A Structure-Adaptive Random Feature Method for High-Dimensional Elliptic PDEs
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 coordinate blocks using closed Sobol indices of the PDE residual, identifies oblique low-rank features from fitted-predictor gradients, and couples all retained features in one regularized least-squares solve. Under structural and stability hypotheses, we establish an $L^2$ error bound that links solution and residual truncation to finite-width approximation and regularized finite-sample fitting, and we derive guarantees...
| Authors | Jiale Linghu, Hao Dong, Yangshuai Wang |
|---|---|
| Primary category | math.NA |
| Published | 22 July 2026 |
| Last updated at source | 22 July 2026 |
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