., Zheng, H., Kovachki, N., Jin, D., Chen, H., Liu, B., Azizzadenesheli, K., Anandkumar, A.: Physics-informed neural operator for learning partial differential equations. ACM/IMS Journal of Data Science1(3), 1–27 (2024)

    2024

  22. [22]

    Nature machine intelligence3(3), 218–229 (2021)

    Lu, L., Jin, P., Pang, G., Zhang, Z., Karniadakis, G.E.: Learning nonlinear op- erators via deeponet based on the universal approximation theorem of operators. Nature machine intelligence3(3), 218–229 (2021)

    2021

  23. [23]

    Advances in Neural Information Processing Systems38, 150039– 150101 (2026)

    Mousavi, S., Wen, S., Lingsch, L., Herde, M., Raonic, B., Mishra, S.: Rigno: A graph-based framework for robust and accurate operator learning for pdes on ar- bitrary domains. Advances in Neural Information Processing Systems38, 150039– 150101 (2026)

    2026

  24. [24]

    Additive Manufacturing95, 104498 (2024)

    Peng, B., Panesar, A.: Multi-layer thermal simulation using physics-informed neu- ral network. Additive Manufacturing95, 104498 (2024)

    2024

  25. [25]

    arXiv preprint arXiv:2204.11127 (2022)

    Rahman, M.A., Ross, Z.E., Azizzadenesheli, K.: U-no: U-shaped neural operators. arXiv preprint arXiv:2204.11127 (2022)

    work page arXiv 2022

  26. [26]

    In: Dynamics of Earth’s Fluid System, pp

    Reddy, J.N.: An introduction to the finite element method. In: Dynamics of Earth’s Fluid System, pp. 199–226. CRC Press (2026)

    2026

  27. [27]

    IEEE Transactions on Plasma Science46(7), 2672–2676 (2018)

    Shi, B., Yang, C., Yang, Z., Cheng, D., Wang, H., Yang, J., Zhang, H., Qi, J., Zhang, Q., Gong, X., et al.: Study of temperature and heat flux on the east divertor target plate in lhw+ nbi/icrh h-mode. IEEE Transactions on Plasma Science46(7), 2672–2676 (2018)

    2018

  28. [28]

    Chinese Physics Letters34(9), 095201 (2017)

    Shi, B., Yang, Z.D., Zhang, B., Yang, C., Gan, K.F., Chen, M.W., Yang, J.H., Zhang, H., Qi, J.L., Gong, X.Z., et al.: Heat flux on east divertor plate in h-mode with lhcd/lhcd+ nbi. Chinese Physics Letters34(9), 095201 (2017)

    2017

  29. [29]

    In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition

    Sun, D., Zhou, X., Wang, X., Si, H., Lyu, W., Tang, J., Luo, B.: Nestor: A nested moe-based neural operator for large-scale pde pre-training. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 6147– 6156 (2026)

    2026

  30. [30]

    arXiv preprint arXiv:2111.13802 (2021)

    Tran, A., Mathews, A., Xie, L., Ong, C.S.: Factorized fourier neural operators. arXiv preprint arXiv:2111.13802 (2021)

    work page arXiv 2021

  31. [31]

    Computer Methods in Applied Mechanics and Engineering404, 115783 (2023)

    Tripura,T.,Chakraborty,S.:Waveletneuraloperatorforsolvingparametricpartial differential equations in computational mechanics problems. Computer Methods in Applied Mechanics and Engineering404, 115783 (2023)

    2023

  32. [32]

    Advances in Neural Information Pro- cessing Systems30(2017)

    Vaswani,A.,Shazeer,N.,Parmar,N.,Uszkoreit,J.,Jones,L.,Gomez,A.N.,Kaiser, Ł., Polosukhin, I.: Attention is all you need. Advances in Neural Information Pro- cessing Systems30(2017)

    2017

  33. [33]

    Advances in Neural Information Processing Systems38, 31498–31527 (2026)

    Wang, H., Xin, H., Wang, J., Yang, X., Zha, F., Jiang, Y., et al.: Mixture-of- experts operator transformer for large-scale pde pre-training. Advances in Neural Information Processing Systems38, 31498–31527 (2026)

    2026

  34. [34]

    In: International Conference on Neural Information Processing

    Wang, T., Wang, C.: Latent neural operator pretraining for solving time-dependent pdes. In: International Conference on Neural Information Processing. pp. 163–178. Springer (2024)

    2024

  35. [35]

    Machine Intelligence Research20(4), 447–482 (2023)

    Wang, X., Chen, G., Qian, G., Gao, P., Wei, X.Y., Wang, Y., Tian, Y., Gao, W.: Large-scale multi-modal pre-trained models: A comprehensive survey. Machine Intelligence Research20(4), 447–482 (2023)

    2023

  36. [36]

    arXiv preprint arXiv:2404.09516 (2024)

    Wang, X., Wang, S., Ding, Y., Li, Y., Wu, W., Rong, Y., Kong, W., Huang, J., Li, S., Yang, H., et al.: State space model for new-generation network alternative to transformers: A survey. arXiv preprint arXiv:2404.09516 (2024)

    work page arXiv 2024

  37. [37]

    arXiv preprint arXiv:2508.03776 (2025) 20 Zikang Yan et al

    Wang,X.,Yan,Z.,Si,H.,Yang,Z.,Yang,Q.,Sun,D.,Lyu,W.,Tang,J.:Revisiting heat flux analysis of tungsten monoblock divertor on east using physics-informed neural network. arXiv preprint arXiv:2508.03776 (2025) 20 Zikang Yan et al

    work page arXiv 2025

  38. [38]

    Advances in Neural Information Pro- cessing Systems38, 155423–155501 (2026)

    Wen, S., Kumbhat, A., Lingsch, L., Mousavi, S., Zhao, Y., Chandrashekar, P., Mishra, S.: Geometry aware operator transformer as an efficient and accurate neu- ral surrogate for pdes on arbitrary domains. Advances in Neural Information Pro- cessing Systems38, 155423–155501 (2026)

    2026

  39. [39]

    arXiv preprint arXiv:2301.12664 (2023)

    Wu, H., Hu, T., Luo, H., Wang, J., Long, M.: Solving high-dimensional pdes with latent spectral models. arXiv preprint arXiv:2301.12664 (2023)

    work page arXiv 2023

  40. [40]

    Transolver: A Fast Transformer Solver for PDEs on General Geometries

    Wu, H., Luo, H., Wang, H., Wang, J., Long, M.: Transolver: A fast transformer solver for pdes on general geometries. arXiv preprint arXiv:2402.02366 (2024)

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  41. [41]

    International Journal of Heat and Mass Transfer217, 124671 (2023)

    Xu, J., Wei, H., Bao, H.: Physics-informed neural networks for studying heat trans- fer in porous media. International Journal of Heat and Mass Transfer217, 124671 (2023)

    2023

  42. [42]

    Fusion Engineering and Design152, 111448 (2020)

    Yang, Z., He, P., Yan, H., Bin, Z., Shuangbao, S., Wang, F., Chen, M., Jia, G., Gong, X.: The development of a three-dimensional finite element method code for the heat flux analysis of tungsten monoblock divertor on east. Fusion Engineering and Design152, 111448 (2020)

    2020

  43. [43]

    International Communications in Heat and Mass Transfer175, 111125 (2026)

    Yuan, J., Zeng, L., Gui, Y., Shi, Y., Xia, B., Wei, D.: A transient heat conduction prediction method for complex structures based on neural operators. International Communications in Heat and Mass Transfer175, 111125 (2026)

    2026

  44. [44]

    Physics of Fluids34(11) (2022)

    Zhang, B., Wu, G., Gu, Y., Wang, X., Wang, F.: Multi-domain physics-informed neural network for solving forward and inverse problems of steady-state heat con- duction in multilayer media. Physics of Fluids34(11) (2022)

    2022