Paper Citation Record · LEDGER

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators

As of 5 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 1 inbound Pith citation observation for arXiv:2605.10154.

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

pith.paper-citation-record.v1
2605.10154 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-12T03:23:42.788576Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-30T13:41:03.499592Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

43 of 43 outbound references displayed

verified exact11
verified fuzzy28
unresolved1
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4def25a5-83b4-4bb0-82fa-39caf282895c · outbound

This paper cites Deep learning for physical processes: Incorporating prior scientific knowledge.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Deep learning for physical processes: Incorporating prior scientific knowledge

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.196229Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 11c95ea8-ef9c-4420-9194-7695e2c408a8 · outbound

This paper cites Machine Learning for Partial Differential Equations.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Machine Learning for Partial Differential Equations

Reference 2

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T03:26:19.778393Z

Source-reported events for the cited work

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Observation d67e922a-e5a9-418d-b97d-f309fd598dc5 · outbound

This paper cites DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-15T03:17:25.491231Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 89b09eb4-2c9b-411b-ae0d-bcba732e880d · outbound

This paper cites Neural operator: Learning maps between function spaces with applications to pdes.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Neural operator: Learning maps between function spaces with applications to pdes

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.207671Z

Source-reported events for the cited work

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Observation c7c4160d-cb4b-4bb1-8197-0d5011454f8d · outbound

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

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Fourier Neural Operator for Parametric Partial Differential Equations

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-05-12T03:26:19.798561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation d2737d0c-bda0-4b2a-b101-ecd1dbdc3743 · outbound

This paper cites Convolutional neural operators for robust and accurate learning of pdes.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Convolutional neural operators for robust and accurate learning of pdes

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.256517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 5190ee43-b9b1-42e3-b936-6bba032019f2 · outbound

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

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Gnot: A general neural operator transformer for operator learning

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.190564Z

Source-reported events for the cited work

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Observation e57fcda0-4a1d-4e54-b70b-c28a62f88f95 · outbound

This paper cites A neural pde solver with temporal stencil modeling.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators A neural pde solver with temporal stencil modeling

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.274337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 03e7cb45-dfc3-4d07-9df6-b82f52560c9c · outbound

This paper cites Message Passing Neural PDE Solvers.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Message Passing Neural PDE Solvers

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:26:19.786803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4c6cecf1-8af9-45a7-befc-969ab07e6427 · outbound

This paper cites Transfer learning enhanced deeponet for long-time prediction of evolution equations.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Transfer learning enhanced deeponet for long-time prediction of evolution equations

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.184395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 14ee7b02-aca2-42ca-9180-4fccb7ad5210 · outbound

This paper cites Recurrent Neural Operators: Stable Long-Term PDE Prediction.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Recurrent Neural Operators: Stable Long-Term PDE Prediction

Reference 11

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T03:26:19.757874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 3170ba55-1267-4f04-8a54-0704265c7d4a · outbound

This paper cites On the difficulty of learning chaotic dynamics with rnns.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators On the difficulty of learning chaotic dynamics with rnns

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.212643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 62302b47-8e1c-4e85-bd90-7552c30fcabc · outbound

This paper cites Pde-refiner: Achiev- ing accurate long rollouts with neural pde solvers.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Pde-refiner: Achiev- ing accurate long rollouts with neural pde solvers

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.229063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a9b5621d-9dea-4a44-940a-a7863210cc75 · outbound

This paper cites Coast: Intelligent time-adaptive neural operators.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Coast: Intelligent time-adaptive neural operators

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.168626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4523c900-e045-45e0-8d03-cf369e665a7f · outbound

This paper cites Learning to accelerate partial differential equations via latent global evolution.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Learning to accelerate partial differential equations via latent global evolution

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.269960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 41a6e8b9-a321-49d3-83fe-9200deec4134 · outbound

This paper cites Latent neural pde solver: A reduced-order modeling framework for partial differential equations.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Latent neural pde solver: A reduced-order modeling framework for partial differential equations

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T19:56:49.659175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation dcfa2641-a9f9-4e2a-86a7-1ae115c65a36 · outbound

This paper cites Latent neural operator for solving forward and inverse pde problems.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Latent neural operator for solving forward and inverse pde problems

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T19:56:49.656391Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4b5ec53d-a5a4-492f-a346-5da2b4bb7883 · outbound

This paper cites Aroma: Preserving spatial structure for latent pde modeling with local neural fields.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Aroma: Preserving spatial structure for latent pde modeling with local neural fields

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T19:56:49.663986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation d8288648-8bb1-493e-b140-4c1223a4f291 · outbound

This paper cites Calm-pde: Continuous and adap- tive convolutions for latent space modeling of time-dependent pdes.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Calm-pde: Continuous and adap- tive convolutions for latent space modeling of time-dependent pdes

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:26:19.774212Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation e71ccf63-f494-46bb-b4aa-1ca3c9799893 · outbound

This paper cites Universal physics transformers: A framework for efficiently scaling neural operators.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Universal physics transformers: A framework for efficiently scaling neural operators

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.248331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 36a3be24-a659-4488-8903-88cf7ca08628 · outbound

This paper cites Koopman neural operator as a mesh-free solver of non-linear partial differential equations.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Koopman neural operator as a mesh-free solver of non-linear partial differential equations

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.238734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 310cae0c-b7c6-48a8-a3d6-1f6b3bd901f8 · outbound

This paper cites Invertible Koopman neural operator for data-driven modeling of partial differential equations.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Invertible Koopman neural operator for data-driven modeling of partial differential equations

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:26:19.790543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation f98af5bb-2afb-4a97-88fd-a73e559bd20c · outbound

This paper cites Equivariance and partial observations in Koopman operator theory for partial differential equations.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Equivariance and partial observations in Koopman operator theory for partial differential equations

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:26:19.750258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 0e133269-c7cd-4180-b59b-2a9142ec2589 · outbound

This paper cites Numerical Solution Partial Differential Equations using the Discrete Fourier Transform.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Numerical Solution Partial Differential Equations using the Discrete Fourier Transform

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:26:19.762212Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 1845821a-432f-4d46-936d-7b487b91e10d · outbound

This paper cites U-fno—an en- hanced fourier neural operator-based deep-learning model for multiphase flow.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators U-fno—an en- hanced fourier neural operator-based deep-learning model for multiphase flow

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.278971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 6808aca5-65d8-4ed4-a274-1bd9ce07729c · outbound

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

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators U-NO: U-shaped Neural Operators

Reference 26

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T03:26:19.746069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 74c2949e-b05d-4179-ba18-4cb768e753fa · outbound

This paper cites Factorized Fourier Neural Operators.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Factorized Fourier Neural Operators

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:26:19.794744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 7618beb0-8c52-4fdc-9be7-583eba5cb9ca · outbound

This paper cites Mionet: Learning multiple-input operators via tensor product.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Mionet: Learning multiple-input operators via tensor product

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.252524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 8fb7cfe3-bf3c-4d3d-98e8-cf3441c36016 · outbound

This paper cites Physics-informed neural operator for learning partial differential equations.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Physics-informed neural operator for learning partial differential equations

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.265506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 0a4a36fa-4664-4079-99d7-7325d785fcd3 · outbound

This paper cites Fourier neural operator with learned deformations for pdes on general geometries.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Fourier neural operator with learned deformations for pdes on general geometries

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.218827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 82f57aab-197f-48b7-9906-b50787a8c403 · outbound

This paper cites CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:26:19.753870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation e66cdd03-2579-4b8b-a861-e048b1a14636 · outbound

This paper cites Learning nonlinear reduced models from data with operator inference.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Learning nonlinear reduced models from data with operator inference

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.234061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 334cb0fb-0672-43c1-bdfc-df5736035da5 · outbound

This paper cites Physics-informed reduced order modeling of time-dependent pdes via differentiable solvers.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Physics-informed reduced order modeling of time-dependent pdes via differentiable solvers

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:26:19.766177Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation c4a83948-5d7f-4d41-964d-da13d83894a2 · outbound

This paper cites Latent Mamba Operator for Partial Differential Equations.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Latent Mamba Operator for Partial Differential Equations

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-05-12T03:26:19.782464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation b4e328aa-71f7-4728-8647-886f8e73ced5 · outbound

This paper cites Nonintrusive reduced-order models for parametric partial differential equations via data-driven operator inference.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Nonintrusive reduced-order models for parametric partial differential equations via data-driven operator inference

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.261398Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 6a0481ea-4861-43d8-a5ec-ff85585d3905 · outbound

This paper cites A deep learning approach to reduced or- der modelling of parameter dependent partial differential equations.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators A deep learning approach to reduced or- der modelling of parameter dependent partial differential equations

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.224093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 6749a42a-c918-4927-878b-d6f3f7789d42 · outbound

This paper cites an unresolved cited work.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-05-12T19:56:49.661530Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4abf1825-5921-4236-8203-2eeb914823de · outbound

This paper cites Canuto, M.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Canuto, M

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.202089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation ae7d4724-e2e8-4243-96d9-3c878eee32fb · outbound

This paper cites Sagaut,Large eddy simulation for incompressible flows: an introduction.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Sagaut,Large eddy simulation for incompressible flows: an introduction

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.178113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation fa7889af-8039-473b-93f1-3d716909abfb · outbound

This paper cites Turbulent flows.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Turbulent flows

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T20:01:48.243879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 3cc8c8ef-d205-49e4-ac32-e0adbce97c95 · outbound

This paper cites Optimal prediction of underresolved dynamics.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Optimal prediction of underresolved dynamics

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T19:56:49.649581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation b95ebe11-85a4-4a30-9ca2-293a57452de6 · outbound

This paper cites Neural ordinary differential equations.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Neural ordinary differential equations

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T19:56:49.647060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 574438fe-63c5-4560-9feb-b4e550f8eac4 · outbound

This paper cites Pdebench: An extensive benchmark for scientific machine learning.

Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators Pdebench: An extensive benchmark for scientific machine learning

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T19:56:49.653072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Pith citing papers

Observation 0138aac8-a3af-4e62-82fc-7ff2d098a68f · inbound

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement cites this paper.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Stable Long-Horizon PDE Forecasting via Latent Structured Spectral Propagators

Reference 51

Resolution: unresolved; no resolver link, observed 2026-07-30T13:41:03.499592Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.