Paper Citation Record · LEDGER

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing

As of 12 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2608.09494.

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2608.09494 v1

Coverage vector

measured 35 of 35 reference resolution

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Pith citing papers itemized under the disclosed page cap.

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Reference resolution

35 of 35 outbound references displayed

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External citation measurements

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Outbound references

Observation 4642715b-5216-416b-9457-f1e01a615b01 · outbound

This paper cites Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense

Reference 1

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This paper cites Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations

Reference 2

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This paper cites An overview on deep learning-based approximation methods for partial differential equa- tions.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing An overview on deep learning-based approximation methods for partial differential equa- tions

Reference 3

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Observation 2c2c0fca-5243-41cd-9e45-03cd2d1926a5 · outbound

This paper cites Nonlinear MonteCarlo methodswith polynomial runtimeforBellman equationsof discretetime high-dimensional stochastic optimal control problems.Appl.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Nonlinear MonteCarlo methodswith polynomial runtimeforBellman equationsof discretetime high-dimensional stochastic optimal control problems.Appl

Reference 4

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Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Unresolved cited work

Reference 5

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Observation 4e766fb5-4d74-4e5e-b334-591b43092dfc · outbound

This paper cites From Monte Carlo to neural networks approximations of boundary value problems.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing From Monte Carlo to neural networks approximations of boundary value problems

Reference 6

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Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Unresolved cited work

Reference 7

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Observation 807e1e85-118d-4469-a4cb-8ec259e78b96 · outbound

This paper cites Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations

Reference 8

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Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Unresolved cited work

Reference 9

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Observation f49a724a-e375-4da2-9bcc-be4599240520 · outbound

This paper cites Trudinger.Elliptic partial differential equations of second order.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Trudinger.Elliptic partial differential equations of second order

Reference 10

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Observation 10cda936-a648-4007-b03a-0f9bfb24434e · outbound

This paper cites Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Deep neural network approximation for high-dimensional elliptic PDEs with boundary conditions

Reference 11

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Observation 492c3379-8cc1-43ce-b7f1-bb64524f7bb7 · outbound

This paper cites A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black–Scholes partial differential equations.Mem.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing A proof that artificial neural networks overcome the curse of dimensionality in the numerical approximation of Black–Scholes partial differential equations.Mem

Reference 12

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Observation e92ec158-0c5c-4de5-8ec9-1abe6fb3ff69 · outbound

This paper cites Space- time error estimates for deep neural network approximations for differential equa- tions.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Space- time error estimates for deep neural network approximations for differential equa- tions

Reference 13

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Observation b9169137-4fde-477e-b718-caf93a6c1011 · outbound

This paper cites Deep neural network approxi- mations for solutions of PDEs based on Monte Carlo algorithms.Partial Differ.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Deep neural network approxi- mations for solutions of PDEs based on Monte Carlo algorithms.Partial Differ

Reference 14

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Observation 26203e6b-35cb-4030-87fb-754af2c295f7 · outbound

This paper cites A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations

Reference 15

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Observation 016a5011-45bf-40c8-96d6-89e3ebf884cd · outbound

This paper cites Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality

Reference 16

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Observation 6ff51282-77ad-4621-9f75-4559e1ebf49b · outbound

This paper cites Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory

Reference 17

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Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Unresolved cited work

Reference 18

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Observation 4dad3403-998d-4833-8226-d60ab8874978 · outbound

This paper cites Shreve.Brownian motion and stochastic calculus, volume 113 ofGraduate Texts in Mathematics.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Shreve.Brownian motion and stochastic calculus, volume 113 ofGraduate Texts in Mathematics

Reference 19

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This paper cites Probability theory.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Probability theory

Reference 20

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Observation 95e5c31f-5885-4960-b4b5-349e0b366531 · outbound

This paper cites Unbiased‘walk-on-spheres’ MonteCarlomethodsforthe fractionalLaplacian.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Unbiased‘walk-on-spheres’ MonteCarlomethodsforthe fractionalLaplacian

Reference 21

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Observation 56ec21f6-908f-4fe4-9138-e946588629e4 · outbound

This paper cites Geometry of sets and measures in Euclidean spaces, volume 44 of Cambridge Studies in Advanced Mathematics.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Geometry of sets and measures in Euclidean spaces, volume 44 of Cambridge Studies in Advanced Mathematics

Reference 22

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Observation 89ee5e2b-6771-48f3-a5f4-338ed8623db4 · outbound

This paper cites Some continuous Monte Carlo methods for the Dirichlet problem.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Some continuous Monte Carlo methods for the Dirichlet problem

Reference 23

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Observation 1c59f730-3e8c-4767-9ec5-7ed30bafac63 · outbound

This paper cites Monte Carlo-Algorithmen.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Monte Carlo-Algorithmen

Reference 24

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Observation 44d511a4-41e7-41c9-836a-c183acf3f2b1 · outbound

This paper cites Rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of gradient-dependent semi- linear heat equations.Commun.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of gradient-dependent semi- linear heat equations.Commun

Reference 25

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Observation 06882b59-ba67-4963-bbca-c0718ddc7146 · outbound

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Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Unresolved cited work

Reference 26

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Observation d9577807-55c0-4890-9de6-880b64f21b4d · outbound

This paper cites Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro- differential equations.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Deep ReLU neural networks overcome the curse of dimensionality when approximating semilinear partial integro- differential equations

Reference 27

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Observation b2a80030-57ad-489f-b6d3-3c363d545838 · outbound

This paper cites Port and Charles J.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Port and Charles J

Reference 28

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This paper cites Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Rectified deep neural networks overcome the curse of dimensionality for nonsmooth value functions in zero-sum games of nonlinear stiff systems

Reference 29

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Observation 84c0b27d-dec0-490a-8c35-74e32d8b0aa2 · outbound

This paper cites Sabelfeld.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Sabelfeld

Reference 30

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Observation d986a7f8-3b28-4e26-8364-e984532eca68 · outbound

This paper cites Sabelfeld and Anastasya Kireeva.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Sabelfeld and Anastasya Kireeva

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:36:55.108498Z

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Observation 268f6a88-26b1-453f-9561-1cd79e06de78 · outbound

This paper cites Sabelfeld and Anastasya Kireeva.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Sabelfeld and Anastasya Kireeva

Reference 32

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Observation 63a2dbe2-7e04-45b0-8b69-685612b334d8 · outbound

This paper cites Sabelfeld and Denis Talay.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Sabelfeld and Denis Talay

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:36:55.081862Z

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Observation 902ccc5f-03f5-4cd1-a5de-02d5e57549be · outbound

This paper cites Grid-free monte carlo for pdes with spatially varying coefficients.ACM Trans.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Grid-free monte carlo for pdes with spatially varying coefficients.ACM Trans

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:36:55.069668Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 924d2a09-1b13-4c88-ab7e-4259eda55bab · outbound

This paper cites Error bounds for approximations with deep ReLU networks.Neural Networks, 94:103–114, 2017.

Walk-on-Spheres Monte Carlo and deep neural network approximations of elliptic PDEs with drift and killing Error bounds for approximations with deep ReLU networks.Neural Networks, 94:103–114, 2017

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T16:36:55.056018Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

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