Paper Citation Record · LEDGER

Towards Multi-spatiotemporal-scale Generalized PDE Modeling

As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 23 inbound Pith citation observations for arXiv:2209.15616.

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

pith.paper-citation-record.v1
2209.15616 v2

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measured 0 of 0 reference resolution

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measured 23 of 23 standing notices

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

measured 23 of 23 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-08T05:46:28.064390Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T03:09:30.471774Z

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Outbound references

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Pith citing papers

Observation 6dee3787-4062-4e9d-8062-5b53f0bc959d · inbound

A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs cites this paper.

A Deep Learning approach for parametrized and time dependent Partial Differential Equations using Dimensionality Reduction and Neural ODEs Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 22

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Observation c5e90589-aadd-4791-866b-f76f7e07bbb8 · inbound

Governing Equation Discovery from Data Based on Differential Invariants cites this paper.

Governing Equation Discovery from Data Based on Differential Invariants Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T14:32:13.704894Z

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

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

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: unresolved; no resolver link, observed 2026-08-07T14:27:42.758518Z

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Observation ffd09525-c517-4e21-9ff6-33ddd0f0ce21 · inbound

Hierarchical Implicit Neural Emulators cites this paper.

Hierarchical Implicit Neural Emulators Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T10:45:39.745485Z

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Observation 8a4e73ab-4cd4-4e1d-9fd9-e94e81661287 · inbound

PDESpectralRefiner: Achieving More Accurate Long Rollouts with Spectral Adjustment cites this paper.

PDESpectralRefiner: Achieving More Accurate Long Rollouts with Spectral Adjustment Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T04:31:39.984747Z

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Observation 084009fb-fb45-4338-b044-de0008e19dc4 · inbound

SlotPi: Physics-informed Object-centric Reasoning Models cites this paper.

SlotPi: Physics-informed Object-centric Reasoning Models Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T04:25:21.029174Z

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Observation c85b6baf-d111-4190-8b64-5dfa33a66773 · inbound

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning cites this paper.

Principled Approaches for Extending Neural Architectures to Function Spaces for Operator Learning Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-07T04:19:39.765144Z

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Observation d90c0781-78c8-498a-bc04-68eef1efc494 · inbound

Bubbleformer: Forecasting Boiling with Transformers cites this paper.

Bubbleformer: Forecasting Boiling with Transformers Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T13:02:53.297962Z

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Observation 093802e2-5b9e-4c46-95cd-8bb134fcd597 · inbound

Flow marching for a generative PDE foundation model cites this paper.

Flow marching for a generative PDE foundation model Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-18T13:51:25.581096Z

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.

Observation b8881f96-f184-498b-86b3-1aacaaf67c7e · inbound

Conditional Clifford-Steerable CNNs for PDE Modeling cites this paper.

Conditional Clifford-Steerable CNNs for PDE Modeling Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-04T09:41:11.637112Z

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Observation 9a3ed804-3d8b-42c4-825d-a34c5c318820 · inbound

Common Task Framework For a Critical Evaluation of Scientific Machine Learning Algorithms cites this paper.

Common Task Framework For a Critical Evaluation of Scientific Machine Learning Algorithms Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 27

Resolution: metadata mismatch; arxiv_id, observed 2026-05-18T04:00:50.916952Z

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.

Observation 1559d316-82a1-461a-95bf-af25bc64762f · inbound

Multi-Scale Wavelet Transformers for Operator Learning of Dynamical Systems cites this paper.

Multi-Scale Wavelet Transformers for Operator Learning of Dynamical Systems Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-16T08:22:36.039770Z

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

Observation 5e371672-3e2b-4e65-b99a-42130a038719 · inbound

FluxNet: Learning Capacity-Constrained Local Transport Operators for Conservative and Bounded PDE Surrogates cites this paper.

FluxNet: Learning Capacity-Constrained Local Transport Operators for Conservative and Bounded PDE Surrogates Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T05:34:24.906746Z

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Observation ca847c21-7dec-45da-a3bd-d317ba71ac79 · inbound

Latent Generative Solvers for Generalizable Long-Term Physics Simulation cites this paper.

Latent Generative Solvers for Generalizable Long-Term Physics Simulation Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 8

Resolution: metadata mismatch; arxiv_id, observed 2026-05-16T05:22:22.539912Z

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Observation 45d6ff2b-817a-4146-bebe-1289bcff0c43 · inbound

Deep Wave Network for Modeling Multi-Scale Physical Dynamics cites this paper.

Deep Wave Network for Modeling Multi-Scale Physical Dynamics Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 38

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T17:31:04.735147Z

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

Observation cce77767-bee4-4db9-ad3c-92b22b15d1ef · inbound

Physical Fidelity Reconstruction via Improved Consistency-Distilled Flow Matching for Dynamical Systems cites this paper.

Physical Fidelity Reconstruction via Improved Consistency-Distilled Flow Matching for Dynamical Systems Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 42

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T16:41:06.958689Z

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.

Observation ba369593-4c2d-466d-a30f-afac412ef6e6 · inbound

MC$^2$: Monte Carlo Correction for Fast Elliptic PDE Solving cites this paper.

MC$^2$: Monte Carlo Correction for Fast Elliptic PDE Solving Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:41:30.505308Z

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.

Observation 119f2f29-280f-4874-98cb-a75393acb963 · inbound

PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation cites this paper.

PDEAgent-Bench: A Multi-Metric, Multi-Library Benchmark for PDE Solver Generation Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 16

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T07:31:26.716442Z

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.

Observation 9e012f51-123f-43e1-8160-72f2ee575d29 · inbound

Small Models, Strong Priors: Architectural Inductive Bias for Parameter-Efficient Neural PDE Solvers cites this paper.

Small Models, Strong Priors: Architectural Inductive Bias for Parameter-Efficient Neural PDE Solvers Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 13

Resolution: metadata mismatch; arxiv_id, observed 2026-06-29T22:24:00.983556Z

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Observation fd048c18-dfca-402a-bb66-e0a789d1fce9 · inbound

Revisiting Neural Processes via Fourier Transform and Volterra Series cites this paper.

Revisiting Neural Processes via Fourier Transform and Volterra Series Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 128

Resolution: metadata mismatch; arxiv_id, observed 2026-06-28T17:12:24.415455Z

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

Observation 091d4992-0c0a-4f35-aff6-ce7135416560 · inbound

ELADO: Elliptic PDE Assessment Datasets for Operator Learning cites this paper.

ELADO: Elliptic PDE Assessment Datasets for Operator Learning Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 3

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T03:09:30.473523Z

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

Observation 4fa82a63-762f-4082-816d-2088cc5eadf3 · inbound

LLT: Local Linear Transformer for PDE Operator Learning cites this paper.

LLT: Local Linear Transformer for PDE Operator Learning Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 47

Resolution: unresolved; no resolver link, observed 2026-07-11T23:44:26.734234Z

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Observation b8f36590-f774-4418-a4fe-2a7587732918 · inbound

Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows cites this paper.

Neptuna: A Comprehensive Machine Learning Framework for Benchmarking Complex Multiphase Flows Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T05:17:56.927762Z

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Unavailable: canonical work link unavailable.