Related papers: An iterative Monte Carlo method to solve nonlinear…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
Differentiable programming has emerged as a key programming paradigm empowering rapid developments of deep learning while its applications to important computational methods such as Monte Carlo remain largely unexplored. Here we present the…
We introduce Monte Carlo methods to compute the solution of elliptic equations with pure Neumann boundary conditions. We first prove that the solution obtained by the stochastic representation has a zero mean value with respect to the…
We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector.…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
Monte Carlo is a simple and flexible tool that is widely used in computational finance. In this context, it is common for the quantity of interest to be the expected value of a random variable defined via a stochastic differential equation.…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
We consider a wide range of matrix models and study them using the Monte Carlo technique in the large $N$ limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two…
We offer in this short report a simple Monte-Carlo method for solving a well-posed non-linear integral equations of second Fredholm's and Volterra's type and built a confidence region for solution in an uniform norm, applying the grounded…
Partial differential equation is a powerful tool to characterize various physics systems. In practice, measurement errors are often present and probability models are employed to account for such uncertainties. In this paper, we present a…
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…
A Monte Carlo method for computing the action of a matrix exponential for a certain class of matrices on a vector is proposed. The method is based on generating random paths, which evolve through the indices of the matrix, governed by a…
Bayesian inference for models that have an intractable partition function is known as a doubly intractable problem, where standard Monte Carlo methods are not applicable. The past decade has seen the development of auxiliary variable Monte…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
Nonlinear differential equations (DEs) are used in a wide range of scientific problems to model complex dynamic systems. The differential equations often contain unknown parameters that are of scientific interest, which have to be estimated…
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…
Monte Carlo sampling is a powerful toolbox of algorithmic techniques widely used for a number of applications wherein some noisy quantity, or summary statistic thereof, is sought to be estimated. In this paper, we survey the literature for…
We introduce a class of second order backward stochastic differential equations and show relations to fully non-linear parabolic PDEs. In particular, we provide a stochastic representation result for solutions of such PDEs and discuss Monte…
Algorithms which sort lists of real numbers into ascending order have been studied for decades. They are typically based on a series of pairwise comparisons and run entirely on chip. However people routinely sort lists which depend on…
We study the simulation of charged systems in the presence of general boundary conditions in a local Monte Carlo algorithm based on a constrained electric field. We firstly show how to implement constant-potential, Dirichlet, boundary…