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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…
DL_MONTE is an open source, general-purpose software package for performing Monte Carlo simulations. It includes a wide variety of force fields and MC techniques, and thus is applicable to a broad range of problems in molecular simulation.…
In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world scenarios. In this work we focus on kinetic models of traffic flow, where a key step is to design effective numerical…
Sequential Monte Carlo (SMC) methods are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. We propose a new SMC algorithm to compute the expectation of additive functionals recursively.…
Simulating stochastic systems with feedback control is challenging due to the complex interplay between the system's dynamics and the feedback-dependent control protocols. We present a single-step-trajectory probability analysis to…
Lattice Monte Carlo (MC) simulations and the functional Renormalization Group (RG) are powerful approaches that allow for quantitative studies of non-perturbative phenomena such as bound-state formation, spontaneous symmetry breaking and…
We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the…
Accelerated coarse-graining (CG) algorithms for simulating heterogeneous chemical reactions on surface systems have recently gained much attention. In the present paper, we consider such an issue by investigating the oscillation behavior of…
We present a flow-based method for simulating and calculating nucleation rates of first-order phase transitions in scalar field theory on a lattice. Motivated by recent advancements in machine learning tools, particularly normalizing flows…
We present a novel way of performing kinetic Monte Carlo simulations which does not require an {\it a priori} list of diffusion processes and their associated energetics and reaction rates. Rather, at any time during the simulation,…
The behavior of a Lattice Monte Carlo algorithm (if it is designed correctly) must approach that of the continuum system that it is designed to simulate as the time step and the mesh step tend to zero. However, we show for an algorithm for…
Kinetic Monte-Carlo (KMC) simulations are a well-established numerical tool to investigate the time-dependent surface morphology in molecular beam epitaxy (MBE) experiments. In parallel, simplified approaches such as limited mobility (LM)…
Vacancy-mediated diffusion of an Al atom in pure Mg matrix is studied using the atomistic, on-lattice self-learning kinetic Monte Carlo (SLKMC) method. Activation barriers for vacancy-Mg and vacancy-Al atom exchange processes are calculated…
We propose a multilevel Monte Carlo method for a particle-based asymptotic-preserving scheme for kinetic equations. Kinetic equations model transport and collision of particles in a position-velocity phase-space. With a diffusive scaling,…
One of the most active areas of physics in the last decades has been that of critical phenomena, and Monte Carlo simulations have played an important role as a guide for the validation and prediction of system properties close to the…
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…
Monte Carlo simulations of quantum field theories on a lattice become increasingly expensive as the continuum limit is approached since the cost per independent sample grows with a high power of the inverse lattice spacing. Simulations on…
If a stochastic system during some periods of its evolution can be divided into non-interacting parts, the kinetics of each part can be simulated independently. We show that this can be used in the development of efficient Monte Carlo…
Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount…
A hybrid kMC/LLG algorithm is used to simulate experimental MH hysteresis loops for dual layer ECC media. The calculation of the rate coefficients and difficulties arising from low energy barriers, a fundamental problem of the kMC method,…