Paper Citation Record · LEDGER

Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 35 inbound Pith citation observations for arXiv:1912.00873.

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

pith.paper-citation-record.v1
1912.00873 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 35 of 35 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-08T16:20:50.893312Z

measured 1 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

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

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

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

Outbound references

No outbound reference observations are available for this paper version.

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e6ccefbe-5a0e-4b08-90be-733a5b4338fe · inbound

DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling cites this paper.

DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-08T16:20:50.893312Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c7490cfd-d97e-4e0d-a732-c32bfe39cee9 · inbound

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

Resolution: unresolved; no resolver link, observed 2026-08-07T05:01:21.584192Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-07T00:44:57.567695Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-07T10:28:56.790460Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T23:34:41.615648Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T19:21:24.819465Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T18:26:50.373780Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f1ba04a0-8563-4187-97d0-c2e098d60098 · inbound

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

Resolution: unresolved; no resolver link, observed 2026-08-06T15:12:03.495684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T14:57:34.926649Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-06T13:58:31.158919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

Resolution: unresolved; no resolver link, observed 2026-08-05T22:07:40.923622Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb07e9bc-524c-4ae4-b56a-e99b4a7a0d66 · inbound

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

Resolution: unresolved; no resolver link, observed 2026-08-05T21:51:34.292575Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4aa5ed63-dd2c-4a9b-a6ee-35097a9e0646 · inbound

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

Resolution: verified exact; arxiv_id, observed 2026-05-18T03:30:50.417873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T11:15:10.410089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Resolution: verified exact; arxiv_id, observed 2026-05-12T10:51:31.859602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1d46c7f3-2180-4a03-bba0-9d78e1a99983 · 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

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Resolution: verified exact; arxiv_id, observed 2026-05-12T05:46:26.534964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T03:11:19.409175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9cd57287-90ae-4343-90ed-2eecb32dcea4 · inbound

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

Resolution: verified exact; arxiv_id, observed 2026-06-29T22:24:00.818601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c6585251-13e4-4f46-9cd1-c6015bf43455 · inbound

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

Resolution: verified exact; arxiv_id, observed 2026-06-30T19:05:00.820240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 70de021a-dc49-4508-9513-3fb8c1692701 · inbound

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

Resolution: verified exact; arxiv_id, observed 2026-06-28T21:32:38.043362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d917305d-b868-4b4f-b99b-b3fa391ca37f · inbound

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T21:58:59.124582Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 72d863d0-a184-448a-a59d-a82369aa513f · inbound

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

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T05:29:35.967036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

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

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-01T22:37:45.825741Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2858bbf-c8a9-46b0-b44c-4ec387935ca1 · inbound

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

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-01T10:04:20.101596Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b4d3931c-fec7-4b6c-b27b-1c4a81be6994 · inbound

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

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-02T07:31:22.794518Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dae6461f-32a1-4a35-ac71-5d4e5707c19d · inbound

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

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-01T07:47:22.110721Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.