Paper Citation Record · LEDGER

Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

As of 8 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 34 inbound Pith citation observations for arXiv:1912.00873.

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pith.paper-citation-record.v1
1912.00873 v1

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measured 34 of 34 standing notices

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

measured 34 of 34 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:28:56.790460Z

measured 1 of 1 external citation measurements

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Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

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198
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

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Pith citing papers

Observation e2ecbe1c-deb6-4ae1-9481-5182dc70e7de · inbound

Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems cites this paper.

Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-24T12:44:28.933609Z

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Observation 5d709bb9-0b0a-4370-9986-1b82126ac0e6 · inbound

Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics cites this paper.

Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 285

Resolution: verified exact; arxiv_id, observed 2026-05-24T10:24:20.278434Z

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A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations cites this paper.

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 19

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Observation 847ee41a-44c6-4cdc-8183-8ecaa0426d37 · inbound

PINNs Algorithmic Framework for Simulation of Nonlinear Burgers' Type Models cites this paper.

PINNs Algorithmic Framework for Simulation of Nonlinear Burgers' Type Models Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 23

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Observation 85b50744-0dfd-4501-852f-46ceda7e1e69 · inbound

Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs cites this paper.

Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 34

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Observation 5ca5ed49-11f2-43b8-b1ec-a71d05b22439 · inbound

Rank Inspired Neural Network for solving linear partial differential equations cites this paper.

Rank Inspired Neural Network for solving linear partial differential equations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 10

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Observation f2994b91-9ea1-458d-8558-1e606b8f61e3 · inbound

A posteriori analysis of neural network approximations cites this paper.

A posteriori analysis of neural network approximations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 16

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Observation d39748a3-bb24-43ac-a9f2-ef25925e13c1 · inbound

Discontinuity-aware KAN-based physics-informed neural networks cites this paper.

Discontinuity-aware KAN-based physics-informed neural networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 29

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Data-Driven Adaptive Gradient Recovery for Unstructured Finite Volume Computations cites this paper.

Data-Driven Adaptive Gradient Recovery for Unstructured Finite Volume Computations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 24

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Observation ac212a27-f355-4411-86d9-a5f45008be08 · inbound

A Learning-based Domain Decomposition Method cites this paper.

A Learning-based Domain Decomposition Method Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 11

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Observation fc5887df-8713-4f4a-8015-b5874492c422 · inbound

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems cites this paper.

Multi-Resolution Training-Enhanced Kolmogorov-Arnold Networks for Multi-Scale PDE Problems Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 7

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Observation 866cd00d-3876-48ee-bb22-b99cca81b1fb · inbound

Physics-informed Multiresolution Wavelet Neural Network Method for Solving Partial Differential Equations cites this paper.

Physics-informed Multiresolution Wavelet Neural Network Method for Solving Partial Differential Equations Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 16

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Prediction error certification for PINNs: Theory, computation, and application to Stokes flow cites this paper.

Prediction error certification for PINNs: Theory, computation, and application to Stokes flow Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 30

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A Practitioner's Guide to Kolmogorov-Arnold Networks cites this paper.

A Practitioner's Guide to Kolmogorov-Arnold Networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 4

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Observation be4df9f8-faf7-4170-8005-e1711c61c521 · inbound

HYCO: A Formalism for Hybrid-Cooperative PDE Modelling cites this paper.

HYCO: A Formalism for Hybrid-Cooperative PDE Modelling Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-05-15T19:11:30.510167Z

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Observation 61ba6e51-f5c9-488c-9a9f-f181afa1a949 · inbound

Python library supporting Discrete Variational Formulations and training solutions with Collocation-based Robust Variational Physics Informed Neural Networks (DVF-CRVPINN) cites this paper.

Python library supporting Discrete Variational Formulations and training solutions with Collocation-based Robust Variational Physics Informed Neural Networks (DVF-CRVPINN) Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 12

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Observation 13a8be3b-cc1b-4050-8543-7d1d12727ab7 · inbound

Robust Deep FOSLS for Transmission Problems cites this paper.

Robust Deep FOSLS for Transmission Problems Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-10T05:46:09.542830Z

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Observation ad6c3cd4-d8bf-4c8b-b79f-3c5fe1da45ae · inbound

On Physics-Based Loss Scaling for MF-PINNs applied to the neutron diffusion equation cites this paper.

On Physics-Based Loss Scaling for MF-PINNs applied to the neutron diffusion equation Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-05-11T22:51:21.656281Z

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Observation 7eaee40f-34f2-46ab-81c2-d4af633fbc45 · inbound

Physics-informed neural networks for form-finding of unilateral membrane structures cites this paper.

Physics-informed neural networks for form-finding of unilateral membrane structures Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-10T00:34:47.199167Z

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Observation 97319b04-8211-4756-b72c-85ddf52b45ca · inbound

Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks cites this paper.

Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 33

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Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks cites this paper.

Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 33

Resolution: verified exact; arxiv_id, observed 2026-07-01T00:25:09.682387Z

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Observation 7784af84-f354-4ebe-9c3c-cf77bef20c31 · inbound

Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks cites this paper.

Per-Loss Adapters for Gradient Conflict in Physics-Informed Neural Networks Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 17

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Observation eed8c4ef-8e53-4b44-8b4d-a024aa1404ce · inbound

jNO: A JAX Library for Neural Operator and Foundation Model Training cites this paper.

jNO: A JAX Library for Neural Operator and Foundation Model Training Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 4

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NPSolver: Neural Poisson Solver with Iterative Physics Supervision cites this paper.

NPSolver: Neural Poisson Solver with Iterative Physics Supervision Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 12

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Towards a Foundation Model for the Martian Atmosphere cites this paper.

Towards a Foundation Model for the Martian Atmosphere Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 141

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A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials cites this paper.

A holomorphic neural network framework for 3D boundary value problems governed by harmonic potentials Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 44

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Exact Boundary Enforcement Along Implicit Geometries for Physics-Informed, Deep Learning Problems in Continuum Mechanics cites this paper.

Exact Boundary Enforcement Along Implicit Geometries for Physics-Informed, Deep Learning Problems in Continuum Mechanics Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-06-29T14:13:29.696060Z

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Observation b3e76fa5-5e07-451e-a41a-f56e650d5b18 · inbound

Learning light scattering from operator parameter spaces to Galerkin-consistent solution spaces cites this paper.

Learning light scattering from operator parameter spaces to Galerkin-consistent solution spaces Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-07-03T16:08:37.586956Z

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Observation f00949ba-ce5a-4638-9595-4486a6a93033 · inbound

INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities cites this paper.

INI-VPINN: A Variational Physics-Informed Neural Network with Implicit Neumann and Interface Handling for Multi-Material Domains with Geometric Singularities Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 8

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Neural network approximation in discrete dual norms with adaptive test spaces cites this paper.

Neural network approximation in discrete dual norms with adaptive test spaces Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 32

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Observation 9477c7e7-4c07-422a-86c7-29aca69a9ce6 · inbound

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning cites this paper.

Non-Asymptotic Variational Learning for Monotone Nonlinear Multiscale Elliptic Equations: Scale-Robust Primal-Dual Bounds and Strong-Form Statistical Ill-Conditioning Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs cites this paper.

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws cites this paper.

HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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Double screening in the training dynamics of variational physics-informed neural networks for heterogeneous coupled parabolic systems cites this paper.

Double screening in the training dynamics of variational physics-informed neural networks for heterogeneous coupled parabolic systems Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

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