Paper Citation Record · LEDGER

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems

As of 20 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2607.06237.

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pith.paper-citation-record.v1
2607.06237 v2

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measured 37 of 37 reference resolution

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External citation measurements

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Outbound references

Observation af45ac62-fede-47c5-93cf-c5f2bed27873 · outbound

This paper cites an unresolved cited work.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Unresolved cited work

Reference 1

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Observation ed36b998-5e85-44ff-9211-ad1996b72cdb · outbound

This paper cites A multigrid method for distributed parameter estimation problems.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems A multigrid method for distributed parameter estimation problems

Reference 2

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Observation a2832010-b582-4934-90dd-770987428dae · outbound

This paper cites The cascadic multigrid method for elliptic problems.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems The cascadic multigrid method for elliptic problems

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T08:21:16.653979Z

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Observation 15d814b9-380c-438c-a6b6-27aa587bcb97 · outbound

This paper cites Computational Optimization of Systems Governed by Partial Differential Equations.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Computational Optimization of Systems Governed by Partial Differential Equations

Reference 4

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This paper cites Multigrid methods for PDE optimization.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Multigrid methods for PDE optimization

Reference 5

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This paper cites Fullmulti-grid(FMG)algorithms,in:MultigridTechniques:1984GuidewithApplicationstoFluidDynamics, Revised Edition.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Fullmulti-grid(FMG)algorithms,in:MultigridTechniques:1984GuidewithApplicationstoFluidDynamics, Revised Edition

Reference 6

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Observation 9a7f2a03-077e-4099-bf89-7bfbf0cbec10 · outbound

This paper cites Multibang regularization for electrical impedance tomography.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Multibang regularization for electrical impedance tomography

Reference 7

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Observation 7e17ebde-bc10-45ec-acb7-69cdc6c21854 · outbound

This paper cites Lundisim: Model meshes for flow simulation and scientific data compression benchmarks.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Lundisim: Model meshes for flow simulation and scientific data compression benchmarks

Reference 8

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This paper cites Neuralmessagepassingforquantumchemistry,in:Proceedingsofthe 34thInternationalConferenceonMachineLearning,PMLR.pp.1263–1272.URL:https://proceedings.mlr.press/v70/gilmer17a.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Neuralmessagepassingforquantumchemistry,in:Proceedingsofthe 34thInternationalConferenceonMachineLearning,PMLR.pp.1263–1272.URL:https://proceedings.mlr.press/v70/gilmer17a

Reference 9

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Observation 6ed60055-4455-4941-a90b-ffa60d47ae94 · outbound

This paper cites Optimization with PDE Constraints.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Optimization with PDE Constraints

Reference 10

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Observation bb9b1f3b-f26e-4912-b954-432bb5c2b660 · outbound

This paper cites Statistical and Computational Inverse Problems.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Statistical and Computational Inverse Problems

Reference 11

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Observation a765997e-d560-4a2f-9022-da0a8f8516f3 · outbound

This paper cites PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers

Reference 12

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Observation 91aaeff3-8155-48c5-aca6-d11755a26d21 · outbound

This paper cites Solving inverse problems in physics by optimizing a discrete loss: Fast and accurate learning without neural networks.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Solving inverse problems in physics by optimizing a discrete loss: Fast and accurate learning without neural networks

Reference 13

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Observation 2a9b6dc1-6019-4de4-ba5b-11b27e3575e8 · outbound

This paper cites Physics-informed machine learning.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Physics-informed machine learning

Reference 14

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This paper cites Adam: A Method for Stochastic Optimization.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Adam: A Method for Stochastic Optimization

Reference 15

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Observation cc9ebcff-74dc-4c2e-bae9-212012b2c35f · outbound

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

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Fourier Neural Operator for Parametric Partial Differential Equations

Reference 16

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Observation 4afd5049-f675-462e-afe5-c052e9554902 · outbound

This paper cites Optimal Control of Systems Governed by Partial Differential Equations.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Optimal Control of Systems Governed by Partial Differential Equations

Reference 17

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This paper cites On the limited memory BFGS method for large scale optimization.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems On the limited memory BFGS method for large scale optimization

Reference 18

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This paper cites LearningnonlinearoperatorsviaDeepONetbasedontheuniversalapproximation theorem of operators.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems LearningnonlinearoperatorsviaDeepONetbasedontheuniversalapproximation theorem of operators

Reference 19

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ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Unresolved cited work

Reference 20

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Observation 55b034a0-b6ba-42b6-afe8-5b40c83e4afe · outbound

This paper cites A multigrid approach to discretized optimization problems.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems A multigrid approach to discretized optimization problems

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-02T08:21:16.740307Z

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Observation 6cbf59bf-67e5-4b48-9128-9cfbf0a87b2d · outbound

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ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Numerical Optimization

Reference 22

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ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems A threshold selection method from gray-level histograms

Reference 23

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This paper cites Learning mesh-based simulation with graph networks.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Learning mesh-based simulation with graph networks

Reference 24

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This paper cites Anefficienthierarchicalbayesianmethodforthekuopiotomographychallenge2023.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Anefficienthierarchicalbayesianmethodforthekuopiotomographychallenge2023

Reference 25

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Observation 05f090ba-5e4e-4b51-9a4a-4639cb1468cf · outbound

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

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 26

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ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Kuopio tomography challenge 2023– electrical impedance tomography competition and open dataset

Reference 27

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ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Kuopio tomography challenge 2023 open electrical impedance tomographic dataset (KTC 2023)

Reference 28

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This paper cites Algebraicmultigrid(AMG),in:McCormick,S.F.(Ed.),MultigridMethods.SocietyforIndustrialandApplied Mathematics, Philadelphia.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Algebraicmultigrid(AMG),in:McCormick,S.F.(Ed.),MultigridMethods.SocietyforIndustrialandApplied Mathematics, Philadelphia

Reference 29

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This paper cites Existence and uniqueness for electrode models for electric current computed tomography.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Existence and uniqueness for electrode models for electric current computed tomography

Reference 30

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This paper cites MG-GNN: Multigrid graph neural networks for learning multilevel domain decomposition methods, in: Proceedings of the 40th International Conference on Machine Learning, PMLR.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems MG-GNN: Multigrid graph neural networks for learning multilevel domain decomposition methods, in: Proceedings of the 40th International Conference on Machine Learning, PMLR

Reference 31

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Observation fc86a058-41b4-4350-acf3-06f9b4901abc · outbound

This paper cites Inverse Problem Theory and Methods for Model Parameter Estimation.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Inverse Problem Theory and Methods for Model Parameter Estimation

Reference 32

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This paper cites Computational Methods for Inverse Problems.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Computational Methods for Inverse Problems

Reference 33

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

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems When and why PINNs fail to train: A neural tangent kernel perspective

Reference 34

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This paper cites Multileveloptimizationforinverseproblems,in:Proceedingsofthe35thConferenceonLearning Theory, PMLR.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Multileveloptimizationforinverseproblems,in:Proceedingsofthe35thConferenceonLearning Theory, PMLR

Reference 35

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ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems Iterative methods by space decomposition and subspace correction

Reference 36

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Observation e26ff22a-3ed2-4254-a0c4-1df6e21bce95 · outbound

This paper cites AppliedMathematics for Modern Challenges 2, 165–186.

ResiPhy-MDNF: A Residual-Based Physics-Aware Multilevel Discrete Neural Field Framework for PDE-Constrained Inverse Problems AppliedMathematics for Modern Challenges 2, 165–186

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-02T08:21:16.644109Z

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