Data-driven approximation of the Koopman generator: Model reduction, system identification, and control
We derive a data-driven method for the approximation of the Koopman generator called
gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic …
gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic …
Slicing and dicing: Optimal coarse-grained representation to preserve molecular kinetics
The aim of molecular coarse-graining approaches is to recover relevant physical properties
of the molecular system via a lower-resolution model that can be more efficiently simulated …
of the molecular system via a lower-resolution model that can be more efficiently simulated …
[HTML][HTML] Computing committors via Mahalanobis diffusion maps with enhanced sampling data
The study of phenomena such as protein folding and conformational changes in molecules
is a central theme in chemical physics. Molecular dynamics (MD) simulation is the primary …
is a central theme in chemical physics. Molecular dynamics (MD) simulation is the primary …
Partial observations, coarse graining and equivariance in Koopman operator theory for large-scale dynamical systems
The Koopman operator has become an essential tool for data-driven analysis, prediction
and control of complex systems, the main reason being the enormous potential of identifying …
and control of complex systems, the main reason being the enormous potential of identifying …
tgEDMD: Approximation of the Kolmogorov operator in tensor train format
Extracting information about dynamical systems from models learned off simulation data has
become an increasingly important research topic in the natural and engineering sciences …
become an increasingly important research topic in the natural and engineering sciences …
Optimal reaction coordinates: Variational characterization and sparse computation
Reaction coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that
govern the long-term behavior of high-dimensional stochastic processes. We present a …
govern the long-term behavior of high-dimensional stochastic processes. We present a …
Kinetically Consistent Coarse Graining using Kernel-based Extended Dynamic Mode Decomposition
In this paper, we show how kernel-based approximation to the Koopman generator--the
kgEDMD algorithm--can be used to identify implied timescales and meta stable sets in …
kgEDMD algorithm--can be used to identify implied timescales and meta stable sets in …
Geometric path augmentation for inference of sparsely observed stochastic nonlinear systems
D Maoutsa - arXiv preprint arXiv:2301.08102, 2023 - arxiv.org
Stochastic evolution equations describing the dynamics of systems under the influence of
both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying …
both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying …
Non-parametric estimation of stochastic differential equations from stationary time-series
X Chen, I Timofeyev - Journal of Statistical Physics, 2022 - Springer
We study efficiency of non-parametric estimation of diffusions (stochastic differential
equations driven by Brownian motion) from long stationary trajectories. First, we introduce …
equations driven by Brownian motion) from long stationary trajectories. First, we introduce …
Mahalanobis Diffusion Maps for Quantifying Rare Events: Theory and Application to Molecular Dynamics
AL Evans - 2023 - search.proquest.com
The study of rare events in molecular and atomic systems such as conformal changes and
cluster rearrangements has been one of the most important research themes in chemical …
cluster rearrangements has been one of the most important research themes in chemical …