Kernel methods for Koopman-based modeling in molecular simulation

The on-site event will be followed by fika in the Analysen coffee area (fika from 16:00-16:30).

Abstract:

Koopman operator theory, and its main algorithm extended dynamic mode decomposition (EDMD), has emerged as a powerful modeling approach for complex dynamical systems arising in physics, chemistry, materials science, and engineering. The basic idea is to leverage existing simulation data to learn a linear model that allows to predict expectation values of observable functions at future times. Though the algorithm is conceptually quite simple, its underlying mathematical structure is very rich, and can be used for different purposes including control, coarse graining, or the identification of metastable states in complex molecules and materials.

The success of the method depends critically on the choice of finite-dimensional subspace (called dictionary), which reflects a priori knowledge of the system. Here, kernel methods emerge as very useful, since they allow using a rich dictionary defined implicitly by the data. On the other hand, the application of kernel methods typically leads to large linear algebra problems that can be challenging to solve in practice.

In this talk, I will present recent results on the efficient use of kernel-based EDMD in the context of molecular simulation. I will first introduce the general Koopman framework and the associated variational formulation for metastable systems. Then, I will show how to introduce kernels in this context. Finally, I will show how low-rank approximations based on random Fourier features (RFFs) can be used to solve the resulting linear algebra problems efficiently.

About the speaker:

Dr. Feliks Nüske is a research group leader at the Max-Planck-Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany. His research is on data-driven methods for modelling and simulation of molecular systems. Feliks received his Ph.D. in applied mathematics from Freie Universität Berlin in 2017. He then joined the Center for Theoretical Biological Physics at Rice University, U.S., for a postdoc. Before moving to his current position Dr. Nüske did a second postdoc in the Department of Mathematics at Paderborn University, Germany.