Coupled coarse graining and Markov Chain Monte Carlo for lattice systems

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 algorithm with the proposal probability transition matrix based on the coarse-grained approximating measures introduced in a series of works of M. Katsoulakis, A. Majda, D. Vlachos and P. Plechac, L. Rey-Bellet and D.Tsagkarogiannis,. We prove that the proposed algorithm reduces the computational cost due to energy differences and has comparable mixing properties with the classical microscopic Metropolis algorithm, controlled by the level of coarsening and reconstruction procedure. The properties and effectiveness of the algorithm are demonstrated with an exactly solvable example of a one dimensional Ising-type model, comparing efficiency of the single spin-flip Metropolis dynamics and the proposed coupled Metropolis algorithm.Comment: 20 pages, 4 figure

Unfolding the prospects of computational (bio)materials modelling

In this perspective communication, we briefly sketch the current state of computational (bio)material research and discuss possible solutions for the four challenges that have been increasingly identified within this community: (i) the desire to develop a unified framework for testing the consistency of implementation and physical accuracy for newly developed methodologies, (ii) the selection of a standard format that can deal with the diversity of simulation data and at the same time simplifies data storage, data exchange, and data reproduction, (iii) how to deal with the generation, storage, and analysis of massive data, and (iv) the benefits of efficient 'core' engines. Expressed viewpoints are the result of discussions between computational stakeholders during a Lorentz center workshop with the prosaic title Workshop on Multi-scale Modeling and are aimed at (i) improving validation, reporting and reproducibility of computational results, (ii) improving data migration between simulation packages and with analysis tools, (iii) popularizing the use of coarse-grained and multi-scale computational tools among non-experts and opening up these modern computational developments to an extended user community

Spatial multi-level interacting particle simulations and information theory-based error quantification

We propose a hierarchy of multi-level kinetic Monte Carlo methods for sampling high-dimensional, stochastic lattice particle dynamics with complex interactions. The method is based on the efficient coupling of different spatial resolution levels, taking advantage of the low sampling cost in a coarse space and by developing local reconstruction strategies from coarse-grained dynamics. Microscopic reconstruction corrects possibly significant errors introduced through coarse-graining, leading to the controlled-error approximation of the sampled stochastic process. In this manner, the proposed multi-level algorithm overcomes known shortcomings of coarse-graining of particle systems with complex interactions such as combined long and short-range particle interactions and/or complex lattice geometries. Specifically, we provide error analysis for the approximation of long-time stationary dynamics in terms of relative entropy and prove that information loss in the multi-level methods is growing linearly in time, which in turn implies that an appropriate observable in the stationary regime is the information loss of the path measures per unit time. We show that this observable can be either estimated a priori, or it can be tracked computationally a posteriori in the course of a simulation. The stationary regime is of critical importance to molecular simulations as it is relevant to long-time sampling, obtaining phase diagrams and in studying metastability properties of high-dimensional complex systems. Finally, the multi-level nature of the method provides flexibility in combining rejection-free and null-event implementations, generating a hierarchy of algorithms with an adjustable number of rejections that includes well-known rejection-free and null-event algorithms.Comment: 34 page

Multilevel coarse graining and nano--pattern discovery in many particle stochastic systems

In this work we propose a hierarchy of Monte Carlo methods for sampling equilibrium properties of stochastic lattice systems with competing short and long range interactions. Each Monte Carlo step is composed by two or more sub - steps efficiently coupling coarse and microscopic state spaces. The method can be designed to sample the exact or controlled-error approximations of the target distribution, providing information on levels of different resolutions, as well as at the microscopic level. In both strategies the method achieves significant reduction of the computational cost compared to conventional Markov Chain Monte Carlo methods. Applications in phase transition and pattern formation problems confirm the efficiency of the proposed methods.Comment: 37 page

Coarse-graining schemes for stochastic lattice systems with short and long-range interactions

We develop coarse-graining schemes for stochastic many-particle microscopic models with competing short- and long-range interactions on a d-dimensional lattice. We focus on the coarse-graining of equilibrium Gibbs states and using cluster expansions we analyze the corresponding renormalization group map. We quantify the approximation properties of the coarse-grained terms arising from different types of interactions and present a hierarchy of correction terms. We derive semi-analytical numerical schemes that are accompanied with a posteriori error estimates for coarse-grained lattice systems with short and long-range interactions.Comment: 31 pages, 2 figure

Coarse-grained simulations to predict structure and properties of polymer nanocomposites

textPolymer Nanocomposites (PNC) are a new class of materials characterized by their large interfacial areas between the host polymer and nanofiller. This unique feature, due to the size of the nanofiller, is understood to be the cause of enhanced mechanical, electrical, optical, and barrier properties observed of PNCs, relative to the properties of the unfilled polymer. This interface can determine the miscibility of the nanofiller in the polymer, which, in turn, influences the PNC's properties. In addition, this interface alters the polymer's structure near the surface of the nanofiller resulting in heterogeneity of local properties that can be expressed at the macroscopic level. Considering the polymer-nanoparticle interface significantly influences PNC properties, it is apparent that some atomistic level of detail is required to accurately predict the behavior of PNCs. Though an all-atom simulation of a PNC would be able to accomplish the latter, it is an impractical approach to pursue even with the most advanced computational resources currently available. In this contribution, we develop (1) an equilibrium coarse-graining method to predict nanoparticle dispersion in a polymer melt, (2) a dynamic coarse-graining method to predict rheological properties of polymer-nanoparticle melt mixtures, and (3) a numerical approach that includes interfacial layer effects and polymer rigidity when predicting barrier properties of PNCs. In addition to the above, we study how particle and polymer characteristics affect the interfacial layer thickness as well as how the polymer-nanoparticle interface may influence the entanglement network in a polymer melt. More specifically, we use a mean-field theory approach to discern how the concentration of a semiflexible polymer, its rigidity and the particle's size determine the interfacial layer thickness, and the scaling laws to describe this dependency. We also utilize molecular dynamics and simulation techniques on a model PNC to determine if the polymer-nanoparticle interaction can influence the entanglement network of a polymer melt.Chemical Engineerin

Multiscale Coarse-Graining of the Protein Energy Landscape

A variety of coarse-grained (CG) models exists for simulation of proteins. An outstanding problem is the construction of a CG model with physically accurate conformational energetics rivaling all-atom force fields. In the present work, atomistic simulations of peptide folding and aggregation equilibria are force-matched using multiscale coarse-graining to develop and test a CG interaction potential of general utility for the simulation of proteins of arbitrary sequence. The reduced representation relies on multiple interaction sites to maintain the anisotropic packing and polarity of individual sidechains. CG energy landscapes computed from replica exchange simulations of the folding of Trpzip, Trp-cage and adenylate kinase resemble those of other reduced representations; non-native structures are observed with energies similar to those of the native state. The artifactual stabilization of misfolded states implies that non-native interactions play a deciding role in deviations from ideal funnel-like cooperative folding. The role of surface tension, backbone hydrogen bonding and the smooth pairwise CG landscape is discussed. Ab initio folding aside, the improved treatment of sidechain rotamers results in stability of the native state in constant temperature simulations of Trpzip, Trp-cage, and the open to closed conformational transition of adenylate kinase, illustrating the potential value of the CG force field for simulating protein complexes and transitions between well-defined structural states

Systematic coarse-graining of the dynamics of entangled polymer melts: the road from chemistry to rheology

For optimal processing and design of entangled polymeric materials it is important to establish a rigorous link between the detailed molecular composition of the polymer and the viscoelastic properties of the macroscopic melt. We review current and past computer simulation techniques and critically assess their ability to provide such a link between chemistry and rheology. We distinguish between two classes of coarse-graining levels, which we term coarse-grained molecular dynamics (CGMD) and coarse-grained stochastic dynamics (CGSD). In CGMD the coarse-grained beads are still relatively hard, thus automatically preventing bond crossing. This also implies an upper limit on the number of atoms that can be lumped together and therefore on the longest chain lengths that can be studied. To reach a higher degree of coarse-graining, in CGSD many more atoms are lumped together, leading to relatively soft beads. In that case friction and stochastic forces dominate the interactions, and actions must be undertaken to prevent bond crossing. We also review alternative methods that make use of the tube model of polymer dynamics, by obtaining the entanglement characteristics through a primitive path analysis and by simulation of a primitive chain network. We finally review super-coarse-grained methods in which an entire polymer is represented by a single particle, and comment on ways to include memory effects and transient forces.Comment: Topical review, 31 pages, 10 figure

The multiscale coarse-graining method. VI. Implementation of three-body coarse-grained potentials

Journal ArticleMany methodologies have been proposed to build reliable and computationally fast coarse-grained potentials. Typically, these force fields rely on the assumption that the relevant properties of the system under examination can be reproduced using a pairwise decomposition of the effective coarse-grained forces. In this work it is shown that an extension of the multiscale coarse-graining technique can be employed to parameterize a certain class of two-body and three-body force fields from atomistic configurations. The use of explicit three-body potentials greatly improves the results over the more commonly used two-body approximation. The method proposed here is applied to develop accurate one-site coarse-grained water models