HO-FNO extends standard FNO with n-linear spectral mixing and shows improved accuracy on nonlinear PDE benchmarks, sometimes with a single layer beating deeper FNO models.
arXiv preprint arXiv:2412.10354 , year =
12 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 12representative citing papers
OperatorSHAP trains FastSHAP-style explainers for neural operators via a function-space attribution framework that remains consistent across grid resolutions without retraining.
QuadNorm uses quadrature-based moments instead of uniform averaging in normalization layers, achieving O(h²) consistency across resolutions and better cross-resolution transfer in neural operators.
A single neural operator can approximate the map from arbitrary joint densities to their conditionals, backed by new continuity results and illustrated on Gaussian mixtures.
Rank-1 lattice points and hyperbolic crosses are shown to improve the generalization error and efficiency of Fourier neural operators for PDE approximation on the torus.
The paper evaluates twelve correction architectures from linear regression to Fourier Neural Operators for 2D anisotropic acoustic wave simulations using a unified 10-fold cross-validation on 27,000 heterogeneous velocity fields.
Neural operators reframed via an auxiliary base-space act as efficient interpolators for finite-dimensional functions, matching or exceeding MLPs and KANs in accuracy with fewer parameters on analytic benchmarks and achieving 198 keV RMSE on nuclear mass corrections.
Neural operators progressively forget domain geometry with depth due to Markovian layers and global mixing; a geometry memory injection mechanism mitigates this forgetting.
A Fourier Neural Operator trained on PIC simulations yields a resolution-independent machine-learning closure for electron heat flux that reproduces temperature evolution when inserted into the energy equation and generalizes from coarse to fine grids.
Physics-informed neural operators accurately reproduce cardiac electrophysiology dynamics over long horizons, generalize to unseen conditions and higher resolutions, and run faster than traditional numerical solvers.
A constrained hypothesis-class framework for identifying mesoscopic dynamics from data, backed by uniform well-posedness and stability guarantees derived from a generalized Onsager principle.
Neural operators address the challenge of transferring information across scales in multiscale materials modeling and are illustrated through three selected examples.
citing papers explorer
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Higher-Order Fourier Neural Operator: Explicit Mode Mixer for Nonlinear PDEs
HO-FNO extends standard FNO with n-linear spectral mixing and shows improved accuracy on nonlinear PDE benchmarks, sometimes with a single layer beating deeper FNO models.
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OperatorSHAP: Fast and Accurate Shapley Value Estimation for Neural Operators
OperatorSHAP trains FastSHAP-style explainers for neural operators via a function-space attribution framework that remains consistent across grid resolutions without retraining.
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QuadNorm: Resolution-Robust Normalization for Neural Operators
QuadNorm uses quadrature-based moments instead of uniform averaging in normalization layers, achieving O(h²) consistency across resolutions and better cross-resolution transfer in neural operators.
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One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators
A single neural operator can approximate the map from arbitrary joint densities to their conditionals, backed by new continuity results and illustrated on Gaussian mixtures.
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Fourier Neural Operators with rank-1 lattice points and hyperbolic cross
Rank-1 lattice points and hyperbolic crosses are shown to improve the generalization error and efficiency of Fourier neural operators for PDE approximation on the torus.
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Evaluating Operators for Acoustic Wave Simulation Correction
The paper evaluates twelve correction architectures from linear regression to Fourier Neural Operators for 2D anisotropic acoustic wave simulations using a unified 10-fold cross-validation on 27,000 heterogeneous velocity fields.
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Neural Operators as Efficient Function Interpolators
Neural operators reframed via an auxiliary base-space act as efficient interpolators for finite-dimensional functions, matching or exceeding MLPs and KANs in accuracy with fewer parameters on analytic benchmarks and achieving 198 keV RMSE on nuclear mass corrections.
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Do Neural Operators Forget Geometry? The Forgetting Hypothesis in Deep Operator Learning
Neural operators progressively forget domain geometry with depth due to Markovian layers and global mixing; a geometry memory injection mechanism mitigates this forgetting.
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Resolution-Independent Machine Learning Heat Flux Closure for ICF Plasmas
A Fourier Neural Operator trained on PIC simulations yields a resolution-independent machine-learning closure for electron heat flux that reproduces temperature evolution when inserted into the energy equation and generalizes from coarse to fine grids.
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Physics-Informed Neural Operators for Cardiac Electrophysiology
Physics-informed neural operators accurately reproduce cardiac electrophysiology dynamics over long horizons, generalize to unseen conditions and higher resolutions, and run faster than traditional numerical solvers.
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Hypothesis-driven construction of mesoscopic dynamics
A constrained hypothesis-class framework for identifying mesoscopic dynamics from data, backed by uniform well-posedness and stability guarantees derived from a generalized Onsager principle.
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Multiscale modeling of materials and neural operators
Neural operators address the challenge of transferring information across scales in multiscale materials modeling and are illustrated through three selected examples.