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Paper Citation Record · LEDGER

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems

As of 8 August 2026, this Paper Citation Record lists 85 of 85 outbound references and 1 inbound Pith citation observation for arXiv:2505.18857.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2505.18857 v1

Coverage vector

measured 85 of 85 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:27:44.176251Z

measured 86 of 86 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-12T03:55:32.973708Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-12T03:56:21.666336Z

Reference resolution

85 of 85 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3fe6e0fb-9411-45f2-99fd-a054e6e59bed · outbound

This paper cites Universal physics transformers: A framework for efficiently scaling neural operators.Advances in Neural Information Processing Systems, 37:25152–25194, 2024.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Universal physics transformers: A framework for efficiently scaling neural operators.Advances in Neural Information Processing Systems, 37:25152–25194, 2024

Reference 2

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Observation 65503478-2bd2-47d2-a239-ff675b79191c · outbound

This paper cites Relational inductive biases, deep learning, and graph networks.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Relational inductive biases, deep learning, and graph networks

Reference 3

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Observation 16a1984e-0c65-4725-8f8d-26b8c0d1ed7d · outbound

This paper cites Deep neural networks for data-driven les closure models.Journal of Computational Physics, 398:108910, 2019.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Deep neural networks for data-driven les closure models.Journal of Computational Physics, 398:108910, 2019

Reference 4

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Observation 2b653553-b0dd-41fe-b6a2-d8c1cd2900de · outbound

This paper cites Combining differentiable pde solvers and graph neural networks for fluid flow prediction.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Combining differentiable pde solvers and graph neural networks for fluid flow prediction

Reference 5

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Source-reported events for the cited work

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Observation 0ac7c844-f9ed-47b5-ae6c-864ca4d8bcf1 · outbound

This paper cites Prediction of aerodynamic flow fields using convolutional neural networks.Computational Mechanics, 64:525–545, 2019.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Prediction of aerodynamic flow fields using convolutional neural networks.Computational Mechanics, 64:525–545, 2019

Reference 6

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Source-reported events for the cited work

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Observation 37255746-d488-47a1-8a84-5e1b129fe28a · outbound

This paper cites Worrall, and Max Welling.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Worrall, and Max Welling

Reference 7

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Observation e09642b5-8243-49cc-b9b6-3cbc5504807d · outbound

This paper cites Clifford neural layers for PDE modeling.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Clifford neural layers for PDE modeling

Reference 8

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Source-reported events for the cited work

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Observation b688b953-c72b-4968-9af3-1a5197c560b7 · outbound

This paper cites Climformer-a spherical transformer model for long-term climate projections.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Climformer-a spherical transformer model for long-term climate projections

Reference 9

Resolution
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Observation f3b6442d-2a19-4360-9267-da05e7f1fa0e · outbound

This paper cites Choose a transformer: Fourier or galerkin.Advances in neural information processing systems, 34:24924–24940, 2021.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Choose a transformer: Fourier or galerkin.Advances in neural information processing systems, 34:24924–24940, 2021

Reference 10

Resolution
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Source-reported events for the cited work

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Observation 66a7ea31-0242-4515-a821-2ca68c3303ce · outbound

This paper cites Deep spatial transformers for autoregressive data-driven forecasting of geophysical turbulence.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Deep spatial transformers for autoregressive data-driven forecasting of geophysical turbulence

Reference 11

Resolution
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Source-reported events for the cited work

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Observation 7d01dcc6-765d-4bb5-92fb-e565322f6583 · outbound

This paper cites Deep learning method based on physics informed neural network with resnet block for solving fluid flow problems.Water, 13(4):423, 2021.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Deep learning method based on physics informed neural network with resnet block for solving fluid flow problems.Water, 13(4):423, 2021

Reference 12

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation ed7b66e2-2413-4258-a147-2d3e54602d89 · outbound

This paper cites Generative-machine-learning surrogate model of plasma turbulence.Physical Review E, 111(1):L013202, 2025.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Generative-machine-learning surrogate model of plasma turbulence.Physical Review E, 111(1):L013202, 2025

Reference 13

Resolution
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Source-reported events for the cited work

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Observation 487bda35-e7e4-4c5c-846b-730b3f9e66a9 · outbound

This paper cites Comparing different nonlinear dimen- sionality reduction techniques for data-driven unsteady fluid flow modeling.Physics of Fluids, 34(11), 2022.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Comparing different nonlinear dimen- sionality reduction techniques for data-driven unsteady fluid flow modeling.Physics of Fluids, 34(11), 2022

Reference 14

Resolution
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Source-reported events for the cited work

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Observation 778f5ea6-7c8e-4f9f-8228-8e79f8027ded · outbound

This paper cites Magnet: A graph u-net architecture for mesh-based simulations.Engineering Applications of Artificial Intelligence, 133:108055, 2024.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Magnet: A graph u-net architecture for mesh-based simulations.Engineering Applications of Artificial Intelligence, 133:108055, 2024

Reference 15

Resolution
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Source-reported events for the cited work

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Observation 342744fd-1ae3-462c-8061-75c39b92ba6b · outbound

This paper cites Physics-informed neural networks as surrogate models of hydrodynamic simulators.Science of the Total Environment, 912:168814, 2024.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Physics-informed neural networks as surrogate models of hydrodynamic simulators.Science of the Total Environment, 912:168814, 2024

Reference 16

Resolution
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Observation 5afc75c2-ba7b-4471-8c2a-1356b009bc7b · outbound

This paper cites An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale

Reference 17

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Observation 164207e2-3e28-42c6-a690-4f89b45aae0e · outbound

This paper cites Dudson, M.V.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Dudson, M.V

Reference 18

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Observation 43cb8934-cbdf-4e95-804e-832a4fd99645 · outbound

This paper cites Deep encoder–decoder hierarchical convolutional neural networks for conjugate heat transfer surro- gate modeling.Applied Energy, 372:123723, 2024.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Deep encoder–decoder hierarchical convolutional neural networks for conjugate heat transfer surro- gate modeling.Applied Energy, 372:123723, 2024

Reference 19

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Source-reported events for the cited work

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Observation 3b0b617f-22d3-4f8c-aca7-361be380a9ce · outbound

This paper cites Deep neural networks for nonlinear model order reduction of unsteady flows.Physics of Fluids, 32(10), 2020.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Deep neural networks for nonlinear model order reduction of unsteady flows.Physics of Fluids, 32(10), 2020

Reference 20

Resolution
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Source-reported events for the cited work

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Observation 736570f8-5106-477f-a4db-8b1d934b89be · outbound

This paper cites Physics-informed neural networks for solving reynolds-averaged navier–stokes equations.Physics of Fluids, 34 (7), 2022.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Physics-informed neural networks for solving reynolds-averaged navier–stokes equations.Physics of Fluids, 34 (7), 2022

Reference 21

Resolution
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Source-reported events for the cited work

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Reference 22

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Observation ab054f3d-a214-48f4-b30a-e6cbdfc614b9 · outbound

This paper cites Scientific machine learning based reduced-order models for plasma turbulence simulations.Physics of Plasmas, 31(11), 2024.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Scientific machine learning based reduced-order models for plasma turbulence simulations.Physics of Plasmas, 31(11), 2024

Reference 23

Resolution
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Source-reported events for the cited work

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Observation 34644148-ad6d-4395-90b2-5ddfd2100246 · outbound

This paper cites Earthformer: Exploring space-time transformers for earth system forecasting.Advances in Neural Information Processing Systems, 35:25390–25403, 2022.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Earthformer: Exploring space-time transformers for earth system forecasting.Advances in Neural Information Processing Systems, 35:25390–25403, 2022

Reference 24

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Source-reported events for the cited work

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Observation da41827d-e0d8-4e14-aa27-15b6a785e813 · outbound

This paper cites Mesh-based gnn surrogates for time-independent pdes.Scientific reports, 14(1):3394, 2024.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Mesh-based gnn surrogates for time-independent pdes.Scientific reports, 14(1):3394, 2024

Reference 25

Resolution
verified fuzzy
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Source-reported events for the cited work

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Observation f7e4482d-abd3-4c9a-804e-187bb3f7d3ff · outbound

This paper cites Physics-Preserving AI-Accelerated Simulations of Plasma Turbulence.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Physics-Preserving AI-Accelerated Simulations of Plasma Turbulence

Reference 26

Resolution
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Observation 81277806-3030-472a-bba7-167c2fbac83a · outbound

This paper cites Hood: Hierarchical graphs for generalized modelling of clothing dynamics.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Hood: Hierarchical graphs for generalized modelling of clothing dynamics

Reference 27

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 4a622b84-c40a-4d3a-be96-f528a573f0a3 · outbound

This paper cites A comparison of neural network architectures for data-driven reduced-order modeling.Computer Methods in Applied Mechanics and Engineering, 393:114764, 2022.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems A comparison of neural network architectures for data-driven reduced-order modeling.Computer Methods in Applied Mechanics and Engineering, 393:114764, 2022

Reference 28

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation 210f3312-280f-44e8-82dd-e0b306cd4765 · outbound

This paper cites Towards Multi-spatiotemporal-scale Generalized PDE Modeling.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 29

Resolution
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Observation 07040150-f5a0-472c-bb3b-595d4b070608 · outbound

This paper cites Gnot: A general neural operator transformer for operator learning.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Gnot: A general neural operator transformer for operator learning

Reference 30

Resolution
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Source-reported events for the cited work

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Observation 61586406-88fa-4a05-9efe-5280186fcbff · outbound

This paper cites Springer Science & Business Media, 2012.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Springer Science & Business Media, 2012

Reference 31

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verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

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Observation fa6832f3-9703-4b61-89b5-b0a18472822f · outbound

This paper cites Pseudo-three-dimensional turbulence in magnetized nonuniform plasma.The physics of Fluids, 21(1):87–92, 1978.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Pseudo-three-dimensional turbulence in magnetized nonuniform plasma.The physics of Fluids, 21(1):87–92, 1978

Reference 32

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:43.005656Z digest=sha256:27c8734a244eff1beee54319e849c67730fff030464968b5c254960a4d23ba88

Observation 2b62a513-5b97-41ff-932b-5ad63e7d400d · outbound

This paper cites Plasma edge turbulence.Physical Review Letters, 50 (9):682, 1983.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Plasma edge turbulence.Physical Review Letters, 50 (9):682, 1983

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Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.906395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:43.064360Z digest=sha256:88193a316b4d3c6d657d6aa3c31b03aaa507afaa61b7c5575c3b8a6f139505c5

Observation 56fd68f9-b100-4846-9d99-20390eead3a7 · outbound

This paper cites Deep residual learning for image recognition.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Deep residual learning for image recognition

Reference 34

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:43.216269Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:43.216269Z digest=sha256:cb29863496a542fd3c44e05b030c2beeec708d0998ac4bf9722a67f0a661dfca

Observation 418358ca-3eff-46d3-86af-054664ae8efb · outbound

This paper cites Turbulence model reduction by deep learning.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Turbulence model reduction by deep learning

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.888634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:43.270342Z digest=sha256:ef2b5d027ad56b04b4c2e649f20135c9287fcd7baeb1aafe3729c98630205994

Observation b32cd65e-098e-460f-9ce4-e22f07b9a4b0 · outbound

This paper cites Group Equivariant Fourier Neural Operators for Partial Differential Equations.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Group Equivariant Fourier Neural Operators for Partial Differential Equations

Reference 36

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:43.397479Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:43.397479Z digest=sha256:f32288ad95fd8db7c03b071f56f2531d485b77c3cc6d061a24eb1e74549b2580

Observation 2dc890a8-2a5c-4186-abf4-3b3ff37cc749 · outbound

This paper cites Reduced-order modeling of fluid flows with transformers.Physics of Fluids, 35(5), 2023.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Reduced-order modeling of fluid flows with transformers.Physics of Fluids, 35(5), 2023

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.878125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:43.504237Z digest=sha256:f5b088984a3be361c4f8f87ee86c89e359a8981df5ce8d703ce6eba59404b0b7

Observation df31c8cc-43be-4c8d-9ff5-0989c433fb1b · outbound

This paper cites Densely connected convolutional networks.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Densely connected convolutional networks

Reference 38

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:43.575281Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:43.575281Z digest=sha256:62c7224355f161d697f9afd3968a9abd2a69bb96956bd1371e4ace0466a4f912

Observation 78c49828-7f41-47c2-bd83-a2676a819597 · outbound

This paper cites The one hundred layers tiramisu: Fully convolutional densenets for semantic segmentation.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems The one hundred layers tiramisu: Fully convolutional densenets for semantic segmentation

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.860357Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:43.733048Z digest=sha256:fa6450ce1564567d9df2ec3c6b058ab78aeb14dd2735c915107d6258bb130255

Observation aed4178b-a655-4355-bd2a-786fe2161773 · outbound

This paper cites Nsfnets (navier-stokes flow nets): Physics-informed neural networks for the incompressible navier-stokes equations.Journal of Computational Physics, 426:109951, 2021.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Nsfnets (navier-stokes flow nets): Physics-informed neural networks for the incompressible navier-stokes equations.Journal of Computational Physics, 426:109951, 2021

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.849114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:43.901427Z digest=sha256:47b0b60adc279b55e11b41449481e19170e0f8f1a3428bfa49dee1bc2510de50

Observation 1d7030d1-f8bb-4c98-a48a-753c055985ba · outbound

This paper cites Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Physics-informed machine learning.Nature Reviews Physics, 3(6):422–440, 2021

Reference 41

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:43.931443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:43.931443Z digest=sha256:a03c65e448af9d3d0242b65c367566107856b2a375d1e9922e24d9ffc016e09e

Observation bec2d77f-9a1e-4487-b734-25a4c190f7c5 · outbound

This paper cites Deep fluids: A generative network for parameterized fluid simulations.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Deep fluids: A generative network for parameterized fluid simulations

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.831264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:43.999788Z digest=sha256:0ca0ed8986d6239dacf26f577b57695aca6afd513c22b48b43774d5cdad5012d

Observation f53a8713-07e5-4e32-91ce-6d7e3b0a4eda · outbound

This paper cites Smith, Ayya Alieva, Qing Wang, Michael P.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Smith, Ayya Alieva, Qing Wang, Michael P

Reference 43

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:44.016024Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.016024Z digest=sha256:0b0d23778d41f404b611fed5d35f0a5c10556d9d39f528bc870bf113b764287b

Observation 79997729-b9cc-444c-b9cd-c2d6ea9ca8c3 · outbound

This paper cites an unresolved cited work.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:27:44.820508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.021175Z digest=sha256:2bd3b1fa4f95f34c4281aaadda04bd26af683b32f10e68008a1c3b4aecf39b1a

Observation 215bbe43-9a80-4723-accd-a38dddaef2ad · outbound

This paper cites Fundamental statistical descriptions of plasma turbulence in magnetic fields.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Fundamental statistical descriptions of plasma turbulence in magnetic fields

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.809107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.024435Z digest=sha256:76e3cfa6c40837ee9ce5864b55be5a3a5765a2eac6051b9073c0a50cb8ecf373

Observation 7d53a405-fa89-4fbd-8500-9b1376eec1c6 · outbound

This paper cites Harnessing Equivariance: Modeling Turbulence with Graph Neural Networks.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Harnessing Equivariance: Modeling Turbulence with Graph Neural Networks

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:44.027178Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.027178Z digest=sha256:43b4fe2bbff310f4024703f572932aa8197c0860b54b1b637d57c73df32ce2fd

Observation 6c7925fe-0ebf-4096-8b69-fa5ff778e27e · outbound

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

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Learning skillful medium-range global weather forecasting.Science, 382(6677):1416–1421, 2023

Reference 47

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:44.030108Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.030108Z digest=sha256:0c8549f549e7eacffe39ceb7e42303394055757472be6ad2e2f85e44160b4425

Observation 1a07c775-59ae-44e4-bb40-2c7b75fb3824 · outbound

This paper cites Identification of high order closure terms from fully kinetic simulations using machine learning.Physics of Plasmas, 29(3), 2022.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Identification of high order closure terms from fully kinetic simulations using machine learning.Physics of Plasmas, 29(3), 2022

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.792059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.032899Z digest=sha256:6d629e5aee73acda1c68fd67660dc08256edc86c736f35dcae91fee2d8a70518

Observation ec323fc2-941e-4a8a-91dc-e6d7785ff216 · outbound

This paper cites Training convolutional neural networks to estimate turbulent sub-grid scale reaction rates.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Training convolutional neural networks to estimate turbulent sub-grid scale reaction rates

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.779970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.035672Z digest=sha256:7f54b129c897ff4cc7948fd5ebe639e5e657d626e004ab26417352452c6e1689

Observation 5360e0fb-ceed-45bb-a091-0be5776df321 · outbound

This paper cites Transformer for partial differential equations’ operator learning.Transactions on Machine Learning Research, 2023.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Transformer for partial differential equations’ operator learning.Transactions on Machine Learning Research, 2023

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.768267Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.038682Z digest=sha256:a713be923eb30e942406bec5e24b68beb0282acb52e08a6092d99a9d11fa265d

Observation 688645ca-1a21-4874-8e55-225e34380214 · outbound

This paper cites Scalable transformer for pde surrogate modeling.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Scalable transformer for pde surrogate modeling

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.756832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.042210Z digest=sha256:d2175ff1091ebb35466efb02a3b3fd823dc3a159316a1bafaf8cb32649c19f33

Observation 023928f4-3c64-42a1-9b77-57a93dd1a016 · outbound

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

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Fourier Neural Operator for Parametric Partial Differential Equations

Reference 52

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:44.045064Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.045064Z digest=sha256:80e77a759a0e17d6aba8fb056f5ecc7f21802f50eb9df75df9c2e7c086ce7847

Observation c8b7f5c2-50dd-4927-9172-7d5634048c61 · outbound

This paper cites Current and emerging deep-learning methods for the simulation of fluid dynamics.Proceedings of the Royal Society A, 479(2275):20230058, 2023.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Current and emerging deep-learning methods for the simulation of fluid dynamics.Proceedings of the Royal Society A, 479(2275):20230058, 2023

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.746611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.048156Z digest=sha256:8734941c09957e084d22750c92912ded847488d25799c9f753e6929b5902c386

Observation 169f50e1-c7d6-41da-9032-abe7427f750f · outbound

This paper cites Veeling, Paris Perdikaris, Richard E Turner, and Johannes Brandstetter.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Veeling, Paris Perdikaris, Richard E Turner, and Johannes Brandstetter

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.734580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.051312Z digest=sha256:51a27d7fdf7ac404d741bdffee1b049dadffc1d0a266bb52ccd4e8e1807b4ce7

Observation b6f77f90-c99a-4b4c-a34f-be58c7259ed1 · outbound

This paper cites Enhancing Fourier Neural Operators with Local Spatial Features.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Enhancing Fourier Neural Operators with Local Spatial Features

Reference 55

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:44.054494Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.054494Z digest=sha256:57024e8a679919e9ced829bc6dc858aa0eaa7c425ab0db9e9324a62086114c24

Observation 36b8ba10-9d85-4bfd-b31c-c562aae07ff0 · outbound

This paper cites Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Learning nonlinear operators via deeponet based on the universal approximation theorem of operators

Reference 56

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:44.057629Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.057629Z digest=sha256:b15399ee14e58ae4d4e9749efd57414aa9135de33e49961d7dabbc7bb06b8dc1

Observation 73e66721-a05a-466d-8211-aa13eda29bf5 · outbound

This paper cites Stacked convolutional auto-encoders for hierarchical feature extraction.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Stacked convolutional auto-encoders for hierarchical feature extraction

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.717081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.060435Z digest=sha256:1d0a93d9450ee6b1fb8a2875f652b5ffcab41439ce490340b2ea80736a20c970

Observation f0cf7fd3-3fab-4e12-97d2-34589a7dbb4b · outbound

This paper cites Multiple physics pretraining for spatiotemporal surrogate models.Advances in Neural Information Processing Systems, 37:119301–119335, 2024.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Multiple physics pretraining for spatiotemporal surrogate models.Advances in Neural Information Processing Systems, 37:119301–119335, 2024

Reference 58

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:44.064121Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.064121Z digest=sha256:493ea149e660a030e58fecff322ae1ee132dd32f32d84b988bb3523eb3d4fe00

Reference 59

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:44.067366Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.067366Z digest=sha256:9c9c639fb1df89adb6914aaf5e6c14ae0320a66d95fa458dc88718949453a560

Observation 5b73e65c-e7cb-49ae-a674-4d45c1cd3149 · outbound

This paper cites Cfdnet: a deep learning-based accelerator for fluid simulations.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Cfdnet: a deep learning-based accelerator for fluid simulations

Reference 60

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:44.070941Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.070941Z digest=sha256:5f5c9929516ae763dcaf56a90efa9f9eb166ed45c116812c73a25213a6ede247

Observation d85d2673-de5c-44ad-8169-ac1b0e9f537a · outbound

This paper cites Learning mesh- based simulation with graph networks.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Learning mesh- based simulation with graph networks

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.699581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.073909Z digest=sha256:de5f2b4f90a72637abb4b80ea425e2ba74b4908d77e17dc9aedb2c8a7162546f

Observation 7062be86-0d94-46c1-9cd1-451d8e50de7b · outbound

This paper cites Transform once: Efficient operator learning in frequency domain.Advances in Neural Information Processing Systems, 35:7947–7959, 2022.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Transform once: Efficient operator learning in frequency domain.Advances in Neural Information Processing Systems, 35:7947–7959, 2022

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.688325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.077543Z digest=sha256:6e50cf3d42b7931e8510024ecb134c2eb55ac9107e3467fe777502d4ac177ad0

Reference 63

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unresolved
no resolver link, observed 2026-08-07T14:27:44.081163Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.081163Z digest=sha256:2f0eaf7e42a1a918e30f4afe5dc7fb2f2a8adb194d4640ee9195446563a6a921

Observation 69d67eb2-23b2-4469-98f1-38488ff0c1cc · outbound

This paper cites an unresolved cited work.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Unresolved cited work

Reference 64

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:44.085534Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.085534Z digest=sha256:777007f356b0def5bd4de4e9e4ce313d2eccdd689a7cf6777d39e6cad9ff78b0

Observation 42a873a2-cd1d-4c00-ab3d-db6cce6757a6 · outbound

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

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems U-net: Convolutional networks for biomedical image segmentation

Reference 65

Resolution
unresolved
no resolver link, observed 2026-08-07T14:27:44.089589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:27:44.089589Z digest=sha256:e74795fd64feb75bdc5f1c8cb4876852835b171f3f1305b968447361c8c056f7

Observation 49a0956a-49e0-4942-985b-a4d8ffedf9e8 · outbound

This paper cites Graph networks as learnable physics engines for inference and control.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Graph networks as learnable physics engines for inference and control

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:27:44.666164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

source=pdf_text observed=2026-08-07T14:27:44.093682Z digest=sha256:508f1f80b206ec4f70c7c505c7f45f8b34feae6800ef3a328682d63ab6427ebd

Observation 6b99ff01-4aa0-4881-8451-87c5fede2c27 · outbound

This paper cites Learning to simulate complex physics with graph networks.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Learning to simulate complex physics with graph networks

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Observation 207f9e14-8507-4fd4-96e1-55ade8525b30 · outbound

This paper cites Stacked U-Nets: A No-Frills Approach to Natural Image Segmentation.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Stacked U-Nets: A No-Frills Approach to Natural Image Segmentation

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Observation 97431978-11c5-4c0b-b546-8999a391b315 · outbound

This paper cites Self-Attention with Relative Position Representations.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Self-Attention with Relative Position Representations

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Observation dd0246c4-c5d4-4705-8eab-93b03ccb648d · outbound

This paper cites Learned coarse models for efficient turbulence simulation.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Learned coarse models for efficient turbulence simulation

Reference 70

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Observation fff91e57-5d44-4dd0-8651-0fed91bbfd68 · outbound

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Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Unresolved cited work

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Observation 6681a248-1e31-4c61-ac82-70cd8aa75543 · outbound

This paper cites Pdebench: An extensive benchmark for scientific machine learning.Advances in Neural Information Processing Systems, 35:1596–1611, 2022.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Pdebench: An extensive benchmark for scientific machine learning.Advances in Neural Information Processing Systems, 35:1596–1611, 2022

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Observation bbb916fc-106d-4ea5-b96b-8ac3708f50b5 · outbound

This paper cites Factorized fourier neural operators.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Factorized fourier neural operators

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Observation 9e3da6ec-b279-4aee-b0f5-5f69cd1fda6e · outbound

This paper cites Solver-in-the- loop: Learning from differentiable physics to interact with iterative pde-solvers.Advances in neural information processing systems, 33:6111–6122, 2020.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Solver-in-the- loop: Learning from differentiable physics to interact with iterative pde-solvers.Advances in neural information processing systems, 33:6111–6122, 2020

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Observation 5e3377e5-d277-42f0-b058-cfb71104a57c · outbound

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

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Attention is all you need.Advances in neural information processing systems, 30, 2017

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Observation d139c86c-544f-4785-a6c4-3a8c5e19acc8 · outbound

This paper cites Extracting and composing robust features with denoising autoencoders.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Extracting and composing robust features with denoising autoencoders

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Observation 44086395-9540-4d3c-a0b7-76cc19aca556 · outbound

This paper cites Enhancing computational fluid dynamics with machine learning.Nature Computational Science, 2(6):358–366, 2022.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Enhancing computational fluid dynamics with machine learning.Nature Computational Science, 2(6):358–366, 2022

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Observation d8bf9b9d-a277-47d3-b566-ba6faa0a5a0d · outbound

This paper cites Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey

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Observation 1004a2ba-cede-41b6-8efb-ce44a3925503 · outbound

This paper cites Towards physics- informed deep learning for turbulent flow prediction.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Towards physics- informed deep learning for turbulent flow prediction

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Observation ac613a94-24a1-4c39-8b19-e31f7d20d681 · outbound

This paper cites Learning the solution operator of paramet- ric partial differential equations with physics-informed deeponets.Science advances, 7(40): eabi8605, 2021.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Learning the solution operator of paramet- ric partial differential equations with physics-informed deeponets.Science advances, 7(40): eabi8605, 2021

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Observation 1aeb3cc1-9fc5-4f93-a200-3428066ac627 · outbound

This paper cites DCW industries La Canada, CA, 1998.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems DCW industries La Canada, CA, 1998

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Observation 972f29c2-53f6-4988-b080-d22bd444b581 · outbound

This paper cites Rethinking and improving relative position encoding for vision transformer.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Rethinking and improving relative position encoding for vision transformer

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Observation 0dbb0fb1-48b8-4cc1-8997-68c723de8a5e · outbound

This paper cites W-Net: A Deep Model for Fully Unsupervised Image Segmentation.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems W-Net: A Deep Model for Fully Unsupervised Image Segmentation

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Observation ba827e3d-fa22-4213-9696-660b704785a1 · outbound

This paper cites Sinenet: Learning temporal dynamics in time-dependent partial differential equations.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems Sinenet: Learning temporal dynamics in time-dependent partial differential equations

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Resolution
verified fuzzy
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Source-reported events for the cited work

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Observation 53c51dd3-5fd3-4605-b0f3-758f16778186 · outbound

This paper cites PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks

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Observation 7e8ac49b-a2fb-42e9-807d-a1fe757fa80e · outbound

This paper cites NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations

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Pith citing papers

Observation a0fcbe26-bb58-4422-bc61-a4d7b29e6610 · inbound

Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency cites this paper.

Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems

Reference 15

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