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Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…

To investigate the impact of non-linear interactions on dynamic coarse graining, we study a simplified model system, featuring a tracer particle in a complex environment. Using a projection operator formalism and computer simulations, we…

Soft Condensed Matter · Physics 2023-07-18 Bernd Jung , Gerhard Jung

We propose an efficient Markov Chain Monte Carlo method for sampling equilibrium distributions for stochastic lattice models, capable of handling correctly long and short-range particle interactions. The proposed method is a Metropolis-type…

Numerical Analysis · Mathematics 2010-06-21 Evangelia Kalligiannaki , Markos A. Katsoulakis , Petr Plechac

We study coarse-graining methods for stochastic differential equations. In particular we consider averaging and a type of projection operator method, sometimes referred to as effective dynamic via conditional expectations. The projection…

Probability · Mathematics 2025-06-19 Manh Hong Duong , Carsten Hartmann , Michela Ottobre

Multiscale molecular modeling is widely applied in scientific research of molecular properties over large time and length scales. Two specific challenges are commonly present in multiscale modeling, provided that information between the…

Computational Physics · Physics 2024-07-23 Jun Zhang , Xiaohan Lin , Weinan E , Yi Qin Gao

We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps.…

Computational Physics · Physics 2015-06-11 Phanish Suryanarayana , Kaushik Bhattacharya , Michael Ortiz

We present a dynamic coarse-graining technique that allows to simulate the mechanical unfolding of biomolecules or molecular complexes on experimentally relevant time scales. It is based on Markov state models (MSM), which we construct from…

Soft Condensed Matter · Physics 2018-08-17 Fabian Knoch , Ken Schäfer , Gregor Diezemann , Thomas Speck

This paper considers the reduction of the Langevin equation arising from bio-molecular models. To facilitate the construction and implementation of the reduced models, the problem is formulated as a reduced-order modeling problem. The…

Numerical Analysis · Mathematics 2019-10-04 Lina Ma , Xiantao Li , Chun Liu

Big data often has emergent structure that exists at multiple levels of abstraction, which are useful for characterizing complex interactions and dynamics of the observations. Here, we consider multiple levels of abstraction via a…

Functional inequalities such as the Poincar\'e and log-Sobolev inequalities quantify convergence to equilibrium in continuous-time Markov chains by linking generator properties to variance and entropy decay. However, many applications,…

Probability · Mathematics 2026-02-20 Bastian Hilder , Patrick van Meurs , Upanshu Sharma

A coarse grid correction (CGC) approach is proposed to enhance the efficiency of the matrix exponential and $\varphi$ matrix function evaluations. The approach is intended for iterative methods computing the matrix-vector products with…

Numerical Analysis · Mathematics 2024-04-23 Mike A. Botchev

Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however,…

Systems and Control · Computer Science 2016-11-01 Michalis Michaelides , Dimitrios Milios , Jane Hillston , Guido Sanguinetti

We propose a novel coarse graining tensor renormalization group method based on the higher-order singular value decomposition. This method provides an accurate but low computational cost technique for studying both classical and quantum…

Statistical Mechanics · Physics 2015-03-19 Z. Y. Xie , J. Chen , M. P. Qin , J. W. Zhu , L. P. Yang , T. Xiang

We explain a method, inspired by control theory model reduction and interpolation theory, that rigorously establishes the types of coarse graining that are appropriate for systems with quadratic, generalized Hamiltonians. For such systems,…

Statistical Mechanics · Physics 2007-05-23 David E. Reynolds

We propose a systematic coarse-grained representation of block copolymers, whereby each block is reduced to a single ``soft blob'' and effective intra- as well as intermolecular interactions act between centres of mass of the blocks. The…

Soft Condensed Matter · Physics 2009-11-11 C. I. Addison , J. P. Hansen , V. Krakoviack , A. A. Louis

We present a new approach to coarse-graining of variables describing dust flow in GR. It is based on assigning quasi-local shear, twist and expansion to 2-dimensional surfaces with the help of isometric embeddings into the 3-dimensional…

General Relativity and Quantum Cosmology · Physics 2015-05-14 Mikolaj Korzynski

We propose that Kreimer's method of Feynman diagram renormalization via a Hopf algebra of rooted trees can be fruitfully employed in the analysis of block spin renormalization or coarse graining of inhomogeneous statistical systems.…

High Energy Physics - Theory · Physics 2007-05-23 Fotini Markopoulou

In recent years, it has become increasingly popular to construct coarse-grained models with non-Markovian dynamics to account for an incomplete separation of time scales. One challenge of a systematic coarse-graining procedure is the…

Soft Condensed Matter · Physics 2017-09-25 Gerhard Jung , Martin Hanke , Friederike Schmid

Difficult, in particular NP-complete, optimization problems are traditionally solved approximately using search heuristics. These are usually slowed down by the rugged landscapes encountered, because local minima arrest the search process.…

Artificial Intelligence · Computer Science 2023-11-08 Konstantin Klemm , Anita Mehta , Peter F. Stadler

Hybrid multiscale modelling has emerged as a useful framework for modelling complex biological phenomena. However, when accounting for stochasticity in the internal dynamics of agents, these models frequently become computationally…

Quantitative Methods · Quantitative Biology 2021-05-11 Daria Stepanova , Helen M. Byrne , Philip K. Maini , Tomás Alarcón