Zobrazeno 1 - 10
of 594
pro vyhledávání: '"A. Nüske"'
Using normalizing flows and reweighting, Boltzmann Generators enable equilibrium sampling from a Boltzmann distribution, defined by an energy function and thermodynamic state. In this work, we introduce Thermodynamic Interpolation (TI), which allows
Externí odkaz:
http://arxiv.org/abs/2411.10075
Autor:
Harder, Hans, Nüske, Feliks, Philipp, Friedrich M., Schaller, Manuel, Worthmann, Karl, Peitz, Sebastian
This paper explores the integration of symmetries into the Koopman-operator framework for the analysis and efficient learning of equivariant dynamical systems using a group-convolutional approach. Approximating the Koopman operator by finite-dimensio
Externí odkaz:
http://arxiv.org/abs/2411.00905
We present a data-driven approach to use the Koopman generator for prediction and optimal control of control-affine stochastic systems. We provide a novel conceptual approach and a proof-of-principle for the determination of optimal control policies
Externí odkaz:
http://arxiv.org/abs/2410.09452
Autor:
Nateghi, Vahid, Nüske, Feliks
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 stochastic dynamical systems, and to learn a coarse-grained dynamics on reduc
Externí odkaz:
http://arxiv.org/abs/2409.16396
We consider the Koopman operator semigroup $(K^t)_{t\ge 0}$ associated with stochastic differential equations of the form $dX_t = AX_t\,dt + B\,dW_t$ with constant matrices $A$ and $B$ and Brownian motion $W_t$. We prove that the reproducing kernel H
Externí odkaz:
http://arxiv.org/abs/2405.14429
Autor:
Philipp, Friedrich M., Schaller, Manuel, Boshoff, Septimus, Peitz, Sebastian, Nüske, Feliks, Worthmann, Karl
We rigorously derive novel error bounds for extended dynamic mode decomposition (EDMD) to approximate the Koopman operator for discrete- and continuous time (stochastic) systems; both for i.i.d. and ergodic sampling under non-restrictive assumptions.
Externí odkaz:
http://arxiv.org/abs/2402.02494
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the Koopman operator for deterministic and stochastic (control) systems. This operator is linear and encompasses full information on the (expected stochastic) d
Externí odkaz:
http://arxiv.org/abs/2312.10460
Autor:
Peitz, Sebastian, Harder, Hans, Nüske, Feliks, Philipp, Friedrich, Schaller, Manuel, Worthmann, Karl
The Koopman operator has become an essential tool for data-driven analysis, prediction and control of complex systems. The main reason is the enormous potential of identifying linear function space representations of nonlinear dynamics from measureme
Externí odkaz:
http://arxiv.org/abs/2307.15325
Autor:
Nüske, Feliks, Klus, Stefan
Slow kinetic processes of molecular systems can be analyzed by computing dominant eigenpairs of the Koopman operator or its generator. In this context, the Variational Approach to Markov Processes (VAMP) provides a rigorous way of discerning the qual
Externí odkaz:
http://arxiv.org/abs/2306.00849
We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic simulations. We
Externí odkaz:
http://arxiv.org/abs/2301.08637