Solver-Integrated Adversarial Attacking and Training of Neural Operators | Paper Citation Record

Observation b69c19a4-59a2-42b2-a279-17b63f109443 · outbound

This paper cites Wikipedia, 2025.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Wikipedia, 2025

Reference 1

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Observation 4fe03df6-9260-4f63-8b6b-592983ca6ae5 · outbound

This paper cites Wikipedia, 2025.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Wikipedia, 2025

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Observation 5ac94912-a26f-4654-92aa-901dde772b82 · outbound

This paper cites Evaluating the Adversarial Robustness for Fourier Neural Operators.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Evaluating the Adversarial Robustness for Fourier Neural Operators

Reference 3

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Observation 92501d2f-ade8-46e7-8c67-3ae6ab2e0341 · outbound

This paper cites Implicit Neural Differential Model for Spatiotemporal Dynamics.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Implicit Neural Differential Model for Spatiotemporal Dynamics

Reference 4

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Observation 28c9486b-1ac6-42ce-829b-abd499c6eb8d · outbound

This paper cites Differentiable programming across the PDE and Machine Learning barrier.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Differentiable programming across the PDE and Machine Learning barrier

Reference 5

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This paper cites Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Dedalus: A Flexible Framework for Numerical Simulations with Spectral Methods

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This paper cites Canuto, M.Y.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Canuto, M.Y

Reference 7

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This paper cites Clercx et al.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Clercx et al

Reference 8

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This paper cites Soft-DTW: a differentiable loss function for time-series.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Soft-DTW: a differentiable loss function for time-series

Reference 9

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Observation 4455aba4-e965-4d3c-87f0-4e8bea0af229 · outbound

This paper cites Soft-dtw: a differentiable loss function for time-series.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Soft-dtw: a differentiable loss function for time-series

Reference 10

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Observation 9e4bb786-5ac3-47b0-8593-0e33a30edc89 · outbound

This paper cites Physics-informed re- duced order modeling of time-dependent pdes via differentiable solvers.arXiv preprint arXiv:2505.14595, 2025.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Physics-informed re- duced order modeling of time-dependent pdes via differentiable solvers.arXiv preprint arXiv:2505.14595, 2025

Reference 11

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Unresolved cited work

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Observation 79d5c7aa-d57a-4587-a8bb-425f281088c6 · outbound

This paper cites The kernel cookbook: Advice on covariance functions, 2014.

Solver-Integrated Adversarial Attacking and Training of Neural Operators The kernel cookbook: Advice on covariance functions, 2014

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Observation b4758c7d-b720-4c3e-8e5e-e95eeaf481b4 · outbound

This paper cites Fourier series representation of periodic signals.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Fourier series representation of periodic signals

Reference 14

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This paper cites GitHub / open source.

Solver-Integrated Adversarial Attacking and Training of Neural Operators GitHub / open source

Reference 15

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This paper cites Advanced gaussian processes (scribed notes, lecture 21).

Solver-Integrated Adversarial Attacking and Training of Neural Operators Advanced gaussian processes (scribed notes, lecture 21)

Reference 16

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This paper cites Explaining and Harnessing Adversarial Examples.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Explaining and Harnessing Adversarial Examples

Reference 17

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This paper cites Discrete fourier transform and wavelet transforms (math 357 notes).

Solver-Integrated Adversarial Attacking and Training of Neural Operators Discrete fourier transform and wavelet transforms (math 357 notes)

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This paper cites Finite fourier transform, circulant matrices, and the fast fourier transform.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Finite fourier transform, circulant matrices, and the fast fourier transform

Reference 19

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This paper cites Knowledge Distillation: A Survey.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Knowledge Distillation: A Survey

Reference 20

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This paper cites A review: Applications of the spectral finite element method.Archives of Computational Methods in Engineering, 2023.

Solver-Integrated Adversarial Attacking and Training of Neural Operators A review: Applications of the spectral finite element method.Archives of Computational Methods in Engineering, 2023

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Observation b97b02bf-39fc-46aa-ae28-9a1db71cc73f · outbound

This paper cites Spectral kernels (gpss 2021).

Solver-Integrated Adversarial Attacking and Training of Neural Operators Spectral kernels (gpss 2021)

Reference 23

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Observation 3e5be8b6-c9f8-41df-adc5-10235593ea21 · outbound

This paper cites Distilling the Knowledge in a Neural Network.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Distilling the Knowledge in a Neural Network

Reference 24

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This paper cites Hou and Ruo Li.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Hou and Ruo Li

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This paper cites Show, Attend and Distill:Knowledge Distillation via Attention-based Feature Matching.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Show, Attend and Distill:Knowledge Distillation via Attention-based Feature Matching

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Observation 8c280bdf-12f1-40e8-9484-15e71eec3b94 · outbound

This paper cites Unsupervised learning of full-waveform inversion: Connecting cnn and partial differential equation in a loop.Preprint / Conference (ICLR), 2022.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Unsupervised learning of full-waveform inversion: Connecting cnn and partial differential equation in a loop.Preprint / Conference (ICLR), 2022

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This paper cites , and Youzuo Lin.

Solver-Integrated Adversarial Attacking and Training of Neural Operators , and Youzuo Lin

Reference 28

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This paper cites Perceptual losses for real-time style transfer and super-resolution.European Conference on Computer Vision (ECCV) Workshops, 2016.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Perceptual losses for real-time style transfer and super-resolution.European Conference on Computer Vision (ECCV) Workshops, 2016

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This paper cites Cambridge University Press, 3rd edition, 2004.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Cambridge University Press, 3rd edition, 2004

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This paper cites Elastic image matching is np-complete.Pattern Recognition Letters, 24(1-3):445–453, 2003.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Elastic image matching is np-complete.Pattern Recognition Letters, 24(1-3):445–453, 2003

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This paper cites Exponax: Fourier spectral etdrk time-steppers in jax.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Exponax: Fourier spectral etdrk time-steppers in jax

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This paper cites A Selective Survey on Versatile Knowledge Distillation Paradigm for Neural Network Models.

Solver-Integrated Adversarial Attacking and Training of Neural Operators A Selective Survey on Versatile Knowledge Distillation Paradigm for Neural Network Models

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Laga and W

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This paper cites Direct image matching by dynamic warping.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Direct image matching by dynamic warping

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This paper cites Adversarial training for physics-informed neural networks (at-pinns), 2023.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Adversarial training for physics-informed neural networks (at-pinns), 2023

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

Solver-Integrated Adversarial Attacking and Training of Neural Operators Fourier Neural Operator for Parametric Partial Differential Equations

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This paper cites Fourier neural operator with learned deformations for pdes on general geometries.Journal of Machine Learning Research, 2023.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Fourier neural operator with learned deformations for pdes on general geometries.Journal of Machine Learning Research, 2023

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This paper cites Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) for Solving Nonlinear Option Pricing models.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) for Solving Nonlinear Option Pricing models

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This paper cites DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.

Solver-Integrated Adversarial Attacking and Training of Neural Operators DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators

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This paper cites Karniadakis.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Karniadakis

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Hilbert $C^*$-module independence

Reference 46

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This paper cites Towards Deep Learning Models Resistant to Adversarial Attacks.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Towards Deep Learning Models Resistant to Adversarial Attacks

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This paper cites To- wards deep learning models resistant to adversarial attacks.

Solver-Integrated Adversarial Attacking and Training of Neural Operators To- wards deep learning models resistant to adversarial attacks

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Majda and Andrea L

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This paper cites Giometto, Marc B.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Giometto, Marc B

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Observation 0c42672e-b966-4c84-95be-b718c3b89872 · outbound

This paper cites Circulant matrices.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Circulant matrices

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Molenaar

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Gladstone, and Hadi Meidani

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This paper cites Learning dtw global constraint for time series classification.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Learning dtw global constraint for time series classification

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Unresolved cited work

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This paper cites AL-PINN: Active Learning-Driven Physics-Informed Neural Networks for Efficient Sample Selection in Solving Partial Differential Equations.

Solver-Integrated Adversarial Attacking and Training of Neural Operators AL-PINN: Active Learning-Driven Physics-Informed Neural Networks for Efficient Sample Selection in Solving Partial Differential Equations

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Observation 5a2af5e7-87ce-452d-888b-a8fc1f8393de · outbound

This paper cites Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

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This paper cites Karniadakis.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Karniadakis

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Unresolved cited work

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Williams.Gaussian Processes for Machine Learning

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This paper cites Fitnets: Hints for thin deep nets.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Fitnets: Hints for thin deep nets

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Wiley, 1990

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Observation f84a3b02-874d-476e-8ba4-cfea37fe3c4d · outbound

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Dynamic programming algorithm optimization for spoken word recog- nition.IEEE Transactions on Acoustics, Speech, and Signal Processing, 26(1):43–49, 1978

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Dynamic time warping algorithm review

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This paper cites Discovering the fourier transform: A tutorial on circulant matrices, circular con- volution, and the dft.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Discovering the fourier transform: A tutorial on circulant matrices, circular con- volution, and the dft

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Observation 36b1e856-f75b-4e70-905a-cd20e3fe4482 · outbound

This paper cites Understanding gaussian process regression using the fourier transform, 2000.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Understanding gaussian process regression using the fourier transform, 2000

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Observation 3cfb60aa-50f9-4192-9b61-e6ae5795347a · outbound

This paper cites Fourier-spectral methods for navier–stokes equations in 2d.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Fourier-spectral methods for navier–stokes equations in 2d

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Observation 734f2627-1fbc-4af0-8990-51950e7e2799 · outbound

This paper cites Physics-based Deep Learning.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Physics-based Deep Learning

Reference 68

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Observation 048dc6e9-015c-4d5d-9e0c-160217531848 · outbound

This paper cites Trefethen.Spectral Methods in MATLAB.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Trefethen.Spectral Methods in MATLAB

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Observation 9f8133e2-a84f-4a14-b75c-cc1636a562be · outbound

This paper cites Physics-informed neural network with adaptive mesh refinement sampling.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Physics-informed neural network with adaptive mesh refinement sampling

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Observation 5284dedc-bd98-4fe6-8a29-8646ad682b70 · outbound

This paper cites Solver-in-the- loop: Learning from differentiable physics to interact with iterative pde-solvers.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Solver-in-the- loop: Learning from differentiable physics to interact with iterative pde-solvers

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Observation d193881c-4aea-4d81-abcf-1f31187a3ae4 · outbound

This paper cites Generalized harmonic analysis.Acta Mathematica, 1930.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Generalized harmonic analysis.Acta Mathematica, 1930

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Observation 4010bd97-746c-4001-bc63-ef38ab22f21a · outbound

This paper cites Gaussian Process Kernels for Pattern Discovery and Extrapolation.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Gaussian Process Kernels for Pattern Discovery and Extrapolation

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Observation 326a4580-a755-4cb2-8912-fb85f91ec84a · outbound

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Unresolved cited work

Reference 74

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Observation 425a983a-6548-4f00-bed1-4d4fe4c33df2 · outbound

This paper cites an unresolved cited work.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Unresolved cited work

Reference 75

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Observation 0d7d9ef1-e7c0-489c-8c62-e379708e9967 · outbound

This paper cites Wood and Grace Chan.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Wood and Grace Chan

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Observation 51f39edf-9d87-4c47-adc2-0b7aa1b39376 · outbound

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Unresolved cited work

Reference 78

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Observation c0caa0eb-383e-4a88-834b-29f698c9529b · outbound

This paper cites On the generalization properties of adversarial training.

Solver-Integrated Adversarial Attacking and Training of Neural Operators On the generalization properties of adversarial training

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Observation f2b37bb6-3bd1-45af-be88-52539bb68df8 · outbound

This paper cites Karniadakis.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Karniadakis

Reference 80

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Observation db1df7cc-d0b6-4eb2-9573-8dd13706fdf2 · outbound

This paper cites Karniadakis.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Karniadakis

Reference 81

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Observation 85e1e3a2-a73e-4c99-9015-6dc4e8b3f44a · outbound

This paper cites Adversarial Training: A Survey.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Adversarial Training: A Survey

Reference 82

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Observation 5c951f97-78c3-4a4e-8cf1-b276d1b81730 · outbound

This paper cites Improving generalization of adversarial training via robust critical fine-tuning.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Improving generalization of adversarial training via robust critical fine-tuning

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Observation 0ffc57b9-1bd5-4c30-9fa0-284fd11ea1f3 · outbound

This paper cites For FFT libraries using real-to-complex transforms (e.g.

Solver-Integrated Adversarial Attacking and Training of Neural Operators For FFT libraries using real-to-complex transforms (e.g

Reference 86

Resolution: unresolved; no resolver link, observed 2026-08-04T08:50:06.216316Z

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Observation 910dec9c-b12d-4757-a5a3-80c34f9fd6df · outbound

This paper cites 2/3 rule):M(k x, ky) = 1 if|k x| ≤N 3 and|k y| ≤N 3 , else 0.

Solver-Integrated Adversarial Attacking and Training of Neural Operators 2/3 rule):M(k x, ky) = 1 if|k x| ≤N 3 and|k y| ≤N 3 , else 0

Reference 87

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Observation 79be1ece-1175-4bbf-a664-578a99087119 · outbound

This paper cites RBF kernel.

Solver-Integrated Adversarial Attacking and Training of Neural Operators RBF kernel

Reference 88

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Observation ad4f23f8-3b85-4ea2-b3e4-d40cfebe9ed6 · outbound

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Solver-Integrated Adversarial Attacking and Training of Neural Operators Unresolved cited work

Reference 89

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Observation 6978b457-6323-4629-afa0-da4f05119ec6 · outbound

This paper cites an unresolved cited work.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Unresolved cited work

Reference 90

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Observation 3938ffee-22bf-488a-b458-441b77e7f63c · outbound

This paper cites an unresolved cited work.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Unresolved cited work

Reference 91

Resolution: unresolved; no resolver link, observed 2026-08-04T08:50:06.779792Z

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Observation 63fad0eb-96af-4d93-a7ef-7e0ae098559c · outbound

This paper cites •Analogy with finite-dimensional Gaussian sampling.In finite-dimensional statistics, sampling a Gaussian vector with covarianceC=QΛQ T is done viaQΛ 1/2 z.

Solver-Integrated Adversarial Attacking and Training of Neural Operators •Analogy with finite-dimensional Gaussian sampling.In finite-dimensional statistics, sampling a Gaussian vector with covarianceC=QΛQ T is done viaQΛ 1/2 z

Reference 92

Resolution: malformed identifier; no resolver link, observed 2026-08-04T08:50:06.930587Z

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Observation ef169d6a-40d6-4b89-bc99-f03bd71a7b95 · outbound

This paper cites an unresolved cited work.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Unresolved cited work

Reference 2011

Resolution: unresolved; no resolver link, observed 2026-08-04T08:49:58.698974Z

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Observation 19deca6c-f009-497c-8077-ce072689bd26 · outbound

This paper cites an unresolved cited work.

Solver-Integrated Adversarial Attacking and Training of Neural Operators Unresolved cited work

Reference 2013

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