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

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27 views

Monte Carlo simulation of a spin model and kinetic term

I have some C code simulating the following spin model (XY model) $$ H = - J \sum_{\langle ij \rangle} cos \left( \theta_i - \theta_j \right) $$ Now I'd want to extend my code to include a "kinetic ...
3
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1answer
78 views

Monte Carlo Simulation - Random Number Motivation

For Monte Carlo simulations, or any other numerical methods that rely heavily on the quality of the pseudo-random numbers generated (i.e even/desired distribution on a certain domain) for that matter, ...
2
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1answer
97 views

Are there companies which create commercial molecular dynamics / monte carlo simulations? [closed]

I would like to know if there is a commercialization of simulations? Or is it only in academic usage?
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1answer
58 views

How to get values from the loop in MATLAB?

Could you tell me please how to obtain separate values of "pi" depending on the value of N (code below)? For example If I write "pi1" I will get a value of "pi" for N(1) where N(1)=100. If I write ...
3
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1answer
48 views

Extract the correlation matrix from Monte Carlo data

I am writing my undergrad thesis on the harmonic oscillator on a lattice. So far I have implemented the Metropolis Monte Carlo algorithm to generate trajectories $x_j$ for $0 \leq j < N$, where $N$ ...
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0answers
27 views

Bootstrap for a histogram

I create a set of $T$ trajectories with $P$ positions, $\{x_j\colon 0 \leq j < M\}$, with a Monte Carlo simulation. From this data, I calculate quantities like $\langle x \rangle$ and $\langle x^2 ...
0
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1answer
114 views

optimizing a discontinous function

I am trying to maximize the following function (variable:\theta, a vector ($\theta_1$,...,$\theta_K$). most likely K <=5 $F(\theta, c_0, c_1) = P_{\theta}(T_0 > c_0, \max T_i >c_1, \min T_i ...
6
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1answer
263 views

Quasi Monte Carlo in Matlab

I want to use Quasi Monte Carlo to try and improve the convergence of a simulation I am running. The random numbers are simply to produce the observation errors for a standard linear regression ...
9
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2answers
148 views

Regarding automatic differentiation, is source-code-transformation (STC) more efficient than operator-overloading (OO)?

We are working on a Bayesian model for a space-time process, and are using a No-U-Turn sampler (NUTS) that requires a model for the log-probability and it's gradient with respect to the model ...
7
votes
1answer
80 views

Shall I derandomize a randomized algorithm in real application?

In general (and in real application), suppose I am using a randomized algorithm (e.g. Use MCMC to sample from a distribution and then compute $E(f(x))$ for some function $f$) Assume my algorithm will ...
9
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2answers
177 views

suggestion for managing simulation runs?

This questions may be a bit off-topic in comp-sci. if it is needed please suggest where does it fit with. The question is regarding on how to manage all the simulation runs efficiently. let's say, ...
5
votes
1answer
138 views

Generation of variable with given auto-correlation function

How can I generate realizations of random complex variable x(t) with given auto-correlation function C(s), defined by C(s) = < x(s)x(0) > and obeying the condition C(-s) = C^*(s) ? Any link ...
3
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3answers
96 views

Separation of degrees of freedom in Monte Carlo simulation

My question is probably very simple and deals with separation of degrees of freedom in a Monte Carlo Brownian dynamics simulation. Dealing with a particle in an external potential, I want to simulate ...
4
votes
3answers
284 views

How to sample numerically from an arbitrary smooth distribution?

I'm given a smooth probability density function via its values on a reasonable fine grid. I assume that cubic spline interpolation (or cubic spline interpolation of the logarithm of the density) will ...
3
votes
0answers
49 views

Stochastic Collocation for time evolving ODE

For an Stochastic Differential Equation, e.g., $$ \frac{du}{dt} = \alpha*\sin(u*t) $$ where $\alpha$ is normally distributed with nonzero mean, I am trying to use a stochastic collocation approach ...
10
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2answers
146 views

Numerical method for equation solving that works on stochastically computed functions

There are many well known numerical methods for solving equations of the type $$ f(x) = 0, \quad x \in \mathbb{R}^n,$$ e.g. bisection method, Newton's method, etc. In my application $f(x)$ is ...
0
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2answers
143 views

What is local Monte Carlo simulation?

"The traditional local Monte Carlo method is simple, extremely general, and versatile." -Wang Swendsen, 2002 What does 'local' Monte Carlo mean ? Is there anything called 'global' Monte Carlo?
9
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2answers
297 views

Confusion about Quantum Monte Carlo

My question is about extracting observables from QMC methods, as described in this reference. I understand the formal derivation of various QMC methods like Path Integral Monte Carlo. However, at the ...
4
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2answers
125 views

Convergence tests in Markov Chain Monte Carlo

For a relatively simple Markov chain Monte Carlo process, such as using Metropolis to find calculate thermal averages for an Ising model, how is it possible to determine whether quantities have ...
3
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1answer
98 views

Is using Monte Carlo method a good approach for solving Boltzmann equation?

I'm trying to solve for electron and hole distribution function using Boltzmann equation with various scattering mechanisms. Since I land up with an integro-differential equation, analytical solution ...
2
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1answer
72 views

What FCIQMC codes are out there?

Full configuration interaction quantum Monte Carlo seems like it is poised to overtake DFT in some applications pretty soon. I am curious if there is any freely available implementation of the ...
1
vote
1answer
43 views

DIST strings - Monte Carlo Simulation

I recently read something that talks about DIST distribution strings. It appears to be a way to take a long string of previously generated numbers and somehow compress them into a string that can ...
2
votes
2answers
207 views

Monte Carlo approximation of PI

I'm trying to understand how to compute the value of Pi by means of the Monte Carlo simulation. I have a circle inside a square where the sides of the square are tangent to the circle. As data I have ...
10
votes
4answers
287 views

Parallel (GPU) algorithms for asynchronous cellular automata

I have a collection of computational models that could be described as asynchronous cellular automata. These models resemble the Ising model, but are slightly more complicated. It seems as if such ...
4
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3answers
143 views

nuclear reaction fluid modelling

I'm pretty ignorant regarding the dark arts of numerical codes and modelling, but i'm interested in trying to pursue it for a particular pet project. It regards modelling of nuclear reactions like ...
7
votes
1answer
81 views

Approximation of partial derivative of a function of stochastic variable

Let $X_t$ be an Ito process $$ dX_t=a(X_t,t)dt + b(X_t,t)dW_t $$ where $W_t$ is a Wiener process. A numerical approximations of the solution of this equations is proposed by Milstein: $$ ...
5
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1answer
240 views

index representation of the diamond lattice

For a kinetic Monte Carlo simulation of solids that crystallize in the diamond lattice structure, I need some efficient representation of the diamond lattice as integer(s), to store it in some ...
4
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0answers
118 views

Rebinning algorithm in VEGAS

I am trying to understand the rebinning algorithm of the VEGAS (original publication and implementation notes) Monte Carlo integration. I will try to explain first what I think I understood and then ...
2
votes
1answer
77 views

Randomly choose among N alternatives

I understand how to generate a random sequence of binary variables where 1 occurs with probability p and ...
8
votes
2answers
220 views

Maximizing unknown noisy function

I'm interested in maximizing a function $f(\mathbf \theta)$, where $\theta \in \mathbb R^p$. The problem is that I don't know the analytic form of the function, or of its derivatives. The only thing ...
10
votes
2answers
159 views

Under what circumstances is Monte Carlo integration better than quasi-Monte Carlo?

A simple enough question: to do a multidimensional integral, given that one has decided that some sort of Monte Carlo method is appropriate, is there any advantage that a regular MC integration using ...
11
votes
3answers
642 views

Numeric integration of multi-dimensional integral with known boundaries

I have a (2-dimensional) improper integral $$I=\int_A \frac{W(x,y)}{F(x,y)}\,\mbox{d}x\mbox{d}y$$ where the domain of integration $A$ is smaller than $x=[-1,1]$, $y=[-1,1]$ but further restricted by ...
4
votes
1answer
281 views

Minimum image convention for triclinic unit cell

The minimum image convention (MIC), see for example a short note of W. Smith, is often used in molecular dynamics or monte carlo simulations of periodic systems with an orthorhombic unit cell. For ...
5
votes
2answers
354 views

Monte Carlo simulation of 3D X-Y model

I need to compute the helicity modulus as a function of temperature for a three-dimensional X-Y model (see N.K. Kultanov, Yu.E. Lozovik, "The critical behavior of the 3D X-Y model and its relation ...
12
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5answers
1k views

How can I approximate an improper integral?

I have a function $f(x,y,z)$ such that $\int_{R^3} f(x,y,z)dV$ is finite, and I want to approximate this integral. I'm familiar with quadrature rules and monte carlo approximations of integrals, ...
4
votes
1answer
64 views

How to use a web-embedded model in a computational workflow?

There is a model embedded in a web browser (Caprio 1998) that I would like to use in an MCMC algorithm. What is the best way to do this? I could implement the model in my favorite language but I ...
16
votes
3answers
2k views

How to add large exponential terms reliably without overflow errors?

A very common problem in Markov Chain Monte Carlo involves computing probabilities that are sum of large exponential terms, $ e^{a_1} + e^{a_2} + ... $ where the components of $a$ can range from ...
9
votes
3answers
776 views

Drawing samples from a finite mixture of normal distributions?

After some Bayesian update steps, I am left with a posterior distribution of the form of a mixture of normal distributions,$$\Pr(\theta| \text{data} ) = \sum_{i=1}^k w_i N(\mu_i, \sigma^2).$$ That is, ...
11
votes
1answer
599 views

Replacing Mathematica's QuasiMonteCarlo integration in C++

I have a Mathematica program which performs some integrals in 3 or 4 dimensions using the QuasiMonteCarlo method. The problem is, it takes an annoyingly long time ...
4
votes
2answers
464 views

3d Ising model simulation - what critical exponents should I be looking for and how do I find them?

For the final project in my computational physics class, I've built and will be presenting results for monte carlo simulations of phase transition in the three dimensional ising model. Using the ...
12
votes
3answers
478 views

PDEs in Many Dimensions

I know that most methods of finding approximate solutions to PDEs scale poorly with the number of dimensions, and that Monte Carlo is used for situations that call for ~100 dimensions. What are good ...
4
votes
0answers
207 views

Convergence rate of Monte-Carlo variance estimate

What is the convergence rate for Monte-Carlo variance estimate for a random variable $X \in {L^q}(\Omega ,R),2 < q < 4$?
2
votes
1answer
346 views

Vegas, Monte Carlo multi integration, QCD

To do some calculation on QCD on Lattice, I needed a Monte Carlo multi integration. I wrote a a C++ program according to what I understood from the paper “ Lepage (1978) “ A New Algorith For Adaptive ...
5
votes
3answers
1k views

Python implementations of Gillespie's direct method

I'm looking for a decent implementation of Gillespie's Direct Method in Python, as if I code the algorithm myself I'm nigh positive I'll do it inefficiently. Anyone have a favorite?
5
votes
4answers
248 views

How do I know which low-discrepancy sequence to use?

Whenever one uses a quasi-Monte Carlo method for cubature or optimization, it seems that there's a wide variety of low-discrepancy sequences to choose from, associated with the names of van der ...