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arXiv Machine Learning By Yu Tan, Shichang Du, Yongxiang Li

PDE-Residual-Informed Kriging

Read the original on arXiv Machine Learning →

The paper introduces PDE‑Residual‑Informed Kriging (PRIK), a Gaussian process framework that embeds global PDE residual information directly into its covariance structure via a PDE‑residual kernel. PRIK yields a posterior mean with minimal integrated squared PDE residual and offers statistical interpretations linking variance to residual energy. The authors prove quasi‑optimality and convergence rates, and demonstrate the method’s PDE‑solving capability through numerical experiments.

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