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

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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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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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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

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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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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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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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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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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

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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

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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

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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

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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: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:45.075392Z

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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

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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

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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

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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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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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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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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: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:45.015052Z

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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

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This paper cites MultiScale MeshGraphNets.

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

Reference 22

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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

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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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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; raw_fallback, observed 2026-08-07T14:27:44.971088Z

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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

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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

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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

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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

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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

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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

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:44.928546Z

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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; raw_fallback, observed 2026-08-07T14:27:44.916985Z

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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

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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

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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

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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

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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

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

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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

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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

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

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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

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

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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

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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

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

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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

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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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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

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

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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

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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

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

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

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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 2026-08-07T06:34:17.273281+00:00.

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

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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 2026-08-07T06:34:17.273281+00:00.

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

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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 2026-08-07T06:34:17.273281+00:00.

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

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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 2026-08-07T06:34:17.273281+00:00.

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.

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

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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 2026-08-07T06:34:17.273281+00:00.

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

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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 2026-08-07T06:34:17.273281+00:00.

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.

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.

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

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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 2026-08-07T06:34:17.273281+00:00.

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.

Observation d167fd03-1f99-430e-9ecb-717b07c86627 · outbound

This paper cites ClimaX: A foundation model for weather and climate.

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems ClimaX: A foundation model for weather and climate

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.

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

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

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

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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 2026-08-07T06:34:17.273281+00:00.

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

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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 2026-08-07T06:34:17.273281+00:00.

Observation 0df0b72d-dfea-4634-acb8-8a92ca39d482 · outbound

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

Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systems U-NO: U-shaped Neural Operators

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

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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.

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.

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

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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 2026-08-07T06:34:17.273281+00:00.

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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Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.097921Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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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Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.102317Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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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Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.106349Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:44.648514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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

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Resolution: unresolved; raw_fallback, observed 2026-08-07T14:27:44.636756Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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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Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.118625Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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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Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:44.618978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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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Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:44.606516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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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Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.131332Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.135757Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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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Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:44.583142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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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Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.143380Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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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Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.146898Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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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Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.151210Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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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Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:27:44.565885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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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Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.159543Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Reference 83

Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.163314Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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; raw_fallback, observed 2026-08-07T14:27:44.549830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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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Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.171921Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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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Resolution: unresolved; no resolver link, observed 2026-08-07T14:27:44.176251Z

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