Author

John Harlim

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Preprint Aug 2026

Diffusion Maps Kernel Ridge Regression

In this paper, we study kernel ridge regression using the data-driven diffusion maps (DM) kernel, which is constructed through algebraic manipulations of the diffusion maps algorithm. Under the assumptions that the data lie on a manifold and are sampled uniformly, we prove that the appropriately scaled DM kernel conver...

John Harlim, Daning Huang, Jiwoo Song · 2 citations · ⚡1

Review Jun 2026

Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression

This manuscript gives an overview of the filtering mechanism behind the weak formulation and provides a bias-variance error decomposition, and combines a weak formulation with a kernel learning strategy to propose Weak-form Kernel Ridge Regression (WKRR) for learning dynamical systems.

Max Kreider, John Harlim, Daning Huang · 2 citations · ⚡1