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In the coarse grained Brownian Dynamics simulation method the many solvent molecules are replaced by random thermal kicks and an effective friction acting on the particles of interest. For Brownian Dynamics the friction has to be so strong…
We present the reduction of generalized Langevin equations to a coordinate-only stochastic model, which in its exact form, involves a forcing term with memory and a general Gaussian noise. It will be shown that a similar…
The generalized Langevin equation is a model for the motion of coarse-grained particles where dissipative forces are represented by a memory term. The numerical realization of such a model requires the implementation of a stochastic…
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…
A dynamical atomistic chain to simulate mechanical properties of a one-dimensional material with zero temperature may be modelled by the molecular dynamics (MD) model. Because the number of particles (atoms) is huge for a MD model, in…
Using the recently introduced Molecular Dynamics Lattice Gas (MDLG) approach, we test fluctuations of coarse-grained quantities. We show that as soon as the system can no longer be considered an ideal gas fluctuations fail to diminish upon…
The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic…
The phenomenon of ergodicity breaking of stochastic dynamics governed by Generalized Langevin Equations (GLE) in the presence of well-behaved exponentially decaying dissipative memory kernels, recently investigated by many authors (Phys.…
For multivariate co-generation in scientific applications, we advocate pairwise block rather than joint modeling of all variables. This design mitigates the computational burden and data imbalance. To this end, we propose an Annealed…
Using the initial-value formulation, a dynamic theory for systems evolving according to a Generalized Langevin Equation is developed, providing more restrictive conditions on the existence of equilibrium behavior and its…
High-dimensional recordings of dynamical processes are often characterized by a much smaller set of effective variables, evolving on low-dimensional manifolds. Identifying these latent dynamics requires solving two intertwined problems:…
Bottom-up coarse-grained molecular dynamics models are parameterized using complex effective Hamiltonians. These models are typically optimized to approximate high dimensional data from atomistic simulations. In contrast, human validation…
The individual motion of a colloidal particle is described by an overdamped Langevin equation. When rotational degrees of freedom are relevant, these are described by a corresponding Langevin process. Our purpose is to show that the…
Proper modeling of complex systems requires innovative mathematical tools. In this sense, we sought to use deformed or fractal derivatives for studying the dynamics of systems, particularly those, such as granular gases, in which the…
We propose an adaptively weighted stochastic gradient Langevin dynamics algorithm (SGLD), so-called contour stochastic gradient Langevin dynamics (CSGLD), for Bayesian learning in big data statistics. The proposed algorithm is essentially a…
Fluctuating hydrodynamics provides a quantitative, large-scale description of many-body systems in terms of smooth variables, with microscopic details entering only through a small set of transport coefficients. Although this framework has…
Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian…
The integral equation coarse-graining (IECG) approach is a promising high-level coarse-graining (CG) method for polymer melts, with variable resolution from soft spheres to multi CG sites, which preserves the structural and thermodynamical…
We present a statistical mechanics framework for modeling equilibrium friction coefficients using the Generalized Langevin Equation (GLE). We show that the kernel, obtained via the Fluctuation-Dissipation Theorem (FDT) from the stochastic…
We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing…