10
votes
Accepted
Parallel Mersenne Twister for Monte Carlo
Like you say, using the Mersenne Twister for parallel computations is almost always done incorrectly, as the correct method is tricky to implement.
By far the easiest and best answer would be to move ...
- 2,493
7
votes
Maximizing unknown noisy function
There are several Bayesian optimization techniques you could try. Easiest are based on Gaussian process:
Harold J. Kushner. A new method of locating the maximum of an arbitrary multipeak curve in the ...
- 870
7
votes
Accepted
Why the magnetisation shows abrupt behaviour for this 3D ising spin system
Your lattice consists of 5 x 5 x 5 = 125 spins, so your number of Montecarlo steps to reach equilibrium should be >> 125, because you randomly picking a site and flipping it, so random numbers should ...
- 276
6
votes
Python implementations of Gillespie's direct method
As part of the lab the developed and maintains StochKit. I am happy to hear that it is highly recommended in the previous answers. However, I wanted to update everyone. There already is a python ...
- 61
5
votes
Accepted
Mean-squared displacement in Monte Carlo studies
This is possible (see [1]) but uncommon, as it requires Monte Carlo moves that alter the current conformations by a very small perturbation. In that setting of "small" Metropolis MC moves, it is ...
- 3,994
5
votes
Mean-squared displacement in Monte Carlo studies
It is in some cases possible to map the dynamics obtained in MC simulations to other (more realistic) dynamics, especially for the case of dense colloidal suspensions. The following two papers talk ...
- 677
5
votes
Accepted
Absence of Discontinuity in Specific Heat Plot Simulated by Ising Model
I sincerely thank @Daniel Shapero for directing me towards this answer.
Discontinuity in the specific heat or susceptibility curves to be visible significantly, you should take much more finer ...
- 276
5
votes
Accepted
Use Monte Carlo integration to compute the volume and centre of mass in Python
Here is a corrected and slightly improved code, set up here for calculation of the full torus volume to verify the result.
...
- 2,440
4
votes
Under what circumstances is Monte Carlo integration better than quasi-Monte Carlo?
Advantages of traditional Monte-Carlo integration over quasi-Monte Carlo integration are discussed in Kocis and Whiten's paper here. They list the following reasons:
The error bound of qmc methods $\...
- 2,125
4
votes
How to sample points in hyperbolic space?
I'm in the middle of doing this for myself. I think the most appropriate analogue to the Gaussian would be the heat kernel in hyperbolic space. Fortunately, this has been figured out before: https://...
- 41
4
votes
Simple Monte Carlo in C++, result dependent from seed
As noted in the comments by Kirill, the y-axes of the two plots are very different. And if they are rescaled accordingly, the boxes will certainly look very similar, if not identical.
Therefore, it ...
- 8,602
4
votes
How to optimize sampling for global sensitivity analysis
What you're looking for goes under the name of quasi-Monte Carlo (QMC) sequences. Quasi Monte Carlo sequences are "more random than random", i.e. they fill high dimensional spaces better ...
- 12.2k
4
votes
Accepted
Automatic Differentiation In the Presence of Jump Points
Finite differences, when applied to a function from $\mathbb{R}$ to $\mathbb{R}$ with a discontinuity, will do a better job of capturing the nature of the derivative, which is no longer a function but ...
- 56
4
votes
Determining the importance of different parameters in a simulation
Optimal sampling will in general depend on one's objective. From the title it seems you are mainly interested in variable importance. This is typically one of the objectives of sensitivity analysis, ...
- 465
3
votes
2D Ising Model in Python
Your specific heat is indeed not correct. You should get a peak centered on the critical temperature $T_c\simeq 2.27$. The specific heat is
$$C=\big[\langle E^2\rangle-\langle E\rangle^2\big]/k_BT^...
- 143
3
votes
Parallel Mersenne Twister for Monte Carlo
If you want to use MT, you can use SFMT as your PRNG and SFMT jump to generate multiple streams.
You can simply initialise MT with one seed, and then jump ahead by e.g. $1 \cdot 10^{60}$, $2 \cdot 10^...
- 131
3
votes
Estimate information entropy through Monte Carlo sampling
If I understand what information you have available, what you want is not possible: the information available to you is not enough to determine the entropy. It's not even enough to approximate the ...
- 400
3
votes
Efficient Quadrature Methods for Indicator Functions?
I found that the grid summing method beat out both the Cubature package and the adaptive Monte Carlo schemes from the GSL package (standard, VEGAS, and MISER) when it came to both speed an accuracy (...
- 12.2k
3
votes
Monte Carlo Metropolis method - trial step algorithm
Well I guess that this question could take place in both computational science and physics, depending on the kind of physicist or computational scientist stubbling upon it.
Yet for your answer, as I ...
- 323
3
votes
Accepted
Convergence of Monte Carlo integration
Let the MC integral estimate be
$$ S_n = \frac{b-a}{n}\sum_{1\leq k\leq n} f(x_k), $$
where $x_k$ are i.u.d. on the interval $[a,b]$. So long as the function $f$ is $L^1$, the mean exists, and
$$\...
- 11.4k
3
votes
How to choose the number of random points in Monte Carlo simulations?
You may not be able to determine the exact number of points required to obtain 1% error, but you can estimate the order of magnitude of points needed to obtain this accuracy.
Monte Carlo converges ...
- 12k
3
votes
Calculation of Mean Square Displacement for Brownian dynamics system with Lennard Jones interactions in python3
This will not an answer to your problem, more an excessive comment and few things you might consider, when writing such code even for self educational purpose.
Constants
You asked whether your ...
- 1,275
3
votes
Accepted
Which are the right configurations in the Markov chain of a Hamiltonian Monte Carlo algorithm?
The algorithm for perfoming a single HMC step is as follows:
Input: Some initial configuration $\vec{y}_i$ and momentum $\vec{p}_i$.
Output: Next configuration $\vec{y}_{i+1}$ and momentum $\vec{p}_{i+...
- 401
3
votes
Accepted
Different questions about "Inverse Physics problems"
As I understand, your ultimate goal is to solve an inverse problem (i.e., infer some parameters from given data / observations). To this end, you want to apply Bayesian Inference, which relates the ...
- 401
3
votes
Monte Carlo simulation of many-body wave function overlaps
You are right that $\psi_2^\ast\psi_1$ is not a probability distribution (not even a non-normalized one) because it is complex-valued and possibly negative. But $p(r)=|\psi_2(r)^\ast\psi_1(r)|$ can ...
- 54.1k
2
votes
Accepted
Variational Monte Carlo: Variational energy is lower than ground state energy
The trial wavefunction, $\exp(-1.2r)$, does not respect the cusp condition - the derivatives of the wavefunction need to cancel the $1/r$ Coulomb term. Without a correct cusp condition, the local ...
- 46
2
votes
Accepted
Use of Metropolis-Hasting algorithm for gathering statistics
Your post actually contains two questions:
1) What should you calculate
This first question will be answered by defining what you are studying. If it is the magnetic properties of your system (usual ...
- 323
2
votes
Why are Hamiltonian dynamics used in MCMC?
I'm a little late to reply but I found this review to be really informative. One particularly nice feature of Hamiltonian flows is that they preserve volume in phase space. If we take an infinitesimal ...
- 10.1k
2
votes
Accepted
Monte Carlo Simulation algorithm
It seems to me you would just be randomly selecting $n$ at each time step, given some distribution you should be sampling $n$ from, and using your dynamics function to propagate the voltage from time $...
- 3,898
2
votes
Estimate information entropy through Monte Carlo sampling
For the second part of your question (estimation of entropy difference between distributions) you may be able to use the identity $$F = \langle E \rangle - T S,$$ where $\langle E \rangle$ is the ...
- 3,994
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