Published: Jul 10, 2026 by Daning Huang
We organized a 3-part minisymposia on “Modern Scientific Computational Methods for Learning Dynamical Systems” in this past SIAM Annual Meeting. The event is co-organized with Dr. Maxwell Kreider and Dr. John Harlim from Penn State Math.
The speakers were highlighted in our earlier news. Here we would like to highlight our streak of work on diffusion maps (DM) kernel:
- Learning Solution Operator of Dynamical Systems with Diffusion Maps Kernel Ridge Regression (DMKRR): Our earlier work demonstrating the effectiveness of DM kernel in learning manifold and chaotic dynamics (paper).
- Learning dynamical systems from noisy data with Weak-form Kernel Ridge Regression: A subsequent work that extends DMKRR to tackle noisy data with a simple but effective approach (paper).
- A Kernel Regression Framework for Data-Driven Modeling and Spectral Analysis of Nonlinear Dynamical Systems: Paper to appear; it extends the nonlinear DMKRR model to reveal spectral characteristics of dynamics.
And one more closely related work, that aims for a deeper understanding of the DM kernel in a manifold setting (paper).
[DM kernel predicts longer horizon in noisy setting]
[DM kernel recovers heat kernel on manifold]