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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws

As of 9 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 0 inbound Pith citation observations for arXiv:2607.10965.

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Observation 21fe54c1-e3d0-4d2c-ae7f-8a743d7c22e4 · outbound

This paper cites Turbulence and the dynamics of coherent structures part III: Dy- namics and scaling.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Turbulence and the dynamics of coherent structures part III: Dy- namics and scaling

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This paper cites Lumley, and Emily Stone.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Lumley, and Emily Stone

Reference 2

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This paper cites A survey of projection-based model reduction methods for parametric dynamical systems.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws A survey of projection-based model reduction methods for parametric dynamical systems

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Unresolved cited work

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Unresolved cited work

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This paper cites Adjacency-based, non-intrusive model reduction for vortex-induced vibrations.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Adjacency-based, non-intrusive model reduction for vortex-induced vibrations

Reference 6

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Unresolved cited work

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Unresolved cited work

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

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Fourier Neural Operator for Parametric Partial Differential Equations

Reference 9

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This paper cites Learning nonlinear operators via DeepONet based on the universal approximation the- orem of operators.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Learning nonlinear operators via DeepONet based on the universal approximation the- orem of operators

Reference 10

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This paper cites Fries, Xiaolong He, and Youngsoo Choi.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Fries, Xiaolong He, and Youngsoo Choi

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Unresolved cited work

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This paper cites A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling

Reference 13

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Southworth, and Marc L

Reference 14

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Plasma surrogate modelling using fourier neural opera- tors

Reference 16

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Carlberg

Reference 17

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws A fast and ac- curate physics-informed neural network reduced order model with shallow masked au- toencoder

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Chen, Jinxu Xiang, Dong H

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Kara, and Yongjie J

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Keo Springer, and Kyle T

Reference 21

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Aslam, and Marc L

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Reduced-order modeling for parameterized PDEs via implicit neural representations

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws tlasdi: Thermodynamics-informed latent space dynamics identification

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Unresolved cited work

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Approximate bayesian neural operators: Uncertainty quantification for para- metric PDEs

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws B-deeponet: An enhanced bayesian deeponet for solving noisy parametric pdes using accelerated replica exchange sgld

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Randomized prior wavelet neural operator for uncertainty quantification

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Psaros, and George E

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Maddix, Shima Alizadeh, Gaurav Gupta, Andrew Stuart, Michael W

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Scalable Uncertainty Quantification for Deep Operator Networks using Randomized Priors

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This paper cites Calibrated uncertainty quantification for operator learning via conformal prediction.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Calibrated uncertainty quantification for operator learning via conformal prediction

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Conformalized-deeponet: A distribution-free framework for uncertainty quantification in deep operator networks

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Probabilistic neural operators for functional uncertainty quantification

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Neural operator induced gaus- sian process framework for probabilistic solution of parametric partial differential equa- tions

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Towards gaussian process for operator learning: An uncertainty aware resolution independent operator learning al- gorithm for computational mechanics

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Operator learning with gaussian processes

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Unresolved cited work

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Nature Communications, 15:10416, 2024

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This paper cites Kingma and Max Welling.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Kingma and Max Welling

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Learning in latent spaces improves the predictive accuracy of deep neural operators

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This paper cites Approximation by superpositions of a sigmoidal function.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Approximation by superpositions of a sigmoidal function

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Multilayer feedforward net- works are universal approximators

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This paper cites DDMI: Domain-Agnostic Latent Diffusion Models for Synthesizing High-Quality Implicit Neural Representations.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws DDMI: Domain-Agnostic Latent Diffusion Models for Synthesizing High-Quality Implicit Neural Representations

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This paper cites Ln3diff++: Scalable latent neural fields diffusion for speedy 3d generation.

Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Ln3diff++: Scalable latent neural fields diffusion for speedy 3d generation

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws beta-V AE: Learning basic visual concepts with a constrained variational framework

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Karniadakis

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Representation of divergence-free vector fields

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Kelliher

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Unresolved cited work

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Adam: A Method for Stochastic Optimization

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Decoupled Weight Decay Regularization

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Efficient implementation of weighted ENO schemes

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Efficient implementation of essentially non-oscillatory shock-capturing schemes

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Score-Based Generative Modeling through Stochastic Differential Equations

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Observation d30b2f9f-60ad-45f2-bca9-d93340437dae · outbound

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Structure-preserving variational neural fields: Uncertainty-quantified reduced-order modeling of nonlinear conservation laws Unresolved cited work

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