Paper Citation Record · LEDGER

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems

As of 12 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 4 inbound Pith citation observations for arXiv:2412.03161.

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

pith.paper-citation-record.v1
2412.03161 v2

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T22:48:13.424353Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:13:16.611531Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-19T18:57:43.148432Z

Reference resolution

21 of 21 outbound references displayed

verified exact0
verified fuzzy9
unresolved11
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 02bd4192-1f2a-465a-bd86-c1452c5a7e93 · outbound

This paper cites an unresolved cited work.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Unresolved cited work

Reference 1

Resolution: malformed identifier; raw_fallback, observed 2026-08-11T22:48:14.914845Z

Source-reported events for the cited work

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

Observation 51ea12c6-13c3-4b16-83ec-b9e40797899c · outbound

This paper cites an unresolved cited work.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:48:14.451063Z

Source-reported events for the cited work

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

Observation 8ad1b7c1-4e12-40da-9f9e-298099b2f34e · outbound

This paper cites an unresolved cited work.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:48:15.204755Z

Source-reported events for the cited work

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

Observation 15cc45c3-536d-4e71-83f9-ac0e18c4e2f0 · outbound

This paper cites P {xk}K k=1 ∈ Ω, {xj}M j=1 ∈ ∂Ω, {u(i)}N i=1 ∈ U sup η,θ | eLphysics(η, θ) − Lphysics(η, θ,{xk}K k=1, {xj}M j=1)| > 4α ! ≤ 8Ncexp − α2N K 32|Ω|2R4 N + 8Ncexp − α2N M 32|∂Ω|2R4 B.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems P {xk}K k=1 ∈ Ω, {xj}M j=1 ∈ ∂Ω, {u(i)}N i=1 ∈ U sup η,θ | eLphysics(η, θ) − Lphysics(η, θ,{xk}K k=1, {xj}M j=1)| > 4α ! ≤ 8Ncexp − α2N K 32|Ω|2R4 N + 8Ncexp − α2N M 32|∂Ω|2R4 B

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:48:14.104755Z

Source-reported events for the cited work

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

Observation 8de005e9-ea48-4bfb-ac39-3b76c0fc2e2e · outbound

This paper cites Variable-Input Deep Operator Networks.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Variable-Input Deep Operator Networks

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T22:48:13.044664Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e5ab7d9d-ad35-4881-a164-ebd6d7df4057 · outbound

This paper cites The final embedding is obtained by computing the inner product of their outputs.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems The final embedding is obtained by computing the inner product of their outputs

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:48:14.714756Z

Source-reported events for the cited work

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

Observation c00aaa94-1692-4973-ac6c-b7ec65169268 · outbound

This paper cites Latent Neural Operator for Solving Forward and Inverse PDE Problems.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Latent Neural Operator for Solving Forward and Inverse PDE Problems

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T22:48:13.107656Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6a96373-8245-4b85-8046-c04b4a9b47e0 · outbound

This paper cites The inverse branch network takes partial measurement data as input and produces the coefficient vector for the target function.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems The inverse branch network takes partial measurement data as input and produces the coefficient vector for the target function

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:48:15.334847Z

Source-reported events for the cited work

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

Observation b0e9e663-3976-44e1-832a-abe19f2e46db · outbound

This paper cites an unresolved cited work.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:48:14.562888Z

Source-reported events for the cited work

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

Observation fd6de86f-1c4a-429f-a621-d2879d5f8542 · outbound

This paper cites an unresolved cited work.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:48:14.294792Z

Source-reported events for the cited work

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

Observation 871b6bce-a033-4470-b1c7-7e87bafdfecc · outbound

This paper cites P {xl}L l=1 ∈ Ωm, {u(i)}N i=1 ∈ UN sup η,θ | eLdata(η, θ) − Ldata(η, θ,{xl}L l=1)| > 2α ! ≤ 8Ncexp − α2N L 512|Ωm|2R4 Proof.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems P {xl}L l=1 ∈ Ωm, {u(i)}N i=1 ∈ UN sup η,θ | eLdata(η, θ) − Ldata(η, θ,{xl}L l=1)| > 2α ! ≤ 8Ncexp − α2N L 512|Ωm|2R4 Proof

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:48:14.184908Z

Source-reported events for the cited work

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

Observation b7c6b14e-7a60-4081-a752-d3e6772f1d4b · outbound

This paper cites an unresolved cited work.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:48:13.995217Z

Source-reported events for the cited work

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

Observation 8b963157-3ab5-4e1c-9c2e-f01beb8c4d6f · outbound

This paper cites Assume that the branch network and trunk network in PI-DIONs have continuous, non-polynomial activation functions.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Assume that the branch network and trunk network in PI-DIONs have continuous, non-polynomial activation functions

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:48:13.944757Z

Source-reported events for the cited work

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

Observation 5c324959-395d-4c4a-ae81-d123a8cb679c · outbound

This paper cites an unresolved cited work.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Unresolved cited work

Reference 900

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:48:15.075075Z

Source-reported events for the cited work

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

Observation 245cc065-2532-4b2b-aed4-492993b55d20 · outbound

This paper cites N 100 500 1000 2000 Relative L2 error 28.73% 5.07% 1.03% 0.98% C.3 V ARIABLE -INPUT PI-DION S Figure 6: Schematic illustration of variable-input PI-DIONs architecture.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems N 100 500 1000 2000 Relative L2 error 28.73% 5.07% 1.03% 0.98% C.3 V ARIABLE -INPUT PI-DION S Figure 6: Schematic illustration of variable-input PI-DIONs architecture

Reference 1000

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:48:14.774784Z

Source-reported events for the cited work

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

Observation f7adb587-75bc-4bbd-806a-210563e39495 · outbound

This paper cites Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Learning time-dependent PDE via graph neural networks and deep operator network for robust accuracy on irregular grids

Reference 1995

Resolution: unresolved; no resolver link, observed 2026-08-11T22:48:12.884602Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eee76db0-519e-4cee-bb4f-ef7151f2aff5 · outbound

This paper cites A pinn approach for identifying governing parameters of noisy thermoacoustic systems.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems A pinn approach for identifying governing parameters of noisy thermoacoustic systems

Reference 2018

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:48:15.421903Z

Source-reported events for the cited work

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

Observation 48310f07-46d8-46f7-9c2e-417f0c3f9198 · outbound

This paper cites Convolutional neural operators.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Convolutional neural operators

Reference 2019

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:48:15.514890Z

Source-reported events for the cited work

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

Observation 3cc1ea58-5454-45f2-914b-44a65e0f3338 · outbound

This paper cites Neural Inverse Operators for Solving PDE Inverse Problems.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Neural Inverse Operators for Solving PDE Inverse Problems

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-11T22:48:13.011120Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1023262-8899-4a99-8889-48f88f206080 · outbound

This paper cites Deep learning.

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Deep learning

Reference 2021

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:48:15.620148Z

Source-reported events for the cited work

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

Observation cb482939-204e-4c8a-8734-cb106a6438fd · outbound

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

Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems Fourier Neural Operator for Parametric Partial Differential Equations

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-11T22:48:12.964757Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 42f88179-814b-4ae4-abe2-ba35198223c6 · inbound

ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines cites this paper.

ELM-DeepONets: Backpropagation-Free Training of Deep Operator Networks via Extreme Learning Machines Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-10T20:13:16.611531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9697a177-ab4b-40e9-b150-349e0ea450c4 · inbound

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery cites this paper.

Neural Interpretable PDEs: Harmonizing Fourier Insights with Attention for Scalable and Interpretable Physics Discovery Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-07T13:02:02.161582Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 458e7d22-71a6-445f-85fe-ed8631678d8b · inbound

DiLO: Decoupling Generative Priors and Neural Operators via Diffusion Latent Optimization for Inverse Problems cites this paper.

DiLO: Decoupling Generative Priors and Neural Operators via Diffusion Latent Optimization for Inverse Problems Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-11T09:31:05.690666Z

Source-reported events for the cited work

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

Observation 5e7a00c9-7ea5-46c7-8b06-37af7da92559 · inbound

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs cites this paper.

Spatiotemporal decoupled physics-informed Stone-Weierstrass neural operator for long-time prediction of time-dependent parametric PDEs Physics-Informed Deep Inverse Operator Networks for Solving PDE Inverse Problems

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-19T18:57:43.150705Z

Source-reported events for the cited work

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