Adaptive Randomized Neural Networks for PDEs: Structure-Aware Feature Redistribution and Residual-Driven Block Enrichment
Randomized neural networks retain an output-linear least-squares solve, but globally sampled random features may fail to capture the spatial and scale structure of PDE solutions.
ProofPaper ↗
Key points
- We propose SFRBE--RaNN, a two-stage adaptive trial-space construction.
- SFR redistributes a fixed feature budget according to regional indicator masses and adapts regional weight scales through low-dimensional residual-based optimization.
- For fixed linear problems, we establish an exact discrete residual-reduction identity and a conditional solution-error estimate.
- Building on this identity, we combine safeguarded SFR with RBE capture factors to derive a finite-horizon error bound involving baseline best approximation and empirical consistency, together with a conditional random-search success-probability bound.
Sources (1)
- [1]Adaptive Randomized Neural Networks for PDEs: Structure-Aware Feature Redistribution and Residual-Driven Block EnrichmentarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 01:29 AM
Randomized neural networks retain an output-linear least-squares solve, but globally sampled random features may fail to capture the spatial and scale structure of PDE solutions.
We propose SFRBE--RaNN, a two-stage adaptive trial-space construction.
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