REVIEW 7 cited by
Spectral Neural Operators
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
A plentitude of applications in scientific computing requires the approximation of mappings between Banach spaces. Recently introduced Fourier Neural Operator (FNO) and Deep Operator Network (DeepONet) can provide this functionality. For both of these neural operators, the input function is sampled on a given grid (uniform for FNO), and the output function is parametrized by a neural network. We argue that this parametrization leads to 1) opaque output that is hard to analyze and 2) systematic bias caused by aliasing errors in the case of FNO. The alternative, advocated in this article, is to use Chebyshev and Fourier series for both domain and codomain. The resulting Spectral Neural Operator (SNO) has transparent output, never suffers from aliasing, and may include many exact (lossless) operations on functions. The functionality is based on well-developed fast, and stable algorithms from spectral methods. The implementation requires only standard numerical linear algebra. Our benchmarks show that for many operators, SNO is superior to FNO and DeepONet.
Forward citations
Cited by 7 Pith papers
-
Scale-Consistent Learning for Partial Differential Equations
Scale-consistency training, which enforces agreement between global and rescaled sub-domain predictions, enables neural PDE solvers to extrapolate to unseen scale parameters such as Reynolds number or wavenumber.
-
Adaptive Resolution Residual Networks -- Generalizing Across Resolutions Easily and Efficiently
Adaptive Resolution Residual Networks use Laplacian residuals and Laplacian dropout to make fixed-resolution layers adaptive across image resolutions with a guaranteed computation-skipping property under ideal kernels.
-
Optimal Control Operator Perspective and a Neural Adaptive Spectral Method
A neural adaptive spectral operator maps optimal control instances directly to control functions in one forward pass, with approximation error bounds and large inference speedups over classical solvers.
-
Latent Mamba Operator for Partial Differential Equations
LaMO replaces attention in latent-token neural operators with bidirectional state-space models and reports consistent accuracy gains on six PDE benchmarks.
-
Are Two Hidden Layers Still Enough for the Physics-Informed Neural Networks?
A collection of deterministic initialization, loss weighting, data-driven initialization, and gradient-free training methods for shallow physics-informed neural networks, tested on ODEs and PDEs.
-
Optimal Convergence Rates for Neural Operators
Two-layer neural operators trained with early-stopped gradient descent achieve the same minimax convergence rates as kernel methods in the neural tangent kernel regime.
-
About rectified sigmoid function for enhancing the accuracy of Physics-Informed Neural Networks
Rectified sigmoid (hard sigmoid) activation is reported to cut PINN solution errors by about an order of magnitude on two ODE benchmarks, but the result may be an interpolation artifact because the paper never disclos...
Discussion (0). Continue with ORCID to comment.