Paper Citation Record · LEDGER

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

As of 10 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 20 inbound Pith citation observations for arXiv:2502.02414.

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

pith.paper-citation-record.v1
2502.02414 v2

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T12:18:11.364917Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 20 of 20 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T05:22:12.180142Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-30T21:35:04.210949Z

Reference resolution

19 of 19 outbound references displayed

verified exact0
verified fuzzy4
unresolved14
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 73056ffc-f238-4251-9727-6e0c5b5990a9 · outbound

This paper cites an unresolved cited work.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-09T12:18:11.779948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 298967a7-05ee-4645-9248-7bf07b77e6d7 · outbound

This paper cites an unresolved cited work.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Unresolved cited work

Reference 5

Resolution: malformed identifier; raw_fallback, observed 2026-08-09T12:18:11.763095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3298379a-7a11-48dd-a7cb-7e9020989512 · outbound

This paper cites Mitigating spectral bias for the multiscale operator learning.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Mitigating spectral bias for the multiscale operator learning

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-09T12:18:11.289524Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9495ea11-88b2-41b2-a448-4dbf45870a00 · outbound

This paper cites Geometric instability of graph neural networks on large graphs.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Geometric instability of graph neural networks on large graphs

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-09T12:18:11.295095Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 45abcced-0eaa-4c3f-8a46-af4daba8fb05 · outbound

This paper cites Differential Transformer.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Differential Transformer

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-09T12:18:11.313819Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12ec09b6-c993-438e-829e-d91adeca2798 · outbound

This paper cites an unresolved cited work.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-09T12:18:11.745182Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e0116486-0d52-436d-b83f-faef1078f781 · outbound

This paper cites The whole field is discretized to unstructured meshes in the shape of 221 × 51 as the input and the output is the corresponding Mach number on these meshes.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries The whole field is discretized to unstructured meshes in the shape of 221 × 51 as the input and the output is the corresponding Mach number on these meshes

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:18:11.720397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 970ab62a-b568-4141-b83a-997d6ae89abd · outbound

This paper cites Training configurations are identical to previous methods (Wu et al., 2024; Hao et al., 2023; Deng et al., 2024; Elrefaie et al.,.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Training configurations are identical to previous methods (Wu et al., 2024; Hao et al., 2023; Deng et al., 2024; Elrefaie et al.,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:18:11.674055Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation abe84b9b-f688-4f8b-ae26-e4a8c64bd168 · outbound

This paper cites Lv and Ls refer to the loss on volume (surrounding area) and surface physics fields respectively.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Lv and Ls refer to the loss on volume (surrounding area) and surface physics fields respectively

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:18:11.652652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 82d84ae1-e01a-457b-98fe-34b1e6b9c1c6 · outbound

This paper cites an unresolved cited work.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-09T12:18:11.632146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3df65165-1aba-41c3-aae7-ab18fe0d5b41 · outbound

This paper cites an unresolved cited work.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-09T12:18:11.611227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation dd65a395-abb1-4c74-bd27-e2667ff669d4 · outbound

This paper cites The dataset also includes 1000 samples for training and 200 for testing.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries The dataset also includes 1000 samples for training and 200 for testing

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T12:18:11.697408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e0cf44f8-78f8-4da1-9594-cb2b64690d94 · outbound

This paper cites Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism

Reference 2013

Resolution: unresolved; no resolver link, observed 2026-08-09T12:18:11.306944Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36403373-a944-482e-8b69-99fe14111ac3 · outbound

This paper cites The Devil in Linear Transformer.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries The Devil in Linear Transformer

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-09T12:18:11.300761Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14d2092c-a60e-4a68-bba5-fa53ff874f6f · outbound

This paper cites DeepSpeed Ulysses: System Optimizations for Enabling Training of Extreme Long Sequence Transformer Models.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries DeepSpeed Ulysses: System Optimizations for Enabling Training of Extreme Long Sequence Transformer Models

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-09T12:18:11.265678Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d941a35-94e8-48f8-baa3-1d6532d18494 · outbound

This paper cites Geometry-Informed Neural Operator for Large-Scale 3D PDEs.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Geometry-Informed Neural Operator for Large-Scale 3D PDEs

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-09T12:18:11.277928Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 41c063ea-1bb8-4e35-806b-950bb6e9d102 · outbound

This paper cites Ring Attention with Blockwise Transformers for Near-Infinite Context.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Ring Attention with Blockwise Transformers for Near-Infinite Context

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-09T12:18:11.284132Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0290e449-3d5d-4ca4-9af6-abc299055434 · outbound

This paper cites Neural Operator: Graph Kernel Network for Partial Differential Equations.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries Neural Operator: Graph Kernel Network for Partial Differential Equations

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-09T12:18:11.272234Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 88e0627b-e337-4872-ad7c-746e28cb49c7 · outbound

This paper cites DrivAerNet++: A Large-Scale Multimodal Car Dataset with Computational Fluid Dynamics Simulations and Deep Learning Benchmarks.

Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries DrivAerNet++: A Large-Scale Multimodal Car Dataset with Computational Fluid Dynamics Simulations and Deep Learning Benchmarks

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-09T12:18:11.255467Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 0c7540a0-34b2-4e6c-9311-374e99d04c37 · inbound

Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs cites this paper.

Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T05:22:12.180142Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ca3291b-4c5d-4033-a886-f96b37fd41f8 · inbound

Adaptive Physics Transformer with Fused Global-Local Attention for Subsurface Energy Systems cites this paper.

Adaptive Physics Transformer with Fused Global-Local Attention for Subsurface Energy Systems Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T01:14:11.218375Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb21b1ee-2c43-4302-80ff-9eb20ee15f7e · inbound

Multiscale Physics-Informed Neural Network for Complex Fluid Flows with Long-Range Dependencies cites this paper.

Multiscale Physics-Informed Neural Network for Complex Fluid Flows with Long-Range Dependencies Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:20:51.525401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 2e4a3301-997f-48d3-ab47-10a96a211a76 · inbound

One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions cites this paper.

One Scale at a Time: Scale-Autoregressive Modeling for Fluid Flow Distributions Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-11T09:16:03.667671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 5adb0e6f-2c9c-4765-9908-d4fff3644284 · inbound

Neural Shape Operator Surrogates -- Expression Rate Bounds cites this paper.

Neural Shape Operator Surrogates -- Expression Rate Bounds Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 48

Resolution: verified exact; arxiv_id, observed 2026-05-10T11:10:09.871285Z

Source-reported events for the cited work

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Observation f80c1ca7-f2d2-477a-bfd5-54f0b59eb7c7 · inbound

Learning Neural Operator Surrogates for the Black Hole Accretion Code cites this paper.

Learning Neural Operator Surrogates for the Black Hole Accretion Code Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 44

Resolution: verified exact; arxiv_id, observed 2026-05-12T00:21:23.606758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b3112096-d7b0-4581-9331-c317536316ef · inbound

RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics cites this paper.

RETO: A Rotary-Enhanced Transformer Operator for High-Fidelity Prediction of Automotive Aerodynamics Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-11T15:11:04.464403Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 56e48a8b-972d-4618-9da4-efdea7eaa266 · inbound

ShardTensor: Domain Parallelism for Scientific Machine Learning cites this paper.

ShardTensor: Domain Parallelism for Scientific Machine Learning Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 46

Resolution: verified exact; arxiv_id, observed 2026-05-13T03:07:09.022281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e73788da-87f7-44a5-b12e-f686edbcb5fb · inbound

Neural-Schwarz Tiling for Geometry-Universal PDE Solving at Scale cites this paper.

Neural-Schwarz Tiling for Geometry-Universal PDE Solving at Scale Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-13T06:27:24.330876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fdc3bb98-607a-4785-988b-2d8626ee8745 · inbound

Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variation cites this paper.

Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variation Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-05-19T16:42:39.807031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 824abc8e-5175-49bf-a56b-17c4ec6b5827 · inbound

Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variation cites this paper.

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-06-30T21:35:04.212480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6b01e447-c074-4958-af75-0a94a1ef036a · inbound

IKNO: Infinite-order Kernel Neural Operators cites this paper.

IKNO: Infinite-order Kernel Neural Operators Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-22T07:46:14.965962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 46fb0462-b3ec-44c3-a9ba-1afd4b21692a · inbound

Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition cites this paper.

Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-06-30T12:04:38.623662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 9bf561f8-04c6-4aa8-b396-22cbe2594985 · inbound

Adapting Automotive Aerodynamics Surrogates to New Vehicle Families via Transfer Learning cites this paper.

Adapting Automotive Aerodynamics Surrogates to New Vehicle Families via Transfer Learning Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-06-29T10:03:17.296032Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7b0f6683-66b4-4d1c-82c7-20c78f320ff8 · inbound

LEIA: Learned Environment for Interactive Architected Materials cites this paper.

LEIA: Learned Environment for Interactive Architected Materials Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 39

Resolution: verified exact; arxiv_id, observed 2026-06-29T13:43:29.076538Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 3fbb60ee-6bb1-4c7d-82cb-bd971f60e144 · inbound

Physics-Informed Coarsening for Multigrid Graph Neural Surrogates cites this paper.

Physics-Informed Coarsening for Multigrid Graph Neural Surrogates Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 14

Resolution: verified exact; arxiv_id, observed 2026-06-29T00:02:50.450832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d319d0e3-f9e2-47a8-ba70-9ae9306bf042 · inbound

Functional Attention: From Pairwise Affinities to Functional Correspondences cites this paper.

Functional Attention: From Pairwise Affinities to Functional Correspondences Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-06-29T00:02:50.333016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation e7086da5-6190-4e59-94bf-55ca49e0a266 · inbound

Evaluation of State-of-the-Art Deep Learning Architectures for Aerodynamical Predictions cites this paper.

Evaluation of State-of-the-Art Deep Learning Architectures for Aerodynamical Predictions Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 2019

Resolution: unresolved; no resolver link, observed 2026-08-02T03:30:45.443683Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0f2257a-6aab-45d0-872a-c044af71e12b · inbound

Adaptive Mamba Neural Operators cites this paper.

Adaptive Mamba Neural Operators Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-01T16:25:00.535135Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aee16058-e4c5-4ecf-ac2a-a05043d3f956 · inbound

Data-free neural PDE solvers based on Graph Neural Networks and weak forms cites this paper.

Data-free neural PDE solvers based on Graph Neural Networks and weak forms Transolver++: An Accurate Neural Solver for PDEs on Million-Scale Geometries

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-31T23:24:56.512172Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.