# Tagged Questions

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

77 views

### Efficiently rotate vector in 2D (and 3D)

I need to efficiently rotate a 2D (and 3D) vector in a CUDA kernel. I was thinking about generating random unitary rotation matrices. I don't need to know the angle, it just has to be randomly ...
228 views

### Parallel Mersenne Twister for Monte Carlo

Recently, I came across a comment claiming that almost all researchers doing Monte Carlo methods are doing it wrong. It went on to elaborate that merely choosing different seeds for different ...
27 views

### Choosing Size of “Bin” in Umbrella Sampling Simulation of Ising Model

I'm studying Monte Carlo simulation techniques with 2-dimensional Ising model. It was easy to write a code simulating 2D Ising model, based on Metropolis algorithm. However, when it comes to concepts ...
48 views

### Use of Metropolis-Hasting algorithm for gathering statistics

I understand how MH work, I'm able to use it to simulate e.g. 2D Ising model. What I don't understand is what you actually take average of. When I run the simulation, it reaches equlibrium after some ...
64 views

### Efficient Quadrature Methods for Indicator Functions?

I am looking to numerically solve many different integrals where the integrand is simply the indicator function for a region (i.e. 1 on the region, 0 outside. This is for measuring areas). The ...
60 views

### Monte Carlo Metropolis method - trial step algorithm

I'm working on a Magnetization simulation and writing an algorithm using the metropolis method. I am using a change in energy and a Boltzmann distribution, but, my question is about the trial step. ...
92 views

### Convergence of Monte Carlo integration

In my research, one of the steps is to choose a numerical method to estimate $\int_a^b f(t)dt$, where $f$ is Lipschitz continuous but not differentiable. For simplicity, I used midpoint rule but the ...
113 views

### How to choose the number of random points in Monte Carlo simulations?

I am struggling with convergence criteria when performing a Monte carlo simulation on a uniform distribution. Any help would be much appreciated ! Say I want to sample uniformly a 1D interval (for ...
82 views

### Variational Monte Carlo: Variational energy is lower than ground state energy

I'm writing a VMC simulation for hydrogen and helium atoms, but in both my codes my variational energy for certain wavefunctions is not only statistically different from my expectation value, but it ...
80 views

### Maxwellian distribution of velocities with Shake algorithm present

I am writing a code to perform hybrid monte carlo molecular dynamics. To do this, I need to have a code to initialize the velocities of all particles according to a maxwell distribution. The code is ...
41 views

### Variational Monte Carlo to calculate local energy of hydrogen like ions in python

I'm writing up a code to calculate the local energy for electrons in hydrogen like ions for a given wavefunction. My code is giving me weird results, which leads me to believe something is wrong. ...
54 views

### Optimal partitioning of a graph

Consider a planar graph, where each node is associated with a weight. I would like to partition the graph such that the sum of the node weights in each group satisfy a minimum requirement. However, I ...
72 views

### Monte Carlo simulation

I am wondering if I am thinking correct about the following problem : ...
142 views

### Monte Carlo Double Integration Implementation

Am implementing a monte carlo integration routine to compute this double integral in eqn 0.3 of page 2 of this paper 'Mobius energy of knots and unknots', Annals of Mathematics, http://www.math.ucsb....
85 views

### Metropolis Monte Carlo integration of Area with unknown normalization

I probably miss something very basic. I don't see how to use Metropolis–Hastings algorithm for computation of integrals, if I don't know the volume of accessible phase space (i.e. proper normalization ...
74 views

### How to sample points in hyperbolic space?

Hyperbolic space in the Poincaré upper half space model looks like ordinary $\Bbb R^n$ but with the notion of angle and distance distorted in a relatively simple way. In Euclidean space I can sample a ...
51 views

### Monte Carlo sampling of particle system for velocity dependent potential

When sampling configurations of point particles in statistical mechanics by means of (Markov chain) Monte Carlo, we may work with a potential that only depends on the positions of the particles, and ...
70 views

### Choosing how many iterations to use in VEGAS

I'm using VEGAS integration, specifically the GSL implementation, for some QCD calculations, and I've been investigating the behavior of the algorithm for various numbers of iterations in an attempt ...
57 views

1k 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 model,...
244 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 ...
88 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 ...
225 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, ...
150 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 ...
132 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 ...
729 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 ...
67 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 ...
227 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 ...
267 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?
345 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 ...
200 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 ...
121 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 ...
100 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 method,...
58 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 ...
267 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 ...
725 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 ...
148 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 ...
103 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:  X_T=X_t+...