Paper Citation Record · LEDGER

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty

As of 20 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 2 inbound Pith citation observations for arXiv:2505.13501.

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

pith.paper-citation-record.v1
2505.13501 v1

Coverage vector

measured 54 of 54 reference resolution

Typed states for the displayed outbound observations.

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One-hop event checks from named stored sources.

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measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T00:13:20.792435Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-12T07:31:26.814446Z

Reference resolution

54 of 54 outbound references displayed

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External citation measurements

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Outbound references

Observation 443c2019-4782-4af2-859c-26abe75b990b · outbound

This paper cites Computational inelasticity, volume 7.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Computational inelasticity, volume 7

Reference 1

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Observation f4f68178-c380-41fd-913a-40ef4c779ce3 · outbound

This paper cites Dissipative particle dynamics: introduction, methodology and complex fluid applications—a review.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Dissipative particle dynamics: introduction, methodology and complex fluid applications—a review

Reference 2

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Observation e7253448-e3fb-4fe4-bcc0-df2075e2e0eb · outbound

This paper cites Dissipative phenomena in condensed matter: some applications, volume 71.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Dissipative phenomena in condensed matter: some applications, volume 71

Reference 3

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Observation 8996a128-9ece-4a3d-a058-8eb7140c18d7 · outbound

This paper cites Dissipative phenomena in quark-gluon plasmas.Physical Review D, 31(1):53, 1985.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Dissipative phenomena in quark-gluon plasmas.Physical Review D, 31(1):53, 1985

Reference 4

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Observation e8468551-86d5-4c56-b5fa-e2810da77d69 · outbound

This paper cites Modeling materials: continuum, atomistic and multiscale techniques.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Modeling materials: continuum, atomistic and multiscale techniques

Reference 5

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Observation 1e56e9c2-68cc-4aad-9ac0-704d1cd70e69 · outbound

This paper cites Nonequilibrium statistical mechanics.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Nonequilibrium statistical mechanics

Reference 6

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Observation f7c3fff5-a586-4ca7-b41d-468248bbdc6e · outbound

This paper cites Extracting macroscopic dynamics: model problems and algorithms.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Extracting macroscopic dynamics: model problems and algorithms

Reference 7

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Observation 3eb6586c-1577-464d-afb2-e67da04213f2 · outbound

This paper cites Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 8

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Observation 69b1a647-89d1-436d-b5b7-29ad38354879 · outbound

This paper cites Data-driven science and engineering: Machine learning, dynamical systems, and control.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Data-driven science and engineering: Machine learning, dynamical systems, and control

Reference 9

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Observation 172165a5-4d81-428f-bad3-e209f3d1f930 · outbound

This paper cites Dynamics and thermodynamics of complex fluids.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Dynamics and thermodynamics of complex fluids

Reference 10

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Observation 2fb8a9c9-7b33-4777-b954-928022670842 · outbound

This paper cites Dynamics and thermodynamics of complex fluids.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Dynamics and thermodynamics of complex fluids

Reference 11

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Observation 4189295d-0fd5-4fe5-a44b-852e2e4136d2 · outbound

This paper cites Beyond equilibrium thermodynamics.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Beyond equilibrium thermodynamics

Reference 12

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Observation 381c4d79-a8c0-4c1b-96b5-74efc193c339 · outbound

This paper cites Structure- preserving neural networks.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Structure- preserving neural networks

Reference 13

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Observation 181a78c4-5f67-416f-b6ac-e00624a1017a · outbound

This paper cites Machine learning structure preserving brackets for forecasting irreversible processes.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Machine learning structure preserving brackets for forecasting irreversible processes

Reference 14

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Observation 7a286db9-6462-48b9-b90b-2cbd56b446a3 · outbound

This paper cites GFINNs: GENERIC formalism informed neural networks for deterministic and stochastic dynamical systems.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty GFINNs: GENERIC formalism informed neural networks for deterministic and stochastic dynamical systems

Reference 15

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Observation 0441ed08-aa69-4989-8f94-bd5ef9869745 · outbound

This paper cites Efficiently Parameterized Neural Metriplectic Systems.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Efficiently Parameterized Neural Metriplectic Systems

Reference 16

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Observation 50644b32-bbdc-4a08-87ca-b5c23211f03c · outbound

This paper cites Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs

Reference 17

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Observation eb464096-883b-43e2-94da-9ef32ffb5b7a · outbound

This paper cites Statistical-Physics-Informed Neural Networks (Stat-PINNs): A machine learning strategy for coarse-graining dissipative dynamics.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Statistical-Physics-Informed Neural Networks (Stat-PINNs): A machine learning strategy for coarse-graining dissipative dynamics

Reference 18

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Observation 5abdb436-4aa1-45c2-8aaa-76dfcaa8e427 · outbound

This paper cites Harnessing fluctuations to discover dissipative evolution equations.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Harnessing fluctuations to discover dissipative evolution equations

Reference 19

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Observation 6f05a099-cd51-41c2-8b92-f6c45024de5d · outbound

This paper cites Denoising diffusion probabilistic models.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Denoising diffusion probabilistic models

Reference 20

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Observation 8d8f6d05-a25f-411c-9b0d-6c64113b37b1 · outbound

This paper cites Epistemic neural networks.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Epistemic neural networks

Reference 21

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Observation 80e120eb-100e-47a1-8cec-bedb1f00db4b · outbound

This paper cites Simple and scalable predictive uncertainty estimation using deep ensembles.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Simple and scalable predictive uncertainty estimation using deep ensembles

Reference 22

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Observation b3f93111-4a2e-4662-95a2-1d0afb8c0762 · outbound

This paper cites Bayesian learning for neural networks, volume 118.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Bayesian learning for neural networks, volume 118

Reference 23

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This paper cites Gaussian processes in machine learning.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Gaussian processes in machine learning

Reference 24

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Observation 880c73a7-08d9-4fad-b137-f860219f94d0 · outbound

This paper cites Bayesian neural networks.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Bayesian neural networks

Reference 25

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Observation 4f3c4170-660a-4c9a-b6bd-33b8d265248d · outbound

This paper cites Bayesian data analysis.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Bayesian data analysis

Reference 26

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Observation 7af8fa05-f94c-4ecf-a972-34e349d3046b · outbound

This paper cites Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics

Reference 27

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Observation ab55122c-64ce-4a6a-9fc6-57d0a554e119 · outbound

This paper cites Deep Ensembles: A Loss Landscape Perspective.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Deep Ensembles: A Loss Landscape Perspective

Reference 28

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Observation bf72566e-5609-4e80-8615-923e9e7b1f4a · outbound

This paper cites Dropout as a bayesian approximation: Representing model uncertainty in deep learning.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Dropout as a bayesian approximation: Representing model uncertainty in deep learning

Reference 29

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Observation 8dc1585b-76d1-4e4f-a116-bcf56a3e1ab3 · outbound

This paper cites B-PINNs: Bayesian physics-informed neural networks for forward and inverse pde problems with noisy data.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty B-PINNs: Bayesian physics-informed neural networks for forward and inverse pde problems with noisy data

Reference 30

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Observation 28b4c260-9839-4c18-86fb-51f6f60548a0 · outbound

This paper cites Physics-informed polynomial chaos expansions.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Physics-informed polynomial chaos expansions

Reference 31

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Observation 2d1434a9-ccaa-481c-9253-863a24b0ef46 · outbound

This paper cites Quantifying total uncertainty in physics- informed neural networks for solving forward and inverse stochastic problems.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Quantifying total uncertainty in physics- informed neural networks for solving forward and inverse stochastic problems

Reference 32

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Observation 7b72b49d-3506-45c6-a126-42f8f4abe318 · outbound

This paper cites Auto-encoding variational Bayes, 2013.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Auto-encoding variational Bayes, 2013

Reference 33

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Observation a9d092a8-8352-4fe3-8235-6a2f7f9bebb2 · outbound

This paper cites Generative adversarial nets.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Generative adversarial nets

Reference 34

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Observation ae62c752-2291-44ac-8069-a6e8406c47d2 · outbound

This paper cites PI-V AE: Physics-informed variational auto-encoder for stochastic differential equations.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty PI-V AE: Physics-informed variational auto-encoder for stochastic differential equations

Reference 35

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Observation 30891dee-6720-4e80-b995-0bab51f3b73a · outbound

This paper cites Physics-informed variational inference for uncertainty quantification of stochastic differential equations.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Physics-informed variational inference for uncertainty quantification of stochastic differential equations

Reference 36

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Observation 35bec811-4983-451e-be8b-657769b5bf53 · outbound

This paper cites Adversarial uncertainty quantification in physics-informed neural networks.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Adversarial uncertainty quantification in physics-informed neural networks

Reference 37

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Observation 90027f13-1cf1-4ffb-bfe2-bd0d766c9f97 · outbound

This paper cites PID-GAN: A GAN framework based on a physics-informed discriminator for uncertainty quantification with physics.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty PID-GAN: A GAN framework based on a physics-informed discriminator for uncertainty quantification with physics

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:11:54.830108Z

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Observation e79ba4dd-1422-42bb-aa8e-739850ade979 · outbound

This paper cites Wasserstein generative adversarial uncertainty quantification in physics- informed neural networks.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Wasserstein generative adversarial uncertainty quantification in physics- informed neural networks

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:11:54.814751Z

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Observation 539ad4eb-814f-450c-8baa-f724fcfbe194 · outbound

This paper cites Composite Bayesian optimization in function spaces using NEON—Neural Epistemic Operator Networks.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Composite Bayesian optimization in function spaces using NEON—Neural Epistemic Operator Networks

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:11:54.798654Z

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Observation f66baf0c-22e2-4541-88df-1316e5cce0a9 · outbound

This paper cites EVODMs: variational learning of PDEs for stochastic systems via diffusion models with quantified epistemic uncertainty.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty EVODMs: variational learning of PDEs for stochastic systems via diffusion models with quantified epistemic uncertainty

Reference 41

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Observation 6b5e14fe-fdae-4c2a-be0f-71d048353410 · outbound

This paper cites E-PINNs: Epistemic physics-informed neural networks.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty E-PINNs: Epistemic physics-informed neural networks

Reference 42

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Source-reported events for the cited work

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Observation 312410cd-b77c-4ca3-ae9c-4a1defedbe97 · outbound

This paper cites Tutorial on diffusion models for imaging and vision.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Tutorial on diffusion models for imaging and vision

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:11:54.784563Z

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Observation 151fb364-abc8-4c51-bf76-f2970c859f93 · outbound

This paper cites Denoising Diffusion Implicit Models.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Denoising Diffusion Implicit Models

Reference 44

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Observation 8060fdc2-7c0b-4883-a3b5-3870c55878c4 · outbound

This paper cites From Predictions to Decisions: The Importance of Joint Predictive Distributions.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty From Predictions to Decisions: The Importance of Joint Predictive Distributions

Reference 45

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Source-reported events for the cited work

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Observation 69ac60db-e100-4581-a97c-00fc9c8ac49b · outbound

This paper cites The neural testbed: Evaluating joint predictions.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty The neural testbed: Evaluating joint predictions

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:11:54.770274Z

Source-reported events for the cited work

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Observation de734f3d-736c-4bc1-a8b5-aabba2c895c2 · outbound

This paper cites Distilling the Knowledge in a Neural Network.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Distilling the Knowledge in a Neural Network

Reference 47

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Source-reported events for the cited work

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Observation 07e1fa00-9180-49d9-9507-efa76a7d1459 · outbound

This paper cites Derivation and validation of mesoscopic theories for diffusion of interacting molecules.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Derivation and validation of mesoscopic theories for diffusion of interacting molecules

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:11:54.755904Z

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Observation a329f5fe-18cd-40aa-b0d8-c2e0d586f4c2 · outbound

This paper cites The curious case of convex neural networks.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty The curious case of convex neural networks

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T21:11:54.741153Z

Source-reported events for the cited work

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Observation 68eecf07-77e0-4c44-b79c-f7b392b246cd · outbound

This paper cites Understanding the difficulty of training deep feedforward neural networks.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Understanding the difficulty of training deep feedforward neural networks

Reference 50

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This paper cites Adam: A Method for Stochastic Optimization.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Adam: A Method for Stochastic Optimization

Reference 51

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This paper cites When and why PINNs fail to train: A neural tangent kernel perspective.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty When and why PINNs fail to train: A neural tangent kernel perspective

Reference 52

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This paper cites Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning

Reference 53

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This paper cites 41HFfV0NtIe8IWM5ZdD2pkGyZyk=.

SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty 41HFfV0NtIe8IWM5ZdD2pkGyZyk=

Reference 54

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Pith citing papers

Observation 0f61419d-a196-4133-bcf5-d13e27931180 · inbound

Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentials cites this paper.

Nonlinear GENERIC-Embedded Neural Networks (N-GENNs): Learning GENERIC dynamics with non-quadratic dissipation potentials SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty

Reference 69

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Structure-preserving uncertainty quantification for GENERIC dynamics cites this paper.

Structure-preserving uncertainty quantification for GENERIC dynamics SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty

Reference 51

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