Related papers: Machine learning memory kernels as closure for non…
We present a data-driven approach to determine the memory kernel and random noise in generalized Langevin equations. To facilitate practical implementations, we parameterize the kernel function in the Laplace domain by a rational function,…
We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical…
The generalized Langevin equation is used as a model for various coarse-grained physical processes, e.g., the time evolution of the velocity of a given larger particle in an implicitly represented solvent, when the relevant time scales of…
We present efficient finite difference estimators for goal-oriented sensitivity indices with applications to the generalized Langevin equation (GLE). In particular, we apply these estimators to analyze an extended variable formulation of…
We consider the generalized Langevin equation (GLE) in a harmonic potential with power law decay memory. We study the anomalous diffusion of the particle's displacement and velocity. By comparison with the free particle situation in which…
A formulation of Langevin dynamics for discrete systems is derived as a class of generic stochastic processes. The dynamics simplify for a two-state system and suggest a network architecture which is implemented by the Langevin machine. The…
Machine learning provides a novel avenue for the study of experimental realizations of many-body systems, and has recently been proven successful in analyzing properties of experimental data of ultracold quantum gases. We here show that…
We obtain the memory kernel of the generalized Langevin equation, describing a particle interacting with longitudinal phonons in a liquid. The kernel is obtained analytically at T=0 Kelvin and numerically at T>0 Kelvin. We find that it…
The Fractional Langevin Equation (FLE) describes a non-Markovian Generalized Brownian Motion with long time persistence (superdiffusion), or anti-persistence (subdiffusion) of both velocity-velocity correlations, and position increments. It…
In molecular dynamics simulations, dynamically consistent coarse-grained (CG) models commonly use stochastic thermostats to model friction and fluctuations that are lost in a CG description. While Markovian, i.e., time-local, formulations…
Fixed points of recurrent neural networks can be leveraged to store and generate information. These fixed points can be captured by the Boltzmann-Gibbs measure, which leads to neural Langevin dynamics that can be used for sampling and…
We introduce a novel approach for learning memory kernels in Generalized Langevin Equations. This approach initially utilizes a regularized Prony method to estimate correlation functions from trajectory data, followed by regression over a…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
Machine learning algorithms often take inspiration from established results and knowledge from statistical physics. A prototypical example is the Boltzmann machine algorithm for supervised learning, which utilizes knowledge of classical…
The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore,…
The dynamics of unimolecular photo-triggered reactions can be strongly affected by the surrounding medium. An accurate description of these reactions requires knowing the free energy surface (FES) and the friction felt by the reactants.…
Machine learning (ML) is redefining what is possible in data-intensive fields of science and engineering. However, applying ML to problems in the physical sciences comes with a unique set of challenges: scientists want physically…
When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet…
A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a…
Simulation of the dynamics of physical systems is essential to the development of both science and engineering. Recently there is an increasing interest in learning to simulate the dynamics of physical systems using neural networks.…