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The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
The computational cost of traditional first-principles method quickly becomes prohibitively expensive as the number of atoms increases. This challenge is further amplified by the need to evaluate finite-temperature properties with Monte…
Linear kinetic Monte Carlo particle transport models are frequently employed in fusion plasma simulations to quantify atomic and surface effects on the main plasma flow dynamics. Separate codes are used for transport of neutral particles…
Forward and adjoint Monte Carlo (MC) models of radiance are proposed for use in model-based quantitative photoacoustic tomography. A 2D radiance MC model using a harmonic angular basis is introduced and validated against analytic solutions…
We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct…
Random batch algorithms are constructed for quantum Monte Carlo simulations. The main objective is to alleviate the computational cost associated with the calculations of two-body interactions, including the pairwise interactions in 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 present the Monte Carlo with Absorbing Markov Chains (MCAMC) method for extremely long kinetic Monte Carlo simulations. The MCAMC algorithm does not modify the system dynamics. It is extremely useful for models with discrete state spaces…
We present a Markov Chain Monte Carlo algorithm based on the Metropolis algorithm for simulation of the flow of two immiscible fluids in a porous medium under macroscopic steady-state conditions using a dynamical pore network model that…
Sequential Monte Carlo methods are a powerful framework for approximating the posterior distribution of a state variable in a sequential manner. They provide an attractive way of analyzing dynamic systems in real-time, taking into account…
In this paper we study from a numerical analysis perspective the Fractional Step Kinetic Monte Carlo (FS-KMC) algorithms proposed in [1] for the parallel simulation of spatially distributed particle systems on a lattice. FS-KMC are…
A detailed description is provided of a new Worm Algorithm, enabling the accurate computation of thermodynamic properties of quantum many-body systems in continuous space, at finite temperature. The algorithm is formulated within the…
Many high dimensional optimization problems can be reformulated into a problem of finding theoptimal state path under an equivalent state space model setting. In this article, we present a general emulation strategy for developing a state…
A boundary-based net-exchange Monte Carlo method was introduced in [1] that allows to bypass the difficulties encountered by standard Monte Carlo algorithms in the limit of optically thick absorption (and/or for quasi-isothermal…
Using the specific model of a system of like charged ions confined between two planar like charged surfaces, we compare the predictions for the energy and density profile of four simulation methods available to treat the long range Coulomb…
For many decades, quantum chemical method development has been dominated by algorithms which involve increasingly complex series of tensor contractions over one-electron orbital spaces. Procedures for their derivation and implementation…
Global fits of physics models require efficient methods for exploring high-dimensional and/or multimodal posterior functions. We introduce a novel method for accelerating Markov Chain Monte Carlo (MCMC) sampling by pairing a…
The use of computers in statistical physics is common because the sheer number of equations that describe the behavior of an entire system particle by particle often makes it impossible to solve them exactly. Monte Carlo methods form a…
In this paper, we consider a Monte Carlo simulation method (MinMC) that approximates prices and risk measures for a range $\Gamma$ of model parameters at once. The simulation method that we study has recently gained popularity [HS20, FPP22,…
Quantum Monte Carlo (QMC) is an advanced simulation methodology for studies of manybody quantum systems. In this review, we focus on the electronic structure QMC, i.e., methods relevant for systems described by the electron-ion…