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Paper Citation Record · LEDGER

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations

As of 18 August 2026, this Paper Citation Record lists 44 of 44 outbound references and 2 inbound Pith citation observations for arXiv:2505.08740.

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pith.paper-citation-record.v1
2505.08740 v3

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measured 44 of 44 reference resolution

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Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T13:35:13.585468Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T00:06:24.625148Z

Reference resolution

44 of 44 outbound references displayed

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External citation measurements

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Outbound references

Observation 57f24423-acf3-48b1-9668-8f22410e555a · outbound

This paper cites write newline.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations write newline

Reference 1

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Observation 16085c62-6aeb-4321-a3ec-fe80ff4d8eff · outbound

This paper cites A differentiable, physics-informed ecosystem modeling and learning framework for large-scale inverse problems: demonstration with photosynthesis simulations.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations A differentiable, physics-informed ecosystem modeling and learning framework for large-scale inverse problems: demonstration with photosynthesis simulations

Reference 2

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This paper cites Managing computational complexity using surrogate models: a critical review.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Managing computational complexity using surrogate models: a critical review

Reference 3

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This paper cites A surrogate-model-based method for constrained optimization.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations A surrogate-model-based method for constrained optimization

Reference 4

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Observation c0028c31-c98c-4408-8b70-ce50f54978af · outbound

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Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Unresolved cited work

Reference 5

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Observation 398c1023-3909-4f34-a94f-82e2aa6e5755 · outbound

This paper cites Spherical Fourier neural operators: Learning stable dynamics on the sphere.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Spherical Fourier neural operators: Learning stable dynamics on the sphere

Reference 6

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Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Unresolved cited work

Reference 7

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Observation 2145a370-c602-4bfb-8e08-cc799665c499 · outbound

This paper cites Sobolev training for neural networks.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Sobolev training for neural networks

Reference 8

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This paper cites Differentiable, learnable, regionalized process-based models with multiphysical outputs can approach state-of-the-art hydrologic prediction accuracy.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Differentiable, learnable, regionalized process-based models with multiphysical outputs can approach state-of-the-art hydrologic prediction accuracy

Reference 9

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This paper cites The suitability of differentiable, physics-informed machine learning hydrologic models for ungauged regions and climate change impact assessment.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations The suitability of differentiable, physics-informed machine learning hydrologic models for ungauged regions and climate change impact assessment

Reference 10

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Observation 95a83dac-c704-445b-aa82-6b0ae36e21d2 · outbound

This paper cites Model-parallel fourier neural operators as learned surrogates for large-scale parametric pdes.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Model-parallel fourier neural operators as learned surrogates for large-scale parametric pdes

Reference 11

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Observation 8589867a-ce3b-4be5-8c78-48a38cccb726 · outbound

This paper cites Multiwavelet-based Operator Learning for Differential Equations.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Multiwavelet-based Operator Learning for Differential Equations

Reference 12

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This paper cites Tartakovsky.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Tartakovsky

Reference 13

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This paper cites Shah, and Will Tebbutt.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Shah, and Will Tebbutt

Reference 14

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Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Unresolved cited work

Reference 15

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This paper cites NSFnets ( Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations NSFnets ( Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

Reference 16

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This paper cites Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang

Reference 17

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This paper cites Neural operator: Learning maps between function spaces.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Neural operator: Learning maps between function spaces

Reference 18

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This paper cites Fourier Neural Operator for Parametric Partial Differential Equations , May 2021.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Fourier Neural Operator for Parametric Partial Differential Equations , May 2021

Reference 19

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Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Physics-informed neural operator for learning partial differential equations, 2023

Reference 20

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Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Physics- Informed Neural Operator for Learning Partial Differential Equations

Reference 21

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This paper cites Auxiliary Tasks in Multi-task Learning.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Auxiliary Tasks in Multi-task Learning

Reference 22

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This paper cites Gradient-enhanced neural network response surface approximations.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Gradient-enhanced neural network response surface approximations

Reference 23

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Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Discretize- Optimize vs

Reference 24

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This paper cites Differential equations, mechanics, and computation, volume 51.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Differential equations, mechanics, and computation, volume 51

Reference 25

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Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Raissi, P

Reference 26

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This paper cites On the usefulness of overparameterized ecological models.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations On the usefulness of overparameterized ecological models

Reference 27

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This paper cites PhyCRNet : Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations PhyCRNet : Physics-informed convolutional-recurrent network for solving spatiotemporal PDEs

Reference 28

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This paper cites Why so many published sensitivity analyses are false: A systematic review of sensitivity analysis practices.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Why so many published sensitivity analyses are false: A systematic review of sensitivity analysis practices

Reference 29

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Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations JAX MD : A Framework for Differentiable Physics

Reference 30

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This paper cites Appling, Pierre Gentine, Toshiyuki Bandai, Hoshin Gupta, Alexandre Tartakovsky, Marco Baity-Jesi , Fabrizio Fenicia, Daniel Kifer, Li Li, Xiaofeng Liu, Wei Ren, Yi Zheng, Ciaran J.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Appling, Pierre Gentine, Toshiyuki Bandai, Hoshin Gupta, Alexandre Tartakovsky, Marco Baity-Jesi , Fabrizio Fenicia, Daniel Kifer, Li Li, Xiaofeng Liu, Wei Ren, Yi Zheng, Ciaran J

Reference 31

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Observation e357c527-45e4-4c67-b3e2-d1f082a8a23e · outbound

This paper cites When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Reference 32

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This paper cites Improving physics-informed, differentiable hydrologic models for capturing unseen extreme events.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Improving physics-informed, differentiable hydrologic models for capturing unseen extreme events

Reference 33

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Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Unresolved cited work

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This paper cites Wavelet Neural Operator for solving parametric partial differential equations in computational mechanics problems.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Wavelet Neural Operator for solving parametric partial differential equations in computational mechanics problems

Reference 35

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This paper cites From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling

Reference 36

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This paper cites Fully probabilistic deep models for forward and inverse problems in parametric pdes.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Fully probabilistic deep models for forward and inverse problems in parametric pdes

Reference 37

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

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Learning the solution operator of parametric partial differential equations with physics-informed deeponets

Reference 38

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This paper cites Brenowitz, Spencer K.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Brenowitz, Spencer K

Reference 39

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This paper cites O'Gorman.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations O'Gorman

Reference 40

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This paper cites Differentiable Modeling and Optimization of Battery Electrolyte Mixtures Using Geometric Deep Learning , November 2023.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Differentiable Modeling and Optimization of Battery Electrolyte Mixtures Using Geometric Deep Learning , November 2023

Reference 41

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This paper cites @esa (Ref.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations @esa (Ref

Reference 42

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Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations Unresolved cited work

Reference 43

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This paper cites end-to-end.

Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations end-to-end

Reference 44

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Pith citing papers

Observation d776c63f-3eb7-4f5b-b991-22b82d2f9914 · inbound

Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements cites this paper.

Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations

Reference 59

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Spectral Audit of In-Context Operator Networks cites this paper.

Spectral Audit of In-Context Operator Networks Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations

Reference 15

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