2022/04/11 by Oliver Junge, Junge, Oliver, Daniel Matthes +3 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Protein Structure and Dynamics
paper · pdf · doi:10.48550/arxiv.2204.04901
openalex publication_date 2022/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new concept for the regularization and discretization of transfer and Koopman operators in dynamical systems. Our approach is based on the entropically regularized optimal transport between two probability measures. In particular, we use optimal transport plans in order to construct a finite-dimensional approximation of some transfer or Koopman operator which can be analysed computationally. We prove that the spectrum of the discretized operator converges to the one of the regularized original operator, give a detailed analysis of the relation between the discretized and the original peripheral spectrum for a rotation map on the n-torus and provide code for three numerical experiments, including one based on the raw trajectory data of a small biomolecule from which its dominant conformations are recovered.