Paper Citation Record · LEDGER

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs

As of 18 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 3 inbound Pith citation observations for arXiv:2507.00278.

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

pith.paper-citation-record.v1
2507.00278 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T21:26:35.371134Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-15T02:34:15.922046Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-15T02:39:41.714435Z

Reference resolution

35 of 35 outbound references displayed

verified exact1
verified fuzzy25
unresolved8
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 91745541-90f1-4ca4-baa5-0b6d749ffc61 · outbound

This paper cites Amestoy, A.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Amestoy, A

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:39.966733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 79b994eb-a7ba-4011-9a86-2e4be83ef35b · outbound

This paper cites Amestoy, I.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Amestoy, I

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:39.853020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 801c19e8-5212-465e-88f7-3d97d7e2c3e7 · outbound

This paper cites Implicit-explicit runge-kutta methods for time-dependent partial differential equations.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Implicit-explicit runge-kutta methods for time-dependent partial differential equations

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:39.706680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation acfc1a98-cbe1-4b4f-b166-de4c2b196431 · outbound

This paper cites Bashforth and J.C.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Bashforth and J.C

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:39.553871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 59ea3fc1-da47-4829-a7ea-bd3dddf78475 · outbound

This paper cites Finite element procedures.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Finite element procedures

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:39.477923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation af537396-72fd-4431-9728-d68a6339af95 · outbound

This paper cites Parallel multilevel preconditioners.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Parallel multilevel preconditioners

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:39.385960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b0b8666a-2953-47c6-9e93-846d089b4292 · outbound

This paper cites Pareto optimality in multiobjective problems.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Pareto optimality in multiobjective problems

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:39.262476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ac073e45-0bd3-4574-91aa-25ce243af4bd · outbound

This paper cites Automatic selection of the best neural architecture for time series forecasting via multi-objective optimization and pareto optimality conditions.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Automatic selection of the best neural architecture for time series forecasting via multi-objective optimization and pareto optimality conditions

Reference 8

Resolution: verified exact; raw_fallback, observed 2026-08-06T21:26:36.061028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f5396eff-2746-4fc0-bcda-9d40dc05d0df · outbound

This paper cites Physics-informed neural networks (pinns) for fluid mechanics: A review.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Physics-informed neural networks (pinns) for fluid mechanics: A review

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:39.132008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bf5705f5-9c61-451e-a863-c7c4024a3648 · outbound

This paper cites Crank and P.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Crank and P

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:39.021967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 583f0b98-a26b-455c-850c-95a1f5a37234 · outbound

This paper cites U-DeepONet : U-Net enhanced deep operator network for geologic carbon sequestration.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs U-DeepONet : U-Net enhanced deep operator network for geologic carbon sequestration

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:38.900776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f68aaf68-62f8-4117-a89b-4965d68d795e · outbound

This paper cites Ross Ethier and D.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Ross Ethier and D

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:38.772342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 769abaa2-ff62-43ad-94f2-1f88ca38fbab · outbound

This paper cites an unresolved cited work.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T21:26:38.663273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 10dd3c3f-2f60-4ba1-8fc4-41261fc37a9d · outbound

This paper cites Iterative methods for solving linear systems.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Iterative methods for solving linear systems

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:38.519359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5f76cc9c-446a-4121-8bff-821e6be7e2c5 · outbound

This paper cites Solving nonlinear equations with Newton's method.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Solving nonlinear equations with Newton's method

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T21:26:34.112579Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c4e75ae-8b35-45ea-b35e-47b5173d9f69 · outbound

This paper cites DeepONet based preconditioning strategies for solving parametric linear systems of equations.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs DeepONet based preconditioning strategies for solving parametric linear systems of equations

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:38.375635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3d633774-2ff1-45b4-8ced-5f5e124fc1f1 · outbound

This paper cites Physics-informed machine learning: Nature reviews physics.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Physics-informed machine learning: Nature reviews physics

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:38.285266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1b4e4631-634c-431a-842d-0a1d3ee9410c · outbound

This paper cites Neural Operator: Learning Maps Between Function Spaces.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Neural Operator: Learning Maps Between Function Spaces

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T21:26:34.338031Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0fbd08a1-8ca4-49c8-81c9-741129a7dfc7 · outbound

This paper cites Spectral/hp element methods for computational fluid dynamics.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Spectral/hp element methods for computational fluid dynamics

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:38.102455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7a138a94-ee5f-44ed-88ed-ae0157a6370e · outbound

This paper cites Decoupled weight decay regularization.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Decoupled weight decay regularization

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T21:26:34.475428Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d8cd046b-b21e-4a2a-8a5a-98f4a2ca2f69 · outbound

This paper cites Learning nonlinear operators via deeponet based on the universal approximation theorem of operators.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Learning nonlinear operators via deeponet based on the universal approximation theorem of operators

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:37.900666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 101160ed-a1e1-4730-8ee6-209621b7275c · outbound

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

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Fourier Neural Operator for Parametric Partial Differential Equations

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T21:26:34.564150Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7534125d-0080-4d8e-a7f1-a31572bcad77 · outbound

This paper cites Automatic discovery of optimal meta-solvers via multi-objective optimization.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Automatic discovery of optimal meta-solvers via multi-objective optimization

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T21:26:34.654207Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 21bf1e92-3973-4b14-9bdd-7de7c305cb47 · outbound

This paper cites Continual Deep Reinforcement Learning for Decentralized Satellite Routing.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Continual Deep Reinforcement Learning for Decentralized Satellite Routing

Reference 24

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T21:26:35.561148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 609446c5-16c8-4292-b889-8915a8b27d6a · outbound

This paper cites Bayesian physics informed neural networks for real-world nonlinear dynamical systems.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Bayesian physics informed neural networks for real-world nonlinear dynamical systems

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:37.643103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cc1b4e9f-f73a-4da2-8ec9-a1f1faf312f3 · outbound

This paper cites Nonlinear multiobjective optimization , volume 12.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Nonlinear multiobjective optimization , volume 12

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T21:26:34.814943Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ed8c8a6e-0e03-481a-90f7-afd1e85f1769 · outbound

This paper cites On the spectral bias of neural networks.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs On the spectral bias of neural networks

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:37.486804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a5fce69e-cf6e-4add-b918-f142d493b12a · outbound

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

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T21:26:34.928376Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 74db8b8c-1a72-4331-97d6-3492e93c943a · outbound

This paper cites A flexible inner-outer preconditioned gmres algorithm.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs A flexible inner-outer preconditioned gmres algorithm

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:37.284641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4f281c9b-bd75-4e8b-b52b-9a3154b00ffd · outbound

This paper cites Iterative methods for sparse linear systems.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Iterative methods for sparse linear systems

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:37.060288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 83701925-514f-4828-a343-38aaaa0b8f3b · outbound

This paper cites Finite difference schemes and partial differential equations.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Finite difference schemes and partial differential equations

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:36.920942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a8844bba-8961-4b0e-9488-ec2c1da4f4b4 · outbound

This paper cites Bi-cgstab: A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Bi-cgstab: A fast and smoothly converging variant of bi-cg for the solution of nonsymmetric linear systems

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:36.762527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 57e138df-c9fe-4030-ad8a-40be548bc0d6 · outbound

This paper cites Iterative Krylov methods for large linear systems.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Iterative Krylov methods for large linear systems

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:36.583502Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4b1b7a99-1b90-4be5-ab4d-797fe50e710d · outbound

This paper cites Wesseling.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Wesseling

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:36.422489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 645b4070-bd1f-4657-a958-dc56242dc626 · outbound

This paper cites Blending neural operators and relaxation methods in pde numerical solvers.

Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs Blending neural operators and relaxation methods in pde numerical solvers

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T21:26:36.264196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

Observation 37ed778d-6c3d-4d65-9551-577fc14dcbff · inbound

NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces cites this paper.

NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs

Reference 21

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T03:50:57.800252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a50cc221-c8ca-4abe-8d55-c75f816ba35c · inbound

NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces cites this paper.

NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspaces Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs

Reference 21

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T06:46:37.177045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2c557c96-8a20-42a9-ab79-5e31c8dcd250 · inbound

PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems cites this paper.

PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs

Reference 44

Resolution: verified exact; arxiv_id, observed 2026-05-15T02:39:41.716095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.