Paper Citation Record · LEDGER

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems

As of 22 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 2 inbound Pith citation observations for arXiv:2505.01736.

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

pith.paper-citation-record.v1
2505.01736 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T04:15:02.993986Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-10T18:54:43.990959Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T04:17:37.558452Z

Reference resolution

41 of 41 outbound references displayed

verified exact1
verified fuzzy25
unresolved15
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d61fbd62-f744-4db4-b73d-622673e120e8 · outbound

This paper cites Computational Fluid Dynamics , volume.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Computational Fluid Dynamics , volume

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.557898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation aa43910e-0580-4b99-a5a2-08376de82240 · outbound

This paper cites an unresolved cited work.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:15:03.493445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 87b2738f-b5be-4449-9031-0a52b721fea3 · outbound

This paper cites HyperdeepONet: learning operator with complex target function space using the limited re- sources via hypernetwork.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems HyperdeepONet: learning operator with complex target function space using the limited re- sources via hypernetwork

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.456792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 24028add-492a-4924-89cb-ac2169fbd784 · outbound

This paper cites Fourier neural op- erator for parametric partial differential equations.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Fourier neural op- erator for parametric partial differential equations

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.444373Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 436778d5-0b35-4448-b53b-b96098786cd2 · outbound

This paper cites Pde-net 2.0: Learning pdes from data with a numeric- symbolic hybrid deep network.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Pde-net 2.0: Learning pdes from data with a numeric- symbolic hybrid deep network

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.431744Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 461398cb-066b-4130-8866-864a0037d469 · outbound

This paper cites Beyond finite layer neural networks: Bridg- ing deep architectures and numerical differential equa- tions.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Beyond finite layer neural networks: Bridg- ing deep architectures and numerical differential equa- tions

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.417516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 03c62030-0f31-4e99-9ec5-c95b264c987e · outbound

This paper cites Spatiotempo- ral learning on cell-embedded graphs.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Spatiotempo- ral learning on cell-embedded graphs

Reference 16

Resolution: verified exact; raw_fallback, observed 2026-08-16T04:15:03.172845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bcd7fcc1-3b8f-43af-8b1c-a304ab7c576e · outbound

This paper cites The finite volume method in com- putational fluid dynamics.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems The finite volume method in com- putational fluid dynamics

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.389001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 26544fdc-57b4-409a-9ed0-4366d6c57d1a · outbound

This paper cites Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Discovering Nonlinear PDEs from Scarce Data with Physics-encoded Learning

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.921630Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4af4383b-1535-4ee4-a0cb-e46245c97942 · outbound

This paper cites Encoding physics to learn reaction–diffusion processes.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Encoding physics to learn reaction–diffusion processes

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.370793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 34cd5d67-456d-4486-9ca7-8043f191f80c · outbound

This paper cites Phycrnet: Physics-informed convolutional-recurrent network for solving spatiotempo- ral pdes.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Phycrnet: Physics-informed convolutional-recurrent network for solving spatiotempo- ral pdes

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.359145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9bf748e0-305a-4b31-bbdc-66dc308c4d41 · outbound

This paper cites Learning to simulate complex physics with graph networks.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Learning to simulate complex physics with graph networks

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.348317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0b351b12-fc77-4c9c-9a0b-ec15aed387af · outbound

This paper cites an unresolved cited work.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:15:03.336312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation ef6d11aa-a0eb-4404-ae35-2b63b0815d74 · outbound

This paper cites Convolutional lstm network: A machine learning approach for precipitation nowcasting.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Convolutional lstm network: A machine learning approach for precipitation nowcasting

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.939845Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5bcb97da-e729-41f9-ac47-d40d9724c777 · outbound

This paper cites A neural pde solver with temporal stencil modeling.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems A neural pde solver with temporal stencil modeling

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.316630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 32600ebb-78ba-43c4-8420-d1550fc87026 · outbound

This paper cites Factorized fourier neural operators.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Factorized fourier neural operators

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.304091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9851ab8e-bc21-46bc-820a-4a20290f031b · outbound

This paper cites Svd perspectives for augmenting deeponet flexi- bility and interpretability.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Svd perspectives for augmenting deeponet flexi- bility and interpretability

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.292380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f518f6b4-ba4b-4b3d-9f06-fdb8c8855090 · outbound

This paper cites Multi- scale simulations of complex systems by learning their ef- fective dynamics.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Multi- scale simulations of complex systems by learning their ef- fective dynamics

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.281242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4cfe077e-920f-4169-8195-7bcd18a4cf09 · outbound

This paper cites Eca-net: Efficient channel attention for deep convolutional neural networks.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Eca-net: Efficient channel attention for deep convolutional neural networks

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.961398Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9369942a-1003-47e6-87f7-9f9d74a9bf2c · outbound

This paper cites Learning the solution operator of parametric partial differential equations with physics-informed deep- onets.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Learning the solution operator of parametric partial differential equations with physics-informed deep- onets

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.263341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0ae96988-3e56-4871-8b0a-23acabc26e8d · outbound

This paper cites P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.969271Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb36b28f-1dd7-462e-9366-b1948c662c66 · outbound

This paper cites U- fno—an enhanced fourier neural operator-based deep- learning model for multiphase flow.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems U- fno—an enhanced fourier neural operator-based deep- learning model for multiphase flow

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.252074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5a2883f9-aa5f-4284-b67f-fb9e14debea7 · outbound

This paper cites Transolver: A Fast Transformer Solver for PDEs on General Geometries.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Transolver: A Fast Transformer Solver for PDEs on General Geometries

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.976561Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c5debdec-7db1-4ace-997a-739d3f0b6a57 · outbound

This paper cites PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems PhyMPGN: Physics-encoded Message Passing Graph Network for spatiotemporal PDE systems

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.981046Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb72d0ed-d9ab-4047-b311-233d68b1a081 · outbound

This paper cites Deciphering and integrating invariants for neural operator learning with various physical mechanisms.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Deciphering and integrating invariants for neural operator learning with various physical mechanisms

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.239685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d409b64b-e0ec-44fe-acc3-0297078c23e1 · outbound

This paper cites Monte carlo neural pde solver for learning pdes via probabilistic representation.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Monte carlo neural pde solver for learning pdes via probabilistic representation

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.227565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 9cbdc2d4-68a8-4789-b1d3-063e856b98f0 · outbound

This paper cites an unresolved cited work.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-16T04:15:03.203610Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7023963c-423d-4ea9-bb48-b5bf31b579e5 · outbound

This paper cites Learning data-driven discretizations for partial differential equations.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Learning data-driven discretizations for partial differential equations

Reference 1995

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.547211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5eb0d99d-6308-4f17-9f79-492131c3211a · outbound

This paper cites Machine learning–accelerated computational fluid dynamics.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Machine learning–accelerated computational fluid dynamics

Reference 2005

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.481070Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 93188bfe-e392-49b6-9405-c742e0e9fe1b · outbound

This paper cites Towards multi-spatiotemporal-scale generalized pde modeling.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Towards multi-spatiotemporal-scale generalized pde modeling

Reference 2011

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.521699Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 604d94b4-8629-47d7-b080-9eb83dcc60c6 · outbound

This paper cites Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformers

Reference 2013

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.868179Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 856dc51c-31dd-4f1c-ad51-d80b33a44c82 · outbound

This paper cites Learned Coarse Models for Efficient Turbulence Simulation.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Learned Coarse Models for Efficient Turbulence Simulation

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.943136Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c658397-e6ee-47dc-8b00-6b0b4a412866 · outbound

This paper cites Learning Mesh-Based Simulation with Graph Networks.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Learning Mesh-Based Simulation with Graph Networks

Reference 2016

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.909480Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b965dde8-5176-4012-846c-1033696322d1 · outbound

This paper cites Learn- ing nonlinear operators via deeponet based on the univer- sal approximation theorem of operators.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Learn- ing nonlinear operators via deeponet based on the univer- sal approximation theorem of operators

Reference 2018

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.403717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6fbf847e-7390-4cc1-99a2-7927aa325a9e · outbound

This paper cites Nonlinear PDEs: Mathematical models in bi- ology, chemistry and population genetics.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Nonlinear PDEs: Mathematical models in bi- ology, chemistry and population genetics

Reference 2019

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.536684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6d0fe7b2-c940-400d-8bba-f10e86e3bc9f · outbound

This paper cites U-NO: U-shaped Neural Operators.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems U-NO: U-shaped Neural Operators

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.914050Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a594bb8-3012-417a-93f8-ef032f4114f1 · outbound

This paper cites Characterizing possible failure modes in physics-informed neural networks.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Characterizing possible failure modes in physics-informed neural networks

Reference 2021

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.469208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 033e35f2-1781-4b84-9575-360964e5c38d · outbound

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

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Physics-informed neural networks: A deep learning framework for solving forward and in- verse problems involving nonlinear partial differential equations

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.918458Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc6f2735-feed-4e77-8ee1-c2fa9737df82 · outbound

This paper cites Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-16T04:15:02.859879Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23ace4d9-bdbb-4d17-b44c-fd3888e7e088 · outbound

This paper cites An introduction to dynamic meteorology , vol- ume.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems An introduction to dynamic meteorology , vol- ume

Reference 2024

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.507313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e6ddde1d-6a31-4664-ac7f-828ef0aec17d · outbound

This paper cites The Finite Element Method: Its Basis and Fundamentals.

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems The Finite Element Method: Its Basis and Fundamentals

Reference 2025

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T04:15:03.216427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

Observation 13278869-6c21-4508-8a1f-c226b69093e3 · inbound

LEAP: A Rapid Neural Surrogate of Multi-Fluid MHD at Europa cites this paper.

LEAP: A Rapid Neural Surrogate of Multi-Fluid MHD at Europa PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-07-03T04:17:37.560898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2c4e8366-3ed6-4323-a884-b443502955d3 · inbound

From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learning cites this paper.

From Points to Edges: Edge-Conditioned Spectral Operators for Physics-Sensitive PDE Learning PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-10T18:54:43.990959Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.