ELADO provides a benchmark suite of elliptic PDE datasets designed to isolate and quantify failure modes in neural operator architectures.
Mixed citations
arXivabs/2108.08481(2021)
Mixed citation behavior. Most common role is method (60%).
17
Pith papers citing it
Method
60% of classified citations
citation-role summary
method 3
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representative citing papers
Neural operators approximate continuous operators from H^s to H^t with O(N^{-s/d}) error in H^t norm; FNOs on Burgers achieve H^1 errors to 10^{-7} and follow a power-law scaling with exponent ~1.4.
Hybrid FNO-LBM accelerates porous media flow convergence by up to 70% via neural initialization and stabilizes unsteady simulations through embedded FNO rollouts, allowing small models to match larger ones in accuracy.
Physics-informed Fourier neural operators recover plasmoid formation in sparse SRRMHD vortex data where data-only models fail, and transformer operators approximate AMR jet evolution, marking first reported uses in these relativistic MHD settings.
Skala is a neural XC functional trained on wavefunction data that beats state-of-the-art hybrids on main-group chemistry benchmarks at semi-local computational cost.
A Fourier neural operator trained on Boussinesq-compressible simulation pairs corrects Boussinesq predictions for natural convection, achieving SSIM near unity and MSE reductions of one to three orders of magnitude.
A perturbation-based conformal prediction wrapper on Fourier Neural Operators yields narrower uncertainty bands than prior methods for 2D incompressible Navier-Stokes while preserving coverage in data-scarce regimes.
EquiNO with Q-DEIM creates reduced-order physics-informed surrogates for 3D hyperelastic RVEs that enforce equilibrium and periodicity by construction, achieve 10^3 speedups, and accurately interpolate and extrapolate stresses from few snapshots.
LESnets integrates LES equations and the law of the wall into F-FNO to enable data-free, stable long-term predictions of wall-bounded turbulence at Re_tau up to 1000 on coarse grids, matching traditional LES accuracy at higher efficiency.
SFNO surrogate matches or exceeds HUX on several solar-wind metrics while remaining trainable on additional data.
FNO surrogate model learns to predict long-term grain growth evolution from phase-field data while remaining accurate on unseen configurations and higher-resolution grids.
A conditional DDPM framework is introduced to approximate solution operators for parameter-dependent PDEs, achieving accuracy comparable to FNO while recovering noise levels and providing confidence intervals.
GraMO couples graph interactions and temporal state updates in one linear recurrence with input-dependent coefficients to simulate N-body, motion, and robotics systems with lower long-horizon error than prior GNN or SSM approaches.
Presents sequential physics-constrained neural operator models for the Norne reservoir with theoretical stability guarantees and empirical accuracy exceeding 0.99 R² for oil production predictions alongside a 10,000x computational speedup.
Two Kriging variants add linear PDE constraints at collocation points for better interpolation of functions satisfying those equations, tested on ODEs, harmonic PDEs, and cylinder flows.
Proposes dynamics-based analysis of time series models showing partial dynamics learning and end-positioning as key to performance, plus a plug-and-play improvement method.
citing papers explorer
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ELADO: Elliptic PDE Assessment Datasets for Operator Learning
ELADO provides a benchmark suite of elliptic PDE datasets designed to isolate and quantify failure modes in neural operator architectures.
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Quantitative Sobolev Approximation Bounds for Neural Operators with Empirical Validation on Burgers Equation
Neural operators approximate continuous operators from H^s to H^t with O(N^{-s/d}) error in H^t norm; FNOs on Burgers achieve H^1 errors to 10^{-7} and follow a power-law scaling with exponent ~1.4.
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Hybrid Fourier Neural Operator-Lattice Boltzmann Method
Hybrid FNO-LBM accelerates porous media flow convergence by up to 70% via neural initialization and stabilizes unsteady simulations through embedded FNO rollouts, allowing small models to match larger ones in accuracy.
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Learning Neural Operator Surrogates for the Black Hole Accretion Code
Physics-informed Fourier neural operators recover plasmoid formation in sparse SRRMHD vortex data where data-only models fail, and transformer operators approximate AMR jet evolution, marking first reported uses in these relativistic MHD settings.
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Accurate and scalable exchange-correlation with deep learning
Skala is a neural XC functional trained on wavefunction data that beats state-of-the-art hybrids on main-group chemistry benchmarks at semi-local computational cost.
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A Neural Surrogate Approach for Simulating Natural Convection Problems
A Fourier neural operator trained on Boussinesq-compressible simulation pairs corrects Boussinesq predictions for natural convection, achieving SSIM near unity and MSE reductions of one to three orders of magnitude.
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Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime
A perturbation-based conformal prediction wrapper on Fourier Neural Operators yields narrower uncertainty bands than prior methods for 2D incompressible Navier-Stokes while preserving coverage in data-scarce regimes.
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Physics-Informed Reduced-Order Operator Learning for Hyperelasticity in Continuum Micromechanics
EquiNO with Q-DEIM creates reduced-order physics-informed surrogates for 3D hyperelastic RVEs that enforce equilibrium and periodicity by construction, achieve 10^3 speedups, and accurately interpolate and extrapolate stresses from few snapshots.
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Large-eddy simulation nets (LESnets) based on physics-informed neural operator for wall-bounded turbulence
LESnets integrates LES equations and the law of the wall into F-FNO to enable data-free, stable long-term predictions of wall-bounded turbulence at Re_tau up to 1000 on coarse grids, matching traditional LES accuracy at higher efficiency.
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Toward Data-Driven Surrogates of the Solar Wind with Spherical Fourier Neural Operator
SFNO surrogate matches or exceeds HUX on several solar-wind metrics while remaining trainable on additional data.
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Teaching Artificial Intelligence to Perform Rapid, Resolution-Invariant Grain Growth Modeling via Fourier Neural Operator
FNO surrogate model learns to predict long-term grain growth evolution from phase-field data while remaining accurate on unseen configurations and higher-resolution grids.
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Generative diffusion learning for parametric partial differential equations
A conditional DDPM framework is introduced to approximate solution operators for parameter-dependent PDEs, achieving accuracy comparable to FNO while recovering noise levels and providing confidence intervals.
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Graph Mamba Operator: A Latent Simulator for Interacting Particle Systems
GraMO couples graph interactions and temporal state updates in one linear recurrence with input-dependent coefficients to simulate N-body, motion, and robotics systems with lower long-horizon error than prior GNN or SSM approaches.
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Sequential Physics-Constrained Neural Operator Forward Modeling for the $\textit{Norne}$ Reservoir System
Presents sequential physics-constrained neural operator models for the Norne reservoir with theoretical stability guarantees and empirical accuracy exceeding 0.99 R² for oil production predictions alongside a 10,000x computational speedup.
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Optimal Linear Interpolation under Differential Information: application to the prediction of perfect flows
Two Kriging variants add linear PDE constraints at collocation points for better interpolation of functions satisfying those equations, tested on ODEs, harmonic PDEs, and cylinder flows.
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Time Series Forecasting Through the Lens of Dynamics
Proposes dynamics-based analysis of time series models showing partial dynamics learning and end-positioning as key to performance, plus a plug-and-play improvement method.
- Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning