4 papers
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…
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…
Artificial neural network solver for Fokker-Planck and Koopman eigenfunctions
Max Kreider, Peter J. Thomas, Yao Li
For a stochastic differential equation (SDE) that is an Itô diffusion or Langevin equation, the Fokker-Planck operator governs the evolution of the probability density, while its…
-functions, synchronization, and Arnold tongues for coupled stochastic oscillators
Max Kreider, Benjamin Lindner, Peter J. Thomas
Phase reduction is an effective theoretical and numerical tool for studying synchronization of coupled deterministic oscillators. Stochastic oscillators require new definitions of…