Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-12T12:40:42.720102Z
Paper Citation Record · LEDGER
A novel number-theoretic sampling method for neural network solutions of partial differential equations
As of 13 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 0 inbound Pith citation observations for arXiv:2411.17039.
A citation records a reference. It does not transfer a finding from one paper to another.
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Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
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Source: cited_works
Reference resolution
46 of 46 outbound references displayed
- verified exact2
- verified fuzzy37
- unresolved7
- parse uncertain0
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- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 498042ea-27b9-4bd9-80fc-d2582e819b79 · outbound
This paper cites Optimization methods for large-scale machine learning.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Optimization methods for large-scale machine learning
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:44.172284Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 7452401d-8c21-497f-baf2-a342ff18d1de · outbound
This paper cites Monte carlo and quasi-monte carlo methods.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Monte carlo and quasi-monte carlo methods
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:44.145024Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a656e202-9d42-42e6-83a5-5882fc5a73cd · outbound
This paper cites Numerical Mathematics: Theory, Methods & Applications 14.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Numerical Mathematics: Theory, Methods & Applications 14
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:44.117977Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 065db490-cf8f-4c9d-b884-c95ba1b0012e · outbound
This paper cites High-dimensional integration: the quasi-monte carlo way.
A novel number-theoretic sampling method for neural network solutions of partial differential equations High-dimensional integration: the quasi-monte carlo way
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:44.092327Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 3dbcd0bf-54ac-4ac6-8910-a8abf0701256 · outbound
This paper cites Agent-physics-informed neural network solving frequency-domain helmholtz equation related forward and inverse problems.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Agent-physics-informed neural network solving frequency-domain helmholtz equation related forward and inverse problems
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:44.068470Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a6873326-21a6-4a6a-8e15-b1773da30da0 · outbound
This paper cites Theory and application of uniform experimental designs.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Theory and application of uniform experimental designs
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:44.046400Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 2ba20259-ad8e-4b64-b89d-344bec1b57d7 · outbound
This paper cites Number-theoretic methods in statistics.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Number-theoretic methods in statistics
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:44.024631Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b107cb0f-02c2-44c0-9e42-25bc2a309edd · outbound
This paper cites Convergence analysis of a quasi-Monte Carlo-based deep learning algorithm for solving partial differential equations.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Convergence analysis of a quasi-Monte Carlo-based deep learning algorithm for solving partial differential equations
Reference 8
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T12:40:42.876886Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9f0a83b2-ac65-4dbd-803c-0fe984152fb2 · outbound
This paper cites Failure-informed adaptive sampling for pinns, part ii: combining with re-sampling and subset simulation.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Failure-informed adaptive sampling for pinns, part ii: combining with re-sampling and subset simulation
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.860182Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d33ca3cd-f065-4637-a6c2-e8aba37b08d3 · outbound
This paper cites Failure-informed adaptive sampling for pinns.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Failure-informed adaptive sampling for pinns
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.829958Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 10d2c3f6-7152-4c71-8736-82ff88eab637 · outbound
This paper cites A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics.
A novel number-theoretic sampling method for neural network solutions of partial differential equations A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.802718Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0ed0ed12-1a6e-4e08-9030-9d8bfd533074 · outbound
This paper cites On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals.
A novel number-theoretic sampling method for neural network solutions of partial differential equations On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.781372Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 2502f40a-140e-45de-a673-05a1b1f49ab1 · outbound
This paper cites Monte carlo methods.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Monte carlo methods
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.746679Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 8edb2b9b-ca29-4659-b4b7-7086385a03be · outbound
This paper cites Solvinghigh-dimensionalpartialdifferentialequationsusingdeeplearning.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Solvinghigh-dimensionalpartialdifferentialequationsusingdeeplearning
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.725438Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 3e74dbe6-0ad5-4046-9f46-2e6417243c85 · outbound
This paper cites Funktionen von beschränkter variatiou in der theorie der gleichverteilung.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Funktionen von beschränkter variatiou in der theorie der gleichverteilung
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.701890Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation dd23957a-f0d3-4836-a11e-c884d6e97985 · outbound
This paper cites Zur angenäherten berechnung mehrfacher integrale.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Zur angenäherten berechnung mehrfacher integrale
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.671848Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4d7e340d-941b-4c4c-97a6-831e947adf34 · outbound
This paper cites Applications of number theory to numerical analysis.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Applications of number theory to numerical analysis
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.645191Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 30213f28-485b-4a6f-a055-37930f497ae0 · outbound
This paper cites Nsfnets (navier-stokes flow nets): Physics-informed neural networks for the incompressible navier-stokes equations.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Nsfnets (navier-stokes flow nets): Physics-informed neural networks for the incompressible navier-stokes equations
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.599070Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b0bf12d2-2b93-42d8-83fb-732b5f9291c4 · outbound
This paper cites an unresolved cited work.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Unresolved cited work
Reference 19
- Resolution
- unresolved
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 61e2d41d-0a89-41fa-937a-9eac1ad1786e · outbound
This paper cites Adam: A Method for Stochastic Optimization.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Adam: A Method for Stochastic Optimization
Reference 20
- Resolution
- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6bcdc182-c674-4bf2-8da1-9e904c3e89ce · outbound
This paper cites The approximate computation of multiple integrals, in: Dokl.
A novel number-theoretic sampling method for neural network solutions of partial differential equations The approximate computation of multiple integrals, in: Dokl
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.528827Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation bd69f6e5-7fdf-49e4-834c-d83250566208 · outbound
This paper cites The evaluation of multiple integrals by method of optimal coefficients.
A novel number-theoretic sampling method for neural network solutions of partial differential equations The evaluation of multiple integrals by method of optimal coefficients
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.500001Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation afe9b219-5d55-4568-b8d1-ca4eec9a4118 · outbound
This paper cites Characterizing possible failure modes in physics-informed neural networks.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Characterizing possible failure modes in physics-informed neural networks
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.469567Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a2723802-44cc-4165-8947-0090ea6a8424 · outbound
This paper cites Fourier neural operator for parametric partial differential equations, in: International Conference on Learning Representations.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Fourier neural operator for parametric partial differential equations, in: International Conference on Learning Representations
Reference 24
- Resolution
- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6ce739eb-3a61-40ff-bb61-725edcd8a8c4 · outbound
This paper cites Losslandscapesandoptimizationinover-parameterizednon-linearsystemsandneuralnetworks.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Losslandscapesandoptimizationinover-parameterizednon-linearsystemsandneuralnetworks
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.404161Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c63f536f-f107-45db-824e-1bb5234c893b · outbound
This paper cites On the limited memory bfgs method for large scale optimization.
A novel number-theoretic sampling method for neural network solutions of partial differential equations On the limited memory bfgs method for large scale optimization
Reference 26
- Resolution
- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4407cc7d-1040-4e16-b6b4-d9b04a1f94f0 · outbound
This paper cites Learningnonlinearoperatorsviadeeponetbasedontheuniversalapproximation theorem of operators.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Learningnonlinearoperatorsviadeeponetbasedontheuniversalapproximation theorem of operators
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.355413Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 6205efcc-b6ac-4a1f-963e-a58b4b220069 · outbound
This paper cites Deepxde: A deep learning library for solving differential equations.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Deepxde: A deep learning library for solving differential equations
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.329992Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 3da397c7-4f48-444f-b4dd-24fbc2fd0676 · outbound
This paper cites Enforcing exact boundary and initial conditions in the deep mixed residual method.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Enforcing exact boundary and initial conditions in the deep mixed residual method
Reference 29
- Resolution
- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7f71ea84-664e-4d92-b4f3-cdcefdf9c018 · outbound
This paper cites Mim:Adeepmixedresidualmethodforsolvinghigh-orderpartialdifferentialequations.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Mim:Adeepmixedresidualmethodforsolvinghigh-orderpartialdifferentialequations
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.293772Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 7e374668-cdc9-4d7c-a243-6d9a8e786763 · outbound
This paper cites Number Theoretic Accelerated Learning of Physics-Informed Neural Networks.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Number Theoretic Accelerated Learning of Physics-Informed Neural Networks
Reference 31
- Resolution
- verified exact
- local_arxiv, observed 2026-08-12T12:40:42.775269Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 7fd947d4-2a76-4825-ad46-dcfe38fad844 · outbound
This paper cites Pseudo-random numbers and optimal coefficients.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Pseudo-random numbers and optimal coefficients
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.257903Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation cce57834-8e2f-422e-afc2-f305dadc02d2 · outbound
This paper cites Random number generation and quasi-Monte Carlo methods.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Random number generation and quasi-Monte Carlo methods
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.231912Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ccae45a2-eb32-4d27-98c2-cc446b31aede · outbound
This paper cites Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Reference 34
- Resolution
- unresolved
- no resolver link, observed 2026-08-12T12:40:42.639862Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation de0c179c-667a-4efc-8cdf-95dc99c3c9ac · outbound
This paper cites An introduction to partial differential equations.
A novel number-theoretic sampling method for neural network solutions of partial differential equations An introduction to partial differential equations
Reference 35
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.178669Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d8547bfa-481d-440d-8984-d307d77ca2ad · outbound
This paper cites On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type pdes.
A novel number-theoretic sampling method for neural network solutions of partial differential equations On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type pdes
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.153913Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e490212a-db25-4c9a-8709-ca5360af7533 · outbound
This paper cites Dgm: A deep learning algorithm for solving partial differential equations.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Dgm: A deep learning algorithm for solving partial differential equations
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.131050Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 92058329-d241-4f23-83e3-485f58a01259 · outbound
This paper cites Lattice methods for multiple integration.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Lattice methods for multiple integration
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.108502Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0f21a7fd-d17c-4321-935f-73a9f0f4fcdb · outbound
This paper cites On the distribution of points in a cube and the approximate evaluation of integrals.
A novel number-theoretic sampling method for neural network solutions of partial differential equations On the distribution of points in a cube and the approximate evaluation of integrals
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.085894Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 68e203ba-6ebe-482f-9e81-bdbe19e82af7 · outbound
This paper cites Large sample properties of simulations using latin hypercube sampling.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Large sample properties of simulations using latin hypercube sampling
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.064131Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 16f5724e-74e5-4eee-b367-667304d99ebc · outbound
This paper cites Deep density estimation via invertible block-triangular mapping.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Deep density estimation via invertible block-triangular mapping
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.029908Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 6cd771d3-7aa3-4e5c-82ef-6bdc836d64ea · outbound
This paper cites Das-pinns: A deep adaptive sampling method for solving high-dimensional partial differential equations.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Das-pinns: A deep adaptive sampling method for solving high-dimensional partial differential equations
Reference 42
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:43.002514Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 7f88051c-388b-4a5e-9b77-2f25fcc452cc · outbound
This paper cites an unresolved cited work.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Unresolved cited work
Reference 43
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T12:40:42.976041Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 2cdd0508-cd3f-4ed7-b175-df3b994fac35 · outbound
This paper cites Acomprehensivestudyofnon-adaptiveandresidual-basedadaptivesamplingforphysics- informed neural networks.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Acomprehensivestudyofnon-adaptiveandresidual-basedadaptivesamplingforphysics- informed neural networks
Reference 44
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:42.948849Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e4b44f8b-8738-4c0f-81e7-a2c01d88a1b7 · outbound
This paper cites Moving sampling physics-informed neural networks induced by moving mesh pde.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Moving sampling physics-informed neural networks induced by moving mesh pde
Reference 45
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:42.923910Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d83ed9a6-42a5-45f0-915b-efe8c37b072e · outbound
This paper cites Weak adversarial networks for high-dimensional partial differential equations.
A novel number-theoretic sampling method for neural network solutions of partial differential equations Weak adversarial networks for high-dimensional partial differential equations
Reference 46
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T12:40:42.901242Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Pith citing papers
No inbound Pith citation observations are available.