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We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a…
We bring a totally new concept for plasma simulation, other than the conventional two ways: Fluid/Kinetic Continuum (FKC) method and Particle-in-Cell (PIC) method. This method is based on Pure Monte Carlo (PMC), but far beyond traditional…
Markov chain Monte Carlo (MCMC) is a powerful methodology for the approximation of posterior distributions. However, the iterative nature of MCMC does not naturally facilitate its use with modern highly parallel computation on HPC and cloud…
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…
Systems of correlated quantum matter can be a steep challenge to any would-be method of solution. Matrix-product state (MPS)-based methods can describe 1D systems quasiexactly, but often struggle to retain sufficient bipartite entanglement…
This manuscript describes an adjoint/reverse Monte Carlo method to calculate the flux of charged plasma particles to the wall of e.g. a tokamak. Two applications are described: a fusion product activation probe and a neutral beam injection…
Kinetic Monte Carlo (KMC) is an important computational tool in physics and chemistry. In contrast to standard Monte Carlo, KMC permits the description of time dependent dynamical processes and is not restricted to systems in equilibrium.…
Monte Carlo simulation provides a powerful tool for understanding and exploring thermodynamic phase equilibria in many-particle interacting systems. Among the most physically intuitive simulation methods is Gibbs ensemble Monte Carlo…
We describe collective-move Monte Carlo algorithms designed to approximate the overdamped dynamics of self-assembling nanoscale components equipped with strong, short-ranged and anisotropic interactions. Conventional Monte Carlo simulations…
A kinetic Monte Carlo (KMC) method is presented to simulate the electrodeposition of a metal on a single crystal surface of the same metal under galvanostatic conditions. This method utilizes the multi-body embedded-atom method (EAM)…
Optimizing or sampling complex cost functions of combinatorial optimization problems is a longstanding challenge across disciplines and applications. When employing family of conventional algorithms based on Markov Chain Monte Carlo (MCMC)…
Diagrammatic Monte Carlo methods provide robust routines for accurate computations of correlated electronic systems in the thermodynamical limit. Recently, its versatility was extended to SU(N) Hubbard model, where the core is a novel…
Cellular scale decision making is modulated by the dynamics of signalling molecules and their diffusive trajectories from a source to small absorbing sites on the cellular surface. Diffusive capture problems are computationally challenging…
In this paper the application of the multi-level Monte Carlo (MLMC) method on numerical simulations of turbulent flows with uncertain parameters is investigated. Several strategies for setting up the MLMC method are presented, and the…
This work describes methodologies to successfully implement the Implicit Monte Carlo (IMC) scheme for thermal radiative transfer in reduced-precision floating-point arithmetic. The methods used can be broadly categorized into scaling…
Advanced algorithms are necessary to obtain faster-than-real-time dynamic simulations in a number of different physical problems that are characterized by widely disparate time scales. Recent advanced dynamic Monte Carlo algorithms that…
Particle-in-cell methods with stochastic collision models are commonly used to simulate collisional plasma dynamics, with applications ranging from hypersonic flight to semiconductor manufacturing. Code verification of such methods is…
We develop a novel multilevel asymptotic-preserving Monte Carlo method, called Multilevel Kinetic-Diffusion Monte Carlo (ML-KDMC), for simulating the kinetic Boltzmann transport equation with a Bhatnagar-Gross-Krook (BGK) collision…
We consider the problem of estimating the probability of a large loss from a financial portfolio, where the future loss is expressed as a conditional expectation. Since the conditional expectation is intractable in most cases, one may…
This work describes a new 1D hybrid approach for modeling atmospheric pressure discharges featuring complex chemistry. In this approach electrons are described fully kinetically using Particle-In-Cell/Monte-Carlo (PIC/MCC) scheme, whereas…