Related papers: Generalized Langevin equations for systems with lo…
This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with…
For a wide range of phenomena, current computational ability does not always allow for fully atomistic simulations of high-dimensional molecular systems to reach time scales of interest. Coarse-graining (CG) is an established approach to…
We systematically derive the quantum generalized nonlinear Langevin equation using Morozov's projection operator method. This approach extends the linear Mori-Zwanzig projection operator technique, allowing for the inclusion of nonlinear…
We study the statistically invariant structures of the nonlinear generalized Langevin equation (GLE) with a power-law memory kernel. For a broad class of memory kernels, including those in the subdiffusive regime, we construct solutions of…
Mathematical approaches from dynamical systems theory are used in a range of fields. This includes biology where they are used to describe processes such as protein-protein interaction and gene regulatory networks. As such networks increase…
Understanding, predicting and controlling laminar-turbulent boundary-layer transition is crucial for the next generation aircraft design. However, in real flight experiments, or wind tunnel tests, often only sparse sensor measurements can…
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…
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…
The generalized Langevin equation (GLE) is a useful framework for analyzing and modeling the dynamics of many-body systems in terms of low-dimensional reaction coordinates, with its specific form determined by the choice of projection…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
We derive generalized Langevin equations (GLEs) for single beads in linear elastic networks. In particular, the derivations of the GLEs are conducted without employing normal modes, resulting in two distinct representations in terms of…
Federated Learning (FL) addresses the need to create models based on proprietary data in such a way that multiple clients retain exclusive control over their data, while all benefit from improved model accuracy due to pooled resources.…
Langevin dynamics has become a popular tool to simulate the Boltzmann equilibrium distribution. When the repartition of the Langevin equation involves the exact realization of the Ornstein-Uhlenbeck noise, in addition to the conventional…
Simulating the long-timescale dynamics of biomolecules is a central challenge in computational science. While enhanced sampling methods can accelerate these simulations, they rely on pre-defined collective variables that are often difficult…
We present a macroscopic theory of electroencephalogram (EEG) dynamics based on the laws of motion that govern atomic and molecular motion. The theory is an application of Zwanzig-Mori projection operators. The result is a simple equation…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
Coarse-graining complex molecular systems to lower-dimensional reaction coordinates is a powerful approach for capturing their effective dynamics. The generalized Langevin equation (GLE) provides an exact framework for modeling…
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.…
Inferring microbial community structure based on temporal metagenomics data is an important goal in microbiome studies. The deterministic generalized Lotka-Volterra differential (GLV) equations have been used to model the dynamics of…
Technological advances have led to a proliferation of structured big data that have matrix-valued covariates. We are specifically motivated to build predictive models for multi-subject neuroimaging data based on each subject's brain imaging…