arxivmath.NAcs.LG2026-07-22
A Structure-Adaptive Random Feature Method for High-Dimensional Elliptic PDEs
Jiale Linghu, Hao Dong, Yangshuai Wang
Random-feature methods reduce high-dimensional elliptic PDE collocation to linear coefficient problems, but full-dimensional trial spaces overlook lower-dimensional structure. We introduce the Hierarchical Analysis-of-Variance Random Feature Method (HA-RFM), which selects coordin…