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arXiv Machine Learning By You Yang, Fei Wang

Adaptive Randomized Neural Networks for PDEs: Structure-Aware Feature Redistribution and Residual-Driven Block Enrichment

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The paper introduces SFRBE–RaNN, a two‑stage adaptive randomized neural network framework for solving partial differential equations. It first redistributes a fixed feature budget based on regional indicator masses and optimizes regional weight scales using low‑dimensional residuals, then enriches the trial space by selecting nonredundant activation families through residual verification. The authors provide theoretical guarantees for linear problems, including a discrete residual‑reduction identity, error bounds, and a probabilistic success bound, and validate the approach with numerical experiments on localized, multiscale, and nonlinear space–time PDEs.

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