Paper Citation Record · LEDGER

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts

As of 8 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2509.10495.

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

pith.paper-citation-record.v1
2509.10495 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T13:16:44.364253Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

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

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

28 of 28 outbound references displayed

verified exact1
verified fuzzy24
unresolved3
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9547f265-6fb0-40c3-b06c-b41f8341cb9f · outbound

This paper cites an unresolved cited work.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-05T13:16:45.432590Z

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 636c81d3-2dfe-47a1-adc5-0a71c3d7ddfd · outbound

This paper cites and Kutz, J.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Kutz, J

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.408498Z

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 39931d65-3e92-432e-bb51-1d8c465a7058 · outbound

This paper cites (1999) Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts (1999) Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.391601Z

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 d1647ecf-adb4-4059-9fee-b004dc05f870 · outbound

This paper cites (1999) An introduction to chaos in nonequilibrium statistical mechanics.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts (1999) An introduction to chaos in nonequilibrium statistical mechanics

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.371156Z

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 4fec6daf-73cd-4d18-8fe9-46fed502903e · outbound

This paper cites and Yu, B.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Yu, B

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.350198Z

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 eb981242-35b3-4148-92f1-ac096f5b32ee · outbound

This paper cites and Van den Broeck, C.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Van den Broeck, C

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.334035Z

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 f7ed0766-b345-4140-ac6a-a596853ff795 · outbound

This paper cites (2012) Stochastic thermodynamics under coarse graining.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts (2012) Stochastic thermodynamics under coarse graining

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.317374Z

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 0a02db8c-51be-40e2-bda3-0f8891426540 · outbound

This paper cites (2012) An introduction to stochastic differential equations.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts (2012) An introduction to stochastic differential equations

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.302296Z

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 3f311720-c895-4b1d-b20a-9bbb5a30b046 · outbound

This paper cites Gao, Lang, Q.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts Gao, Lang, Q

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-05T13:16:44.271849Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c91a3f57-1313-4ff6-a287-8c40c31cffd9 · outbound

This paper cites and Sasa, S.-I.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Sasa, S.-I

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.287368Z

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 ebb38543-0d1f-42bd-a79c-cf2bc2f7cc5e · outbound

This paper cites and Reina, C.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Reina, C

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.272117Z

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 710ff9e5-1150-4d6c-88c0-d4ae75d105af · outbound

This paper cites and Reina, C.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Reina, C

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.255791Z

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 18e42e15-1b9a-42b9-945c-a6816a83d9dc · outbound

This paper cites and Jiang, D.-H.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Jiang, D.-H

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.225654Z

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 cb00d0bb-90bc-4473-98c2-1f2eae6444a9 · outbound

This paper cites (1998) Langevin equation and thermodynamics.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts (1998) Langevin equation and thermodynamics

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.205967Z

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 eeac51b6-639e-44a4-b155-e1a60e54150d · outbound

This paper cites Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-05T13:16:44.616820Z

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 80a6e5e1-60fc-4477-b820-1aba2c4cd0b7 · outbound

This paper cites and Karniadakis, G.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Karniadakis, G

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:45.175869Z

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 ab0958e5-d259-41f9-84ba-a922706ac4c5 · outbound

This paper cites (1998) Fluctuation theorem for stochastic dynamics.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts (1998) Fluctuation theorem for stochastic dynamics

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:44.990143Z

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 c2d2ef64-a340-496e-917b-bacf8c5efec0 · outbound

This paper cites and Trask, N.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Trask, N

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:44.965904Z

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 ff65a6c8-d08e-44de-81fc-e42abcd32742 · outbound

This paper cites and Ren W.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Ren W

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:44.949206Z

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 f698c465-dd17-484a-b23e-4d5e80654c31 · outbound

This paper cites and Wang Y.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Wang Y

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-05T13:16:44.326112Z

Source-reported events for the cited work

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Observation 04ce17a7-9d9d-44f9-a666-fb851704634d · outbound

This paper cites and Vulpiani, A.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Vulpiani, A

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:44.930528Z

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 9bed19e0-9b9a-459b-84c1-cd3d00aa8f34 · outbound

This paper cites Messenger, D.A.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts Messenger, D.A

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:44.914390Z

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 e1f69ad1-c5d3-4e83-b0f9-0d037972c405 · outbound

This paper cites and Gong, G.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Gong, G

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:44.877725Z

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 d2493114-e0f9-4998-9e19-4c671605379e · outbound

This paper cites and Wang, Z.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Wang, Z

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:44.846180Z

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 58b9c4b6-e09c-4c79-a68a-e705f1aa77c2 · outbound

This paper cites and Probert, M.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Probert, M

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:44.822984Z

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 ddd9e9b7-99e1-4b34-8691-49cd7e2b6a7d · outbound

This paper cites and Karniadakis, G.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Karniadakis, G

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:44.804858Z

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 7fd8778e-9b50-45da-a14a-ee5a8368e833 · outbound

This paper cites and Solin, A.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts and Solin, A

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:44.782111Z

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 43b98cc7-355b-43bd-a32f-b5153cba76aa · outbound

This paper cites best” parameters of the neural networks to reconstruct bNN for learning the drift b. • Phase 2: Minimize the loss function I dyn ψ given by (9) and find the “best.

Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts best” parameters of the neural networks to reconstruct bNN for learning the drift b. • Phase 2: Minimize the loss function I dyn ψ given by (9) and find the “best

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T13:16:44.761693Z

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.

Pith citing papers

No inbound Pith citation observations are available.