arXiv AI By Berkcan Kapusuzoglu, Shunsaku Matsumoto, Yoshitomo Miyagi, Daigo Watanabe, Sankaran Mahadevan

Adaptive surrogate modeling for high-dimensional spatio-temporal output

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This paper introduces an adaptive surrogate modeling framework tailored for problems with extremely high‑dimensional spatio‑temporal outputs. The approach first reduces dimensionality by mapping outputs to a low‑dimensional latent space, then builds a surrogate model there, and finally employs a novel adaptive sampling strategy that balances exploration and exploitation to refine the surrogate with minimal expensive physics‑model runs. The method is validated on a thermo‑mechanical analysis of a gas turbine engine blade.

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arXiv Machine Learning
Jul 8

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

arXiv:2607. 06287v1 Announce Type: cross Abstract: 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.

By R\"udiger Kempf
Hugging Face Trending Papers
Jul 7

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

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 $m$.