Questions tagged [monte-carlo]

Questions on Monte Carlo methods, methods that require the repeated generation of (pseudo-, quasi-)random numbers for computing their results.

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45 views

Importance Sampling for multidimensional integrals and random numbers from multivariable pdf's

I am aiming to get a numerical value for a five-dimensional integral using Monte Carlo Integration. I am getting good results using the Mean Value Method, but I would like to try to use Importance ...
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84 views

What is the best method to do a MC Integration of a multidimensional integral where the integration limits depend upon other variables?

What is the best method to do a Monte Carlo Integration of a multidimensional integral where the integration limits depend upon other variables? I am interested in getting a numerical value of a 5 ...
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1answer
87 views

Looking for GPU support on Markov-chain Monte-Carlo (MCMC) codes

I am looking for MCMC codes with a GPU suport (like NVIDIA or OpenCL libraries) to make faster run chains. I know there is a plenty of codes that does MCMC but which ones could allow to exploit GPU ...
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1answer
83 views

Montecarlo - impact of single / double precision

I am looking at a paper comparing performance of two pricers: same model (based on Monte Carlo simulation) but one implemented on CPU (C++) and one implemented on GPU (Cuda) The paper mentions the ...
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43 views

Comparison of computational complexities of MD versus MC simulations

In my humble understanding MD simulations of systems with short-range(like LJ interactions) and long-range(electrostatic) has a computational complexity $O(N . log(N))$. What will be the computational ...
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2answers
137 views

Generating particles from a distribution function using Monte Carlo

I have been given a 4D ($x, y, v_x, v_y$) distribution function, $f(x,y,v_x, v_y)$, generated by an external code. I want to generate a set of particles from this distribution function, say 10k ...
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1answer
104 views

Good method for correlated samples and estimating autocorrelation times

I'm working on a Monte Carlo project similar to the Ising model. I've found many examples on which I've based my code. From some papers I read on binning analysis, the errors after each binning step ...
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56 views

Why is perfect sampling not used in large-scale lattice model simulations?

The statistical physics literature is replete with papers describing simulations of lattice models, such as the Ising model. Typically, these are done through Monte Carlo methods, such as the ...
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59 views

Error in Monte Carlo integration

I am looking for a concise description to help me understand the error for Monte Carlo Integration using Uniform Sampling and Importance Sampling For Importance Sampling I have that the error is just ...
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2answers
426 views

Use Monte Carlo integration to compute the volume and centre of mass in Python

In particular, I want to focus on finding the volume $V$ because I will need it to start working on solving the centre of mass This $3D$ homogenous body (Torus section) is defined by $$x^2 + \left(\...
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39 views

Discretization formula for a system of two differential equations. "Solution to one of these is the initial condition of the other". In which sense?

Consider the following stochastic differential equation \begin{equation} dy=\left(A-\left(A+B\right)y\right)dt+C\sqrt{y\left(1-y\right)}dW\tag{1} \end{equation} where $A$, $B$ and $C$ are parameters ...
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2answers
236 views

Different questions about "Inverse Physics problems"

I am in a context of forecasts in astrophysics. Don't be too rude if questions seem to you stupid or naive but rather indulgent, I am just looking for better undertsand all these numerical methods of ...
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1answer
64 views

Which are the right configurations in the Markov chain of a Hamiltonian Monte Carlo algorithm?

I have a question about the Markov Chain Hamiltonian Monte Carlo (MCHMC). Hamiltonian Monte Carlo is known as Hybrid Monte Carlo too. I'll describe the steps of the algorithm. We have at the ...
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1answer
76 views

Question regarding the energy computation of the Ising-Spin Model

In most of the Monte-Carlo-Algorithms I studied, I found, at the place where they compute the energy, always a line of code, where they divided by four. For example, this code-snippet is taken from ...
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62 views

Random Orthogonal Matrix Generation

This post is inspired by N. Higham post "What is Random Orthogonal matrix?". In this post, N. Higham links to the two papers: G. W. Stewart, The efficient generation of random orthogonal matrices ...
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1answer
122 views

Is this behaviour normal for a Lennard-Jones monte carlo simulation?

I am simulating a Lennard-Jones fluid using MC simulation. The code always uses a reduced unit. I want to find the potential energy of the system. Periodic boundary condition implemented. I have ...
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1answer
192 views

Why the magnetisation shows abrupt behaviour for this 3D ising spin system

I am trying to simulate a 3D Ising spin system (+1 & -1) using Monte Carlo Metropolis Algorithm. I want to get different physical quantities from this simulation like magnetization, Average Energy,...
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1answer
287 views

Absence of Discontinuity in Specific Heat Plot Simulated by Ising Model

I am working on 2D Ising model, when I plot "specific heat vs temperature", I can't see any discontinuity at critical temperature around Tc ~ 2.7K. I am enclosing results of all other thermodynamic ...
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0answers
52 views

Hit-n-Run Monte Carlo on convex polytope

So, I'm currently trying to implement a MCMC to uniformly sampling hyper-points from the polytope defined as $\mathbb{K}=\{x\in\mathbb{R}^{n}\;\;\text{s.t.}\;\; A\,x=b \}$ in the specific case where, ...
3
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1answer
761 views

Calculation of Mean Square Displacement for Brownian dynamics system with Lennard Jones interactions in python3

I have a problem getting a sensible result for the Mean Square Displacement (MSD) for a simulation of $N$ particles under Brownian dynamics with Lennard-Jones interaction between them with or without ...
3
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1answer
161 views

How to optimize sampling for global sensitivity analysis

What is a good way to sample parameters for performing global sensitivity analysis? Some methods are defined using integrals, some are use Monte Carlo. How do these compare?
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85 views

Probability approximation: monte carlo VS sde

I have a probability measure $\mu$ (say, in $\mathbb{R}^{d}$, with density) and I want to approximate it numerically. Today I noticed that my measure is ergotic for a certain Stochastic Differential ...
3
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1answer
125 views

Computing autocorrelations of configurations in Monte Carlo simulations

In the context of Monte Carlo simulations, I am trying to learn how I should ensure that the configurations of my system are not correlated for the chosen interval of measurements. I have found out ...
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40 views

Monte Carlo domain not-so-dense

I already posted it on Physics SE, but maybe this is a better place: I have a 5D integral being calculated with a Monte Carlo uniform random sampling. The issue is that the region of integration is ...
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2answers
161 views

Dealing neighbor list in NVT Monte Carlo (MC) simulation

I'm making a NVT Monte Carlo (MC) simulation code with only short range interaction. I found many MC tutorial codes (usually Lennard-Jones system) in online. However, most of them are doing energy ...
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1answer
58 views

Change of random variables and check by plot

Question As a test, I transform a uniform distribution over the unit square. But when I check the transformed distribution with Monte Carlo, it is wrong. What went wrong? Thanks. Problem Random ...
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1answer
94 views

Monte Carlo - Random Walk Simulation - polyfit the log log data points?

This is part of the code in matlab for a random-walk simulation. To test the code, I'm using steps=[30]; there will be more values, but I want to run it for 1 trial to decrease code processing. <...
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1answer
93 views

Writing parallel code for molecular computation [duplicate]

I recently moved towards computational biophysics from an experimental science background. As of now, I am learning the fundamentals and doing some basic monte carlo simulations of LJ fluid on my ...
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2answers
52 views

Generating a random number based on a numerical distribution function

I have a probability distribution function that I don't have its analytical form (so I can't determine its CDF). How can I generate random numbers based on this distribution function? I'm looking for ...
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2answers
2k views

2D Ising Model, heat capacity decreases with lattice size

The problem I'm trying to make a metropolis simulation of the 2D Ising model. Basically, it's the following, for each monte-carlo step: Visit each lattice site, Compute energy required to flip ...
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1answer
136 views

Weighted Monte Carlo Integration

I have a function $F(x)$ which drops exponentially (like differential QCD cross section vs. Invariant mass). I want to perform Monte-Carlo integration. The problem is that only small $x$'s which have ...
4
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2answers
310 views

Mean-squared displacement in Monte Carlo studies

Is measuring mean-squared-displacement in Monte Carlo simulations uncommon? I'm very interested to find out if this has actually ever been tried. For instance, in the context of spheres, or ...
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62 views

Is there a software package for Quantum Monte Carlo estimation of the exchange correlation functional?

Quantum Monte Carlo (QMC) calculations historically have been used to parameterise the exchange-correlation functionals for Density Functional Theory (DFT). For example, this article explains a way to ...
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2answers
871 views

Computing the Ising Model for NiO

I am trying to compute the Ising model for NiO. As O carries no magnetic moment, I only need to consider the case of Ni which requires a second nearest neighbour Ising model. As can be seen in the ...
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1answer
112 views

Sampling simulation steps logarithmically

The common case of for instance a Monte Carlo simulation is, if we want to run our simulation for $N$ steps, we define a delta $\Delta,$ such that $N/\Delta = n$ tells us the frequency with which we ...
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1answer
138 views

Diffusion properties of hard spheres in Monte Carlo simulation

In standard Monte Carlo simulations, say for hard sphere systems, how should one compute the mean-squared displacement of the spheres in order to extract dynamical properties such as the diffusion ...
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0answers
23 views

Uniform distribution in 3D space [duplicate]

Posted this at math stack exchange as well, but alas no replies! So, I have been trying to find ways of distributing particles of spherical or other shape in 3D space, e.g. rectangular space. Random() ...
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1answer
13k views

2D Ising Model in Python

I am trying to calculate the energy, magnetization and specific heat of a two dimensional lattice using the metropolis monte carlo algorithm. ...
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0answers
614 views

Using C/C++ for Markov chain Monte Carlo (MCMC) methods

I'm working on optimizing the parameters of a mathematical model to fit experimental data, using an existing formula for the likelihood of observing the data given a set of parameter values. At the ...
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1answer
177 views

Simple Monte Carlo in C++, result dependent from seed

I implemented as an exercise a program to sample the statistics of the escape time of a Brownian particle in a potential well. I used the Euler-Maruyama method to numerically integrate the ...
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2answers
88 views

Physical meaning behind the choice of the proposal distribution in Markov Chain Monte Carlo (MCMC) methods

Let us consider the conventions on names used in the theoretical derivation of Metropolis-Hastings Monte Carlo as outlined here, for the sake of common nomenclature. What we are building is a step-...
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1answer
62 views

Applying pressure on simulation box

We have a 3D simulation box (cubic, side $L$) filled with $N$ non-overlapping objects (say spheres). We are interested to study the evolution of the system under an applied pressure in the z-direction ...
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126 views

How to stochastically estimate the trace of a matrix?

Specifically, the diagonal elements (can possibly both positive and negative) of the matrix can be computed efficiently but the total number is large ($\mathcal O(10^{18})$). My first thought about ...
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2answers
203 views

Monte Carlo Simulation algorithm

The algorthim use for updating the voltage of each componant at every time step is $$v(t+\Delta t)=\begin{cases} v(t)e^{-\gamma \Delta t},& n=0\\ v(t)e^{-\gamma \Delta t}+h_{*}& n=1\end{cases}...
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1k views

Estimate information entropy through Monte Carlo sampling

I am looking for methods that allow estimating the information entropy of a distribution when the only practical ways of sampling from that distribution are Monte Carlo methods. My problem is not ...
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1answer
154 views

Why are Hamiltonian dynamics used in MCMC?

In Hamiltonian Monte Carlo, Hamiltonian dynamics are used to generate new proposals from the current state. I understand why these dynamics are used as opposed to random walk behavior to generate ...
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2answers
422 views

optimization problem. Monte Carlo stochastic method or another one?

I have the following problem, there is an objective function f() depending on 7 variables x=(x1,x2,...x7), so f(x)=f((x1,x2,...x7)) and I want to find the combination of variables that minimize the ...
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1answer
1k views

Use Monte Carlo method to simulate consecutive decay in MATLAB

I'm trying to use MATLAB to simulate an atom decay process by using Monte Carlo approach. The process is as follow: Suppose that atom 1 decay to atom 2, which, in turn, decay to stable atoms of type ...
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80 views

Metropolis algorithm and thermal sine-Gordon model

I try to simulate thermal version of 1D $(x, t)$ sine-Gordon field model. I am interested in finding thermal static solution that minimizes functional of energy $E$: $$E = \int dx \left( \frac{1}{2} \...
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2answers
262 views

Fast Python implementation of short-range interacting particles under Metroplis algorithm

Can anyone write a Python implementation of a set of particles interacting in 2D according to a short-range particle-particle force and evolving in time under a Metropolis algorithm, which randomly ...