WRSWorld Research StateContribute
WORLD RESEARCH STATE

Localized differential and integral kernels for neural operators

Contribution grade

Scientific machine learning · Human-designed research method or resource

Reference score105,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Adds resolution-scaled differential stencil layers and compact-support integral kernels using discrete–continuous convolution bases to neural operators, capturing local detail alongside global spectral layers.

Scientific scope

Adds resolution-scaled differential stencil layers and compact-support integral kernels using discrete–continuous convolution bases to neural operators, capturing local detail alongside global spectral layers. First three authors explicitly share contribution. Differential limits require smooth inputs, regular-grid scaling and kernel constraints; integral layers need suitable quadrature and discretization. Inherits stencils, group convolutions and DISCO; benchmark gains are not certified arbitrary-grid/PDE accuracy or exact finite-discretization equivariance.

Evidence

The linked original sources describe the stated contribution and its evidence limits. WRS has not independently rerun the experiments or certified a proof. First three authors explicitly share contribution. Differential limits require smooth inputs, regular-grid scaling and kernel constraints; integral layers need suitable quadrature and discretization. Inherits stencils, group convolutions and DISCO; benchmark gains are not certified arbitrary-grid/PDE accuracy or exact finite-discretization equivariance.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

Full scientific record · Browse contribution grades · Request a correction