Hugging Face Trending Papers July 7, 2026

Kernel-based Operator Learning: Error Analysis, Budget Allocation, and a Physics-Informed Extension

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We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconstruction operator recovers the output function from predicted observations. Our main theoretical contribution is an explicit budget allocation condition relating the number $N$ of training pairs, the number $n$ of input observations, and the output resolution $m$.

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