AI & ML
Boundary-preserving randomized neural network methods for Poisson equations on general two- and three-dimensional domains
arXiv cs.NA0 views
arXiv:2611.07985v1 Announce Type: new Abstract: In this paper, we propose a boundary-preserving randomized neural network method for Poisson equations with Dirichlet boundary conditions in two and three dimensions. A linear lifting imposes the boundary conditions exactly, without balancing penalty weights between interior and boundary residuals. We construct the liftings by generalized barycentric coordinates and transfinite interpolation on convex and nonconvex polygons and polyhedra, and by radial parameterization on star-shaped curved domains. Numerical experiments on different domains show that the proposed method substantially reduces errors compared with the standard randomized neural network method.
Source：https://arxiv.org/abs/2611.07985PreviousA stability order barrier and SSP bound for Runge--Kutta methods with non-negative coefficients: AI-assisted proofsNextLithoSAGE: Spatially Adaptive and Geometrically Equivariant Neural Operators for Computational Lithography
Related posts
A Simple Way to Check Your Freelance Project Quote
0dev.to Productivity
Drop your dev project URL: I'll test it for 2 minutes, give you unfiltered feedback + spotlight you on Astro Discover
0dev.to Productivity
How many wrong answer keys are left in MMLU?
0dev.to Machine Learning
A neural decoder's sentence is an estimate, not a verified intention
0dev.to Machine Learning
WARN Act and Your Annual Bonus — What Happens to Your Year-End Bonus After a Layoff
0dev.to Career
I turned my life into a city you can walk: building World 001
0dev.to Career