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Markov chain Monte Carlo (MCMC) methods provide powerful framework for sampling unknown probability measures across a wide range of scientific applications. In some settings, the target distribution is supported on a lower-dimensional…
We discuss various ensembles of homogeneous complex networks and a Monte-Carlo method of generating graphs from these ensembles. The method is quite general and can be applied to simulate micro-canonical, canonical or grand-canonical…
Amorphous carbon (a-C) materials have diverse interesting and useful properties, but the understanding of their atomic-scale structures is still incomplete. Here, we report on extensive atomistic simulations of the deposition and growth of…
Amorphous metal-organic frameworks are an important emerging materials class that combine the attractive physical properties of the amorphous state with the versatility of metal-organic framework (MOF) chemistry. The structures of amorphous…
In this paper we consider fully Bayesian inference in general state space models. Existing particle Markov chain Monte Carlo (MCMC) algorithms use an augmented model that takes into account all the variable sampled in a sequential Monte…
Macromolecules can form regular structures on inert surfaces. We have developed a combined empirical and modeling approach to derive the bonding. From experimental scanning tunneling microscopy (STM) images of structures formed on Au(111)…
This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the…
Equilibrium sampling of the configuration space in disordered systems requires algorithms that bypass the glassy slowing down of the physical dynamics. Irreversible Monte Carlo algorithms breaking detailed balance successfully accelerate…
Markov chain Monte Carlo is a class of algorithms for drawing Markovian samples from high-dimensional target densities to approximate the numerical integration associated with computing statistical expectation, especially in Bayesian…
Understanding the structural origins of the properties of amorphous materials remains one of the most important challenges in structural science. In this study we demonstrate that local 'structural simplicity', embodied by the degree to…
Deep generative models are attracting great attention for molecular design with desired properties. Most existing models generate molecules by sequentially adding atoms. This often renders generated molecules with less correlation with…
Monte Carlo methods represent the "de facto" standard for approximating complicated integrals involving multidimensional target distributions. In order to generate random realizations from the target distribution, Monte Carlo techniques use…
A mean field rate theory description of the homo- and co-polymerization of $f$-functional molecules is developed, which contains the formation of short cyclic structures inside the network. The predictions of this model are compared with…
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…
Two coarse-grained models for polymer chains in dense glass-forming polymer melts are studied by computer simulation: the bond-fluctuation model on a simple cubic lattice, where a bond-length potential favors long bonds, is treated by…
Amorphous materials are solids that lack long-range atomic order but possess complex short- and medium-range order. Unlike crystalline materials that can be described by unit cells containing few up to hundreds of atoms, amorphous materials…
Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
Recent decades have seen the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of possible contending atomic- and larger-scale configurations and the intricate…
Metallic spin glass systems, such as dilute magnetic alloys, are characterized by randomly distributed local moments coupled to each other through a long-range electron-mediated effective interaction. We present a scalable machine learning…
Orthogonal Monte Carlo (OMC) is a very effective sampling algorithm imposing structural geometric conditions (orthogonality) on samples for variance reduction. Due to its simplicity and superior performance as compared to its Quasi Monte…