Paper Citation Record · LEDGER

Neural Spline Operators for Risk Quantification in Stochastic Systems

As of 17 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2508.20288.

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

pith.paper-citation-record.v1
2508.20288 v1

Coverage vector

measured 47 of 47 reference resolution

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measured 47 of 47 standing notices

One-hop event checks from named stored sources.

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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

47 of 47 outbound references displayed

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verified fuzzy33
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6aaf9073-186f-4caa-aa5e-1c22080cbf1c · outbound

This paper cites Myopi- cally verifiable probabilistic certificate for long-term safety,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Myopi- cally verifiable probabilistic certificate for long-term safety,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:29.045741Z

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Observation 73095089-86ef-488b-8b4a-3ff9ff65db21 · outbound

This paper cites Rubino and B.

Neural Spline Operators for Risk Quantification in Stochastic Systems Rubino and B

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:29.034931Z

Source-reported events for the cited work

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Observation 0cf8ac7d-f236-4d67-882e-b1ba79372512 · outbound

This paper cites Safe control in the presence of stochastic uncertainties,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Safe control in the presence of stochastic uncertainties,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:29.023996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6d763ecb-0cc2-476c-ba51-e745627298ce · outbound

This paper cites A generalizable physics-informed learning framework for risk probability estimation,.

Neural Spline Operators for Risk Quantification in Stochastic Systems A generalizable physics-informed learning framework for risk probability estimation,

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:29.011755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation de5c19ef-cd29-4d0d-9bd5-4813bd5b6d2d · outbound

This paper cites Physics- informed deep b-spline networks for dynamical systems,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Physics- informed deep b-spline networks for dynamical systems,

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T16:55:28.308899Z

Source-reported events for the cited work

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Observation 20b21d0a-19b5-4143-9305-a1cdfdefc0c7 · outbound

This paper cites Neural operator: Learning maps be- tween function spaces with applications to pdes,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Neural operator: Learning maps be- tween function spaces with applications to pdes,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:29.000306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 03578675-f478-4ac3-8e8f-5fc2d6369b87 · outbound

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

Neural Spline Operators for Risk Quantification in Stochastic Systems Physics-informed neural operator for learning partial differential equations,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.988848Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation a5d9fc5a-7200-4e9e-8e44-29861f4f1fa8 · outbound

This paper cites Neural operators for accelerating scientific simulations and design,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Neural operators for accelerating scientific simulations and design,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.977416Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 42005bb5-1889-41a9-aa5e-0037d538d5b1 · outbound

This paper cites an unresolved cited work.

Neural Spline Operators for Risk Quantification in Stochastic Systems Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:55:28.966648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 560aa31a-1819-4cb2-9f2b-dad8e86babec · outbound

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

Neural Spline Operators for Risk Quantification in Stochastic Systems Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T16:55:28.326967Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0aa87bb5-4174-4ed2-bca8-cc52ed2ba00d · outbound

This paper cites Adaptive safe con- trol for driving in uncertain environments,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Adaptive safe con- trol for driving in uncertain environments,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.949493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation aeeea4fb-a1bd-45ef-8405-542278422166 · outbound

This paper cites 3d dynamic walking on stepping stones with control barrier functions,.

Neural Spline Operators for Risk Quantification in Stochastic Systems 3d dynamic walking on stepping stones with control barrier functions,

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.939384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 642dedfc-de94-4e4b-961e-261ffbc07356 · outbound

This paper cites Monte-carlo based uncertainty analysis: Sampling effi- ciency and sampling convergence,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Monte-carlo based uncertainty analysis: Sampling effi- ciency and sampling convergence,

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.928734Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0e49f864-0dd0-4458-af23-200e25639d56 · outbound

This paper cites Sequential monte carlo for rare event estimation,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Sequential monte carlo for rare event estimation,

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.918384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 87acf9e2-6137-4b0f-a3e1-7817519f51cf · outbound

This paper cites Estimation of small failure probabilities in high dimensions by subset simulation,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Estimation of small failure probabilities in high dimensions by subset simulation,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.907940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6e1fd52d-55f6-4c58-bb86-9143748a7c07 · outbound

This paper cites Multilevel monte carlo methods,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Multilevel monte carlo methods,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.897244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f4e4cd8e-4218-4dd7-8ca6-4069de03ba05 · outbound

This paper cites Dhatt, E.

Neural Spline Operators for Risk Quantification in Stochastic Systems Dhatt, E

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.886224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation be2f7e7f-1569-461f-8d6b-59d582c2c088 · outbound

This paper cites Finite volume methods,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Finite volume methods,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.875624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d91cb16b-5f3d-49dd-a86a-445ada1a6c4a · outbound

This paper cites An assessment of solvers for algebraically stabilized discretizations of convection–diffusion– reaction equations,.

Neural Spline Operators for Risk Quantification in Stochastic Systems An assessment of solvers for algebraically stabilized discretizations of convection–diffusion– reaction equations,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.864669Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0b68b02e-64c6-4d25-a7eb-ecc81fea45a0 · outbound

This paper cites Eliminating gibbs phenomena: A non-linear petrov–galerkin method for the convection– diffusion–reaction equation,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Eliminating gibbs phenomena: A non-linear petrov–galerkin method for the convection– diffusion–reaction equation,

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.854068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e5691aa8-930e-481b-85ee-cebf1b3e4009 · outbound

This paper cites FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators.

Neural Spline Operators for Risk Quantification in Stochastic Systems FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

Reference 21

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 719a9f96-13b8-4838-9699-5c8030ed70d2 · outbound

This paper cites Fourier neural operator approach to large eddy simulation of three-dimensional turbulence,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Fourier neural operator approach to large eddy simulation of three-dimensional turbulence,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.842434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 263f057a-dc74-4e25-959b-df42de927170 · outbound

This paper cites Learning the solution operator of parametric partial differential equations with physics-informed deeponets,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Learning the solution operator of parametric partial differential equations with physics-informed deeponets,

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T16:55:28.370568Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8f839f3b-7091-41df-9740-5894abeaf7b7 · outbound

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

Neural Spline Operators for Risk Quantification in Stochastic Systems Fourier Neural Operator for Parametric Partial Differential Equations

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T16:55:28.373874Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f191ee3-484b-4504-80b9-5e4cd8a32ccb · outbound

This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.

Neural Spline Operators for Risk Quantification in Stochastic Systems Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-15T16:55:28.377538Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18e6471b-214d-4955-b846-472944d5e547 · outbound

This paper cites Spectral neural operators,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Spectral neural operators,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.825169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 77115b2f-d04a-4b74-b418-1077b09d97ef · outbound

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

Neural Spline Operators for Risk Quantification in Stochastic Systems DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T16:55:28.384958Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8fb4d0ff-4bf1-4900-aac0-f45ad327dd74 · outbound

This paper cites Improving physics-informed DeepONets with hard constraints.

Neural Spline Operators for Risk Quantification in Stochastic Systems Improving physics-informed DeepONets with hard constraints

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T16:55:28.389072Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b655c584-7964-4b0c-b2ec-70ac84c2efec · outbound

This paper cites Reproducing kernel triangular b-spline-based fem for solving pdes,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Reproducing kernel triangular b-spline-based fem for solving pdes,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.814372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f61cb747-18e7-4592-b775-a70926d38a91 · outbound

This paper cites Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants.

Neural Spline Operators for Risk Quantification in Stochastic Systems Variational formulation based on duality to solve partial differential equations: Use of B-splines and machine learning approximants

Reference 30

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 34588b90-022f-4d3b-8f4e-57a1fb3f97e0 · outbound

This paper cites Functional networks for b- spline surface reconstruction,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Functional networks for b- spline surface reconstruction,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.803500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 0d4a5a8d-ad49-4411-922d-e01a1e1fbf11 · outbound

This paper cites Modeling nonlinear systems using the tensor network b-spline and the multi-innovation identification the- ory,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Modeling nonlinear systems using the tensor network b-spline and the multi-innovation identification the- ory,

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.793446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 16be748c-422d-499a-8534-5085a2138a76 · outbound

This paper cites Dif- ferentiable spline approximations,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Dif- ferentiable spline approximations,

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.782935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2d752281-5405-4a2e-b18a-9217ba457ca7 · outbound

This paper cites Learning feedforward control using a dilated b-spline network: Frequency domain analysis and design,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Learning feedforward control using a dilated b-spline network: Frequency domain analysis and design,

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.773215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 69697eea-d6af-4ec8-9a91-587fd2e9ee4a · outbound

This paper cites Building hybrid b- spline and neural network operators,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Building hybrid b- spline and neural network operators,

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.762823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1b151b7e-ccaf-4fe3-a962-43418bf97608 · outbound

This paper cites Deep neural networks for smooth approximation of physics with higher order and continuity B-spline base functions.

Neural Spline Operators for Risk Quantification in Stochastic Systems Deep neural networks for smooth approximation of physics with higher order and continuity B-spline base functions

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:55:28.500980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 532afcdf-797e-4a37-b83a-c20e57f1bb59 · outbound

This paper cites A best-fitting b-spline neural network approach to the prediction of advection– diffusion physical fields with absorption and source terms,.

Neural Spline Operators for Risk Quantification in Stochastic Systems A best-fitting b-spline neural network approach to the prediction of advection– diffusion physical fields with absorption and source terms,

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.752388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e6c91da2-e204-465d-a11c-08ab695dcbe4 · outbound

This paper cites Multipole graph neural operator for parametric partial differential equations,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Multipole graph neural operator for parametric partial differential equations,

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.741145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 59a42d8c-7877-408c-b291-6562ba477e40 · outbound

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

Neural Spline Operators for Risk Quantification in Stochastic Systems U-NO: U-shaped Neural Operators

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-15T16:55:28.427251Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb8ba1ff-2dd8-44d9-b6fe-e258b20f46be · outbound

This paper cites Seismic wave propagation and inversion with neural operators,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Seismic wave propagation and inversion with neural operators,

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.729775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 18aac628-a38d-49df-b5e2-e18624cf6545 · outbound

This paper cites Broadband ground-motion synthesis via generative adver- sarial neural operators: Development and validation,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Broadband ground-motion synthesis via generative adver- sarial neural operators: Development and validation,

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.719422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 2dff04f7-a962-4bb7-acbd-f8add3b023a9 · outbound

This paper cites The computation of all the derivatives of a b-spline basis,.

Neural Spline Operators for Risk Quantification in Stochastic Systems The computation of all the derivatives of a b-spline basis,

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.707868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 121c75cc-bd21-4717-8f75-2e9c0bc85a9f · outbound

This paper cites On universal approximation and error bounds for fourier neural operators,.

Neural Spline Operators for Risk Quantification in Stochastic Systems On universal approximation and error bounds for fourier neural operators,

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.695325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 53bb5243-775d-4ed2-99b1-9d375e472772 · outbound

This paper cites an unresolved cited work.

Neural Spline Operators for Risk Quantification in Stochastic Systems Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:55:28.684354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 56a70036-1b73-4ae4-b156-76ff11a3809d · outbound

This paper cites an unresolved cited work.

Neural Spline Operators for Risk Quantification in Stochastic Systems Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:55:28.673087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 8edab4d7-57d9-4382-9809-453ede497ac0 · outbound

This paper cites Orthogonal modal representa- tion in long-term risk quantification for dynamic multi-agent systems,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Orthogonal modal representa- tion in long-term risk quantification for dynamic multi-agent systems,

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.661772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 41aab8bd-e313-4a18-bcd0-80e0267a8dfe · outbound

This paper cites Multilayer feedforward networks are universal approximators,.

Neural Spline Operators for Risk Quantification in Stochastic Systems Multilayer feedforward networks are universal approximators,

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:55:28.650962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

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