Related papers: On the Mathematical foundations of Diffusion Monte…
We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…
We provide a pedagogical introduction to the two main variants of real-space quantum Monte Carlo methods for electronic-structure calculations: variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge on…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
In stochastic processes with absorbing states, the quasi-stationary distribution provides valuable insights into the long-term behaviour prior to absorption. In this work, we revisit two well-established numerical methods for its…
Ab initio quantum Monte Carlo (QMC) is a stochastic approach for solving the many-body Schr\"odinger equation without resorting to one-body approximations. QMC algorithms are readily parallelizable via ensembles of $N_w$ walkers, making…
We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. We take advantage of a basic property of the walker configuration distribution…
Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant developments in the past decades and become one of the go-to methods when accurate ground state energy of molecules and materials is needed. The remaining…
The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte Carlo methods. We study here an advanced version of familiar Markov Chain Monte…
We study lithium systems over a range of number of atoms, e.g., atomic anion, dimer, metallic cluster, and body-centered cubic crystal by the diffusion Monte Carlo method. The calculations include both core and valence electrons in order to…
The aim of this paper is to introduce a new Monte Carlo method based on importance sampling techniques for the simulation of stochastic differential equations. The main idea is to combine random walk on squares or rectangles methods with…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
We briefly review the principles, mathematical bases, numerical shortcuts and applications of fast random walk (FRW) algorithms. This Monte Carlo technique allows one to simulate individual trajectories of diffusing particles in order to…
We present a new efficient method for Monte Carlo simulations of diffusion-reaction processes. First introduced by us in [Phys. Rev. Lett., 97:230602, 2006], the new algorithm skips the traditional small diffusion hops and propagates the…
A Monte Carlo method is presented to evaluate quantum states with many particles moving in the continuum. The scattering state is generated at each time by a Monte Carlo random sampling algorithm. The same calculation are repeated until the…
We have developed a novel Monte Carlo method for simulating the dynamical evolution of stellar systems in arbitrary geometry. The orbits of stars are followed in a smooth potential represented by a basis-set expansion and perturbed after…
In this work we present a detailed study of the Fermion Monte Carlo algorithm (FMC), a recently proposed stochastic method for calculating fermionic ground-state energies [M.H. Kalos and F. Pederiva, Phys. Rev. Lett. vol. 85, 3547 (2000)].…
We recently demonstrated that standard fixed-time lattice random-walk models cannot be modified to properly represent biased diffusion processes in more than two dimensions. The origin of this fundamental limitation appears to be the fact…
This paper proposes an efficient method for the simultaneous estimation of the state of a quantum system and the classical parameters that govern its evolution. This hybrid approach benefits from efficient numerical methods for the…
Monte Carlo simulation is used to study the dynamical crossover from single file diffusion to normal diffusion in fluids confined to narrow channels. We show that the long time diffusion coefficients for a series of systems involving hard…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…