Stabilized sparse dictionary learning with Cholesky factors скачать в хорошем качестве

Stabilized sparse dictionary learning with Cholesky factors

In this video, I talk about some technical details of a dictionary learning method we developed for our paper on kernel learning. The video abstract for that paper is here:    • Kernel Learning for Robust Dynamic Mode De...   This work is in collaboration with Profs Benjamin Herrmann, Beverley McKeon and Steve Brunton. The paper is available on arXiv: Title: Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO) Authors: Peter J. Baddoo, Benjamin Herrmann, Beverley J. McKeon, Steven L. Brunton https://arxiv.org/abs/2106.01510 Here's the technical abstract for the paper: _______________________________________________________________________ Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling high-dimensional systems from data. However, the quality of the linear DMD model is known to be fragile with respect to strong nonlinearity, which contaminates the model estimate. In contrast, sparse identification of nonlinear dynamics (SINDy) learns fully nonlinear models, disambiguating the linear and nonlinear effects, but is restricted to low-dimensional systems. In this work, we present a kernel method that learns interpretable data-driven models for high-dimensional, nonlinear systems. Our method performs kernel regression on a sparse dictionary of samples that appreciably contribute to the underlying dynamics. We show that this kernel method efficiently handles high-dimensional data and is flexible enough to incorporate partial knowledge of system physics. It is possible to accurately recover the linear model contribution with this approach, disambiguating the effects of the implicitly defined nonlinear terms, resulting in a DMD-like model that is robust to strongly nonlinear dynamics. We demonstrate our approach on data from a wide range of nonlinear ordinary and partial differential equations that arise in the physical sciences. This framework can be used for many practical engineering tasks such as model order reduction, diagnostics, prediction, control, and discovery of governing laws. _______________________________________________________________________ Thanks to Prof Steve Brunton at the University of Washington for letting me use his lightboard studio. Steve's channel is here: http://bit.ly/eigensteve You can see more of my research at https://www.baddoo.co.uk.