PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics | Paper Citation Record

Observation eb55cb24-5685-411d-843e-a0b57deba0c8 · outbound

This paper cites Neural operators for accelerating scientific simulations and design.Nature Reviews Physics, 6(5):320–328.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Neural operators for accelerating scientific simulations and design.Nature Reviews Physics, 6(5):320–328

Reference 1

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PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Unresolved cited work

Reference 2

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Observation 5ac4a3d0-becc-44bc-b0df-88068fcb40d6 · outbound

This paper cites Conditional neural field latent diffusion model for generating spatiotemporal turbulence.Nature Communications, 15(1):10416.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Conditional neural field latent diffusion model for generating spatiotemporal turbulence.Nature Communications, 15(1):10416

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.520999Z

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This paper cites Pde-gcn: Novel architectures for graph neu- ral networks motivated by partial differential equa- tions.Advances in neural information processing systems, 34:3836–3849.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Pde-gcn: Novel architectures for graph neu- ral networks motivated by partial differential equa- tions.Advances in neural information processing systems, 34:3836–3849

Reference 4

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This paper cites Gen- erative adversarial networks.Communications of the ACM, 63(11):139–144.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Gen- erative adversarial networks.Communications of the ACM, 63(11):139–144

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.526522Z

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This paper cites Geom-deeponet: A point-cloud- based deep operator network for field predictions on 3d parameterized geometries.Computer Methods in Applied Mechanics and Engineering, 429:117130.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Geom-deeponet: A point-cloud- based deep operator network for field predictions on 3d parameterized geometries.Computer Methods in Applied Mechanics and Engineering, 429:117130

Reference 6

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This paper cites Denoising diffusion probabilistic models.Advances in neural information processing systems, 33:6840–6851.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Denoising diffusion probabilistic models.Advances in neural information processing systems, 33:6840–6851

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.519138Z

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PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-05-19T16:52:40.515479Z

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Observation e0b86e5e-e9de-47b7-b3fa-66c6d7975c31 · outbound

This paper cites Diffusionpde: Generative pde-solving under partial observation.Advances in Neu- ral Information Processing Systems, 37:130291–130323.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Diffusionpde: Generative pde-solving under partial observation.Advances in Neu- ral Information Processing Systems, 37:130291–130323

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.530624Z

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Observation 42c53e4d-a652-485a-8f44-68e8cf2781fb · outbound

This paper cites Auto-Encoding Variational Bayes.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Auto-Encoding Variational Bayes

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-05-19T16:52:39.770794Z

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This paper cites John Wiley & Sons.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics John Wiley & Sons

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.543277Z

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This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Fourier Neural Operator for Parametric Partial Differential Equations

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-05-19T16:52:39.782277Z

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Observation b1c2c0d2-36c8-4de9-8106-d23e49fb1624 · outbound

This paper cites Scalable transformer for pde surrogate model- ing.Advances in Neural Information Processing Systems, 36:28010–28039.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Scalable transformer for pde surrogate model- ing.Advances in Neural Information Processing Systems, 36:28010–28039

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.536280Z

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This paper cites Generative Latent Neural PDE Solver using Flow Matching.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Generative Latent Neural PDE Solver using Flow Matching

Reference 14

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Observation c7b08171-571e-441b-a3a4-78be4aa6bdea · outbound

This paper cites Flow Matching for Generative Modeling.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Flow Matching for Generative Modeling

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-05-19T16:52:39.793556Z

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Observation 67d264c6-e94f-495e-a63b-da3b46f41450 · outbound

This paper cites Pde-refiner: Achieving accurate long rollouts with neural pde solvers.Advances in Neural Information Processing Systems, 36:67398–67433.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Pde-refiner: Achieving accurate long rollouts with neural pde solvers.Advances in Neural Information Processing Systems, 36:67398–67433

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.511955Z

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This paper cites Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-05-19T16:52:39.796639Z

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This paper cites Learn- ing nonlinear operators via deeponet based on the univer- sal approximation theorem of operators.Nature machine intelligence, 3(3):218–229.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Learn- ing nonlinear operators via deeponet based on the univer- sal approximation theorem of operators.Nature machine intelligence, 3(3):218–229

Reference 18

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This paper cites Dpm-solver++: Fast solver for guided sampling of diffusion probabilistic mod- els.Machine Intelligence Research, 22(4):730–751.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Dpm-solver++: Fast solver for guided sampling of diffusion probabilistic mod- els.Machine Intelligence Research, 22(4):730–751

Reference 19

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This paper cites PhySense: Sensor Placement Optimization for Accurate Physics Sensing.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics PhySense: Sensor Placement Optimization for Accurate Physics Sensing

Reference 20

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This paper cites U-NO: U-shaped Neural Operators.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics U-NO: U-shaped Neural Operators

Reference 21

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This paper cites Variational inference with normalizing flows.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Variational inference with normalizing flows

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.548565Z

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This paper cites U-net: Convolutional networks for biomedical image segmentation.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics U-net: Convolutional networks for biomedical image segmentation

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.509926Z

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This paper cites On conditional diffusion models for pde simula- tions.Advances in Neural Information Processing Sys- tems, 37:23246–23300.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics On conditional diffusion models for pde simula- tions.Advances in Neural Information Processing Sys- tems, 37:23246–23300

Reference 24

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This paper cites Denoising Diffusion Implicit Models.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Denoising Diffusion Implicit Models

Reference 25

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Observation 40982080-ef50-4673-a48f-417124cd4027 · outbound

This paper cites Score-Based Generative Modeling through Stochastic Differential Equations.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Score-Based Generative Modeling through Stochastic Differential Equations

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Resolution: verified exact; local_arxiv, observed 2026-05-19T16:52:39.774466Z

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This paper cites Chapman and Hall/CRC.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Chapman and Hall/CRC

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.500687Z

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Observation 1959a716-8c5f-48f5-bd01-82d93da01d24 · outbound

This paper cites A review of numerical meth- ods for nonlinear partial differential equations.Bulletin of the American Mathematical Society, 49(4):507–554.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics A review of numerical meth- ods for nonlinear partial differential equations.Bulletin of the American Mathematical Society, 49(4):507–554

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.504501Z

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Observation a562e833-1c4a-413a-aa69-cd5b322ec0d2 · outbound

This paper cites Factorized fourier neural operators.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Factorized fourier neural operators

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.507997Z

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Observation e5f6e9c1-175e-47ec-95a2-8811d0194d58 · outbound

This paper cites Elsevier.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Elsevier

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.506215Z

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Observation b4cd4dc3-d723-46a0-aa89-6b61873a305b · outbound

This paper cites Pesanet: Physics-encoded spectral attention network for simulating pde-governed complex systems.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Pesanet: Physics-encoded spectral attention network for simulating pde-governed complex systems

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.545016Z

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Observation 1f6d6387-185b-4387-a2a4-7943268a3afa · outbound

This paper cites [Wanget al., 2025 ] Sifan Wang, Zehao Dou, Siming Shan, Tong-Rui Liu, and Lu Lu.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics [Wanget al., 2025 ] Sifan Wang, Zehao Dou, Siming Shan, Tong-Rui Liu, and Lu Lu

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Resolution: verified exact; arxiv_id, observed 2026-05-19T16:52:39.786165Z

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Observation 5dc9d207-512a-4202-b5bc-454748d87fe2 · outbound

This paper cites Diffphycon: A generative approach to control complex physical sys- tems.Advances in Neural Information Processing Sys- tems, 37:4090–4147.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Diffphycon: A generative approach to control complex physical sys- tems.Advances in Neural Information Processing Sys- tems, 37:4090–4147

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Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.539954Z

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Observation 57ec836d-ad4d-4512-a7e6-83d5f902597c · outbound

This paper cites Transolver: A Fast Transformer Solver for PDEs on General Geometries.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Transolver: A Fast Transformer Solver for PDEs on General Geometries

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Resolution: verified exact; local_arxiv, observed 2026-05-19T16:52:39.762636Z

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Observation ccf8ac43-4a51-4661-9f3f-5727184706cc · outbound

This paper cites Koopman neural operator as a mesh-free solver of non-linear partial differential equations.Journal of Computational Physics, 513:113194.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Koopman neural operator as a mesh-free solver of non-linear partial differential equations.Journal of Computational Physics, 513:113194

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Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.538092Z

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Observation ace74706-7b1e-4f14-b926-4086eac3ed54 · outbound

This paper cites GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation

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Resolution: verified exact; arxiv_id, observed 2026-05-19T16:52:39.766835Z

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Observation 6ddbf4ec-4630-42f7-b7ab-fa11e2911a07 · outbound

This paper cites PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems

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Resolution: verified exact; arxiv_id, observed 2026-05-19T16:52:39.803751Z

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Observation 0ccb68c3-ddc1-4de3-9a88-c82af306fb2d · outbound

This paper cites A survey of sparse rep- resentation: algorithms and applications.IEEE access, 3:490–530.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics A survey of sparse rep- resentation: algorithms and applications.IEEE access, 3:490–530

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Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.541687Z

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Observation a1938b89-b0e0-4acd-be36-11860b7aafa9 · outbound

This paper cites Deciphering and integrating invariants for neural operator learning with various physical mechanisms.National Sci- ence Review, 11(4):nwad336.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Deciphering and integrating invariants for neural operator learning with various physical mechanisms.National Sci- ence Review, 11(4):nwad336

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.546817Z

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Observation a2970f5b-0b39-47ef-8102-74d202296fae · outbound

This paper cites Monte carlo neural pde solver for learning pdes via probabilistic representation.IEEE Transactions on Pattern Analysis and Machine Intelligence.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Monte carlo neural pde solver for learning pdes via probabilistic representation.IEEE Transactions on Pattern Analysis and Machine Intelligence

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.550312Z

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Observation c5d862b0-05a4-4080-ac57-7bc13369ae51 · outbound

This paper cites epochs Learning rate 1D Burgers 24 3001×10 −4 2D Darcy 24 5001×10 −4 2D Poisson 24 5001×10 −4 2D NS 10 8001×10 −4 Table 3: Training hyperparameters for different cases.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics epochs Learning rate 1D Burgers 24 3001×10 −4 2D Darcy 24 5001×10 −4 2D Poisson 24 5001×10 −4 2D NS 10 8001×10 −4 Table 3: Training hyperparameters for different cases

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.534470Z

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Observation bd3751d3-1e87-4f22-ac2e-946f4c799642 · outbound

This paper cites Bothfanduhave resolution 128×128.

PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics Bothfanduhave resolution 128×128

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T16:52:40.532497Z

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