Paper Citation Record · LEDGER

Towards Multi-spatiotemporal-scale Generalized PDE Modeling

As of 22 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 35 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 35 of 35 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 35 of 35 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T12:16:22.942955Z

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 c259e428-3908-41d4-aa90-522debbe43a8 · inbound

The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning cites this paper.

The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 37

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Observation c4f28a43-4b9a-4435-af48-cb29590a74a5 · inbound

Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogates cites this paper.

Predicting Change, Not States: An Alternate Framework for Neural PDE Surrogates Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 13

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Observation 56b97bd3-c3d8-4ed5-9806-a621a724efb7 · inbound

On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs cites this paper.

On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 121

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Observation ab3f49c3-27bd-4537-96d3-7a3901fdc596 · inbound

Inverse Evolution Data Augmentation for Neural PDE Solvers cites this paper.

Inverse Evolution Data Augmentation for Neural PDE Solvers Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 9

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Observation 41e0fe6c-30d6-405b-b4b1-6114e859d2b9 · inbound

BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics cites this paper.

BCAT: A Block Causal Transformer for PDE Foundation Models for Fluid Dynamics Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 16

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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 9fdc1283-c31d-429b-a033-810f9a334cea · inbound

Equilibrium Conserving Neural Operators for Super-Resolution Learning cites this paper.

Equilibrium Conserving Neural Operators for Super-Resolution Learning Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 17

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Observation 7eaeaf88-65be-4f2a-af67-b7f0a22fcbf4 · inbound

PLAID: A Unified Data Model for Machine Learning on Heterogeneous Physics Simulations cites this paper.

PLAID: A Unified Data Model for Machine Learning on Heterogeneous Physics Simulations Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 52

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Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models cites this paper.

Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 2021

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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

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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 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

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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

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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

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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

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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

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Observation ccba5998-64ae-4b76-ab1a-2a7ab2b1aa3a · inbound

PhysiX: A Foundation Model for Physics Simulations cites this paper.

PhysiX: A Foundation Model for Physics Simulations Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 18

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Observation 2e311954-18cb-4539-abb5-30804e511d28 · inbound

Scale-Consistent Learning for Partial Differential Equations cites this paper.

Scale-Consistent Learning for Partial Differential Equations Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 36

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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

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Observation 05e5728b-af5d-48ef-8164-9984289c9e6f · inbound

Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction cites this paper.

Learning Turbulent Flows with Generative Models: Super-resolution, Forecasting, and Sparse Flow Reconstruction Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T16:13:09.633401Z

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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

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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

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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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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

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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

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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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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

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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

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+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

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+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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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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

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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 2026-08-22T06:32:14.747728+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

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Observation 87378065-af29-470c-9b6c-7921f1c49bff · inbound

Unsupervised Adaptation of PDE Foundation Models cites this paper.

Unsupervised Adaptation of PDE Foundation Models Towards Multi-spatiotemporal-scale Generalized PDE Modeling

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T15:41:11.454691Z

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