FreqNO-DPS corrects neural operator spectral bias in 3D elastic wavefield prediction by frequency-dependent guidance in diffusion posterior sampling conditioned on sparse observations, achieving near-zero bias at 2-5% sensor coverage.
Toward a better understanding of fourier neural operators from a spectral perspective
7 Pith papers cite this work. Polarity classification is still indexing.
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Neural tangent kernel from neural reparameterization modulates sensitivity and wave tangent kernels to produce spectral filtering, wavenumber modulation, and frequency bias that improve NeurFWI convergence.
A physics-informed Fourier-wavelet transformer model reports the lowest normalized mean-squared error on cylinder-wake and fluid-structure interaction velocity-field benchmarks compared with spectral, transformer, operator-learning, and PINN baselines.
Operator Boosting constructs compact neural-operator PDE surrogates by sequential residual learning with validation-selected shrinkage, yielding 72-95% parameter reduction and accuracy gains on 21 of 30 dataset-architecture pairs.
IRNO augments neural operators with learned fixed-point iterative refinement modules and a progressive spectral loss, achieving up to 56% error reduction on turbulent flow and large drops in high-frequency normalized errors on active matter.
Multi-stage residual learning in quantum circuits mitigates frequency parameterization bias and improves test MSE on synthetic benchmarks with multiple localized frequency components compared to single-stage training.
MENO restores multi-scale structure in neural-operator PDE surrogates via one-step improved MeanFlow, claiming up to 2× better power-spectrum accuracy and up to 14× faster inference than DDIM enhancement.
citing papers explorer
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Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations
FreqNO-DPS corrects neural operator spectral bias in 3D elastic wavefield prediction by frequency-dependent guidance in diffusion posterior sampling conditioned on sparse observations, achieving near-zero bias at 2-5% sensor coverage.
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Deciphering Neural Reparameterized Full-Waveform Inversion with Neural Sensitivity Kernel and Wave Tangent Kernel
Neural tangent kernel from neural reparameterization modulates sensitivity and wave tangent kernels to produce spectral filtering, wavenumber modulation, and frequency bias that improve NeurFWI convergence.
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A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling
A physics-informed Fourier-wavelet transformer model reports the lowest normalized mean-squared error on cylinder-wake and fluid-structure interaction velocity-field benchmarks compared with spectral, transformer, operator-learning, and PINN baselines.
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Operator Boosting Produces Pareto-Efficient PDE Surrogates
Operator Boosting constructs compact neural-operator PDE surrogates by sequential residual learning with validation-selected shrinkage, yielding 72-95% parameter reduction and accuracy gains on 21 of 30 dataset-architecture pairs.
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Iterative Refinement Neural Operators are Learned Fixed-Point Solvers: A Principled Approach to Spectral Bias Mitigation
IRNO augments neural operators with learned fixed-point iterative refinement modules and a progressive spectral loss, achieving up to 56% error reduction on turbulent flow and large drops in high-frequency normalized errors on active matter.
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Mitigating Frequency Learning Bias in Quantum Models via Multi-Stage Residual Learning
Multi-stage residual learning in quantum circuits mitigates frequency parameterization bias and improves test MSE on synthetic benchmarks with multiple localized frequency components compared to single-stage training.
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MENO: MeanFlow-Enhanced Neural Operators for Dynamical Systems
MENO restores multi-scale structure in neural-operator PDE surrogates via one-step improved MeanFlow, claiming up to 2× better power-spectrum accuracy and up to 14× faster inference than DDIM enhancement.