4 papers
Diffusion Maps Kernel Ridge Regression
John Harlim, Daning Huang, Jiwoo Song
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 algorit…
Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression
Max Kreider, John Harlim, Daning Huang
Accurate prediction of complex dynamical systems from noisy measurements remains a significant challenge in scientific computing. Kernel ridge regression learning strategies are of…
Learning solution operator of dynamical systems with diffusion maps kernel ridge regression
Jiwoo Song, Daning Huang, John Harlim
In this work, we propose a simple kernel ridge regression (KRR) framework with a dynamic-aware validation strategy for long-term prediction of complex dynamical systems. By employi…
A model-free method for discovering symmetry in differential equations
Max Kreider, John Harlim, Daning Huang
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesim…