Paper Citation Record · LEDGER

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks

As of 7 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2509.01679.

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

pith.paper-citation-record.v1
2509.01679 v1

Coverage vector

measured 40 of 40 reference resolution

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Reference resolution

40 of 40 outbound references displayed

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Outbound references

Observation 9f2c64a0-1bfb-46c0-87d6-67d4223a5063 · outbound

This paper cites A mathematical guide to operator learning.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks A mathematical guide to operator learning

Reference 1

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Observation ddf9fd55-cd7e-478d-9262-bc2e53bafc05 · outbound

This paper cites Positional knowledge is all you need: position-induced transformer (PiT) for operator learning.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Positional knowledge is all you need: position-induced transformer (PiT) for operator learning

Reference 2

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Observation 0e35f8d7-1f64-4832-8d01-f6580c4f678b · outbound

This paper cites Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks

Reference 3

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This paper cites Exponential time differencing for stiff systems.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Exponential time differencing for stiff systems

Reference 4

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This paper cites 19, u r l: https://bookstore.ams.org/gsm-19-r.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks 19, u r l: https://bookstore.ams.org/gsm-19-r

Reference 5

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This paper cites Burgulence.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Burgulence

Reference 6

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Observation 8192269e-dd92-4ca0-b49e-e1bdb3278d6a · outbound

This paper cites Primary, secondary, and meta-analysis of research.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Primary, secondary, and meta-analysis of research

Reference 7

Resolution: verified exact; raw_fallback, observed 2026-08-05T12:22:12.994691Z

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Observation 08331ebe-1275-4d10-92a2-5c1a130bc119 · outbound

This paper cites Solving high-dimensional partial differential equations using deep learning.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Solving high-dimensional partial differential equations using deep learning

Reference 8

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This paper cites GNOT: a general neural operator transformer for operator learning.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks GNOT: a general neural operator transformer for operator learning

Reference 9

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This paper cites 590, d o i: 10.1007/978-3-319-22470-1.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks 590, d o i: 10.1007/978-3-319-22470-1

Reference 10

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This paper cites Wolfe and Eric Chicken 2013 Nonparametric Statistical Methods, John Wiley & Sons, d o i: 10.1002/9781119196037.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Wolfe and Eric Chicken 2013 Nonparametric Statistical Methods, John Wiley & Sons, d o i: 10.1002/9781119196037

Reference 11

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This paper cites Stacked networks improve physics-informed training: applications to neural networks and deep operator networks.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Stacked networks improve physics-informed training: applications to neural networks and deep operator networks

Reference 12

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Unresolved cited work

Reference 13

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This paper cites Learning operators with coupled attention.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Learning operators with coupled attention

Reference 14

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Observation 1506ad83-a3ea-495f-9ed9-acadbbb6ce7b · outbound

This paper cites Neural operator: learning maps between function spaces with applications to PDEs.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Neural operator: learning maps between function spaces with applications to PDEs

Reference 15

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Observation 571c2d03-6b4f-4688-89a2-25ad3aaff159 · outbound

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

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Characterizing possible failure modes in physics-informed neural networks

Reference 16

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Observation eb44b415-88d0-442e-89b1-fb52e62912f8 · outbound

This paper cites Transformer for Partial Differential Equations' Operator Learning.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Transformer for Partial Differential Equations' Operator Learning

Reference 17

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

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Fourier Neural Operator for Parametric Partial Differential Equations

Reference 18

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This paper cites Learning nonlinear operators via DeepONet based on the universal approx- imation theorem of operators.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Learning nonlinear operators via DeepONet based on the universal approx- imation theorem of operators

Reference 19

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This paper cites Machine-learning-based spectral methods for partial differential equations.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Machine-learning-based spectral methods for partial differential equations

Reference 20

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This paper cites Formal Algorithms for Transformers.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Formal Algorithms for Transformers

Reference 21

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This paper cites Efficient kernel surrogates for neural network-based regression.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Efficient kernel surrogates for neural network-based regression

Reference 22

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Unresolved cited work

Reference 23

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This paper cites 92, d o i: 10.1007/978-3-319-15431-2.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks 92, d o i: 10.1007/978-3-319-15431-2

Reference 24

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 25

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This paper cites A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability

Reference 26

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Transformers as neural operators for solutions of differential equations with finite regularity

Reference 27

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks The proof and measurement of association between two things

Reference 28

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Enhanced DeepONet for Modeling Partial Differential Operators Considering Multiple Input Functions

Reference 29

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This paper cites Attention is all you need.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Attention is all you need

Reference 30

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks SVD perspectives for augmenting DeepONet flexibility and interpretability

Reference 31

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Long-time integration of parametric evolution equations with physics-informed DeepONets

Reference 32

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Reference 33

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks When and why PINNs fail to train: a neural tangent kernel perspective

Reference 34

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Unresolved cited work

Reference 35

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This paper cites 2011 Introduction to Robust Estimation and Hypothesis Testing, Academic press, d o i: 10.1016/C2010-0-67044-1.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks 2011 Introduction to Robust Estimation and Hypothesis Testing, Academic press, d o i: 10.1016/C2010-0-67044-1

Reference 36

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Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Individual comparisons by ranking methods

Reference 37

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This paper cites What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications

Reference 38

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:22:10.436588Z

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Observation 991e54ad-499b-4597-adb9-a40e3d4140db · outbound

This paper cites Separable Operator Networks.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks Separable Operator Networks

Reference 39

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This paper cites R-adaptive DeepONet: Learning Solution Operators for PDEs with Discontinuous Solutions Using an R-adaptive Strategy.

Efficient Transformer-Inspired Variants of Physics-Informed Deep Operator Networks R-adaptive DeepONet: Learning Solution Operators for PDEs with Discontinuous Solutions Using an R-adaptive Strategy

Reference 40

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