Hi everyone,
I currently use MCS method to analyze effect of some uncertain parameters on electrical power system and run 10,000 simulations to calculate the output which approximately takes around 1 hour.
I recently read some methods which can reduce the MCS scenarios thus, resulting in low computational time.
So, can our fellow researchers elaborate more on this topic or suggest me any other techniques which has the potential to significantly reduce the computational time of MCS (say around 5 minutes for my work) with reasonable accuracy?
Cheers
Sam
Importance sampling ?
https://en.wikipedia.org/wiki/Importance_sampling
Sam,
Surrogate models (emulators) are a well established method for reducing the run time in applications like this. Gaussian Processes work particularly well.
10,000 runs of a model in an hour isn’t particularly slow though. Unless you have to do this repeatedly is an hour too long?
I think of the following. (Maybe this is already a standard method?)
Suppose you have a nonlinear function F(X) where X is a random variable with a known distribution. With Monte Carlo, an estimate of the expected value of F is the average of a set of values of F(X) based on random drawings of X.
An alternative, non-random, method is as follows. Assume for simplicity that X has a finite range. Divide this range in a finite number of similar adjacent intervals ("bins"), numbered 1 to N. An estimate of the expected value of F is the sum over i=1..N of F(Xi) times Pi, with Xi being the middle of interval i, and Pi being the probability mass of interval i. This might be much more accurate than N random drawings from the distribution of X.
If the range of X is not finite, as with the normal distribution, then cut off the tails with very low probability; for instance cut off outside 4 times the standard deviation at both ends. Of course, the above estimate must then by divided by the sum of the Pi.
This method is of limited value when X is multidimensional, with a large number of dimensions, say M, since the number of "cells" is N to the power M.
Dear Gurung,
Read the paper "IMPROVING COMPUTATIONAL EFFICIENCY OF MONTE-CARLO
SIMULATIONS WITH VARIANCE REDUCTION".
Good Luck
I don't know if it might help your case, but I would suggest utilizing the Genetic Algorithm. I had used it in my Master Thesis Research for developing a systematic methodology to design a very complex class of high-frequency radar antennas, and I can say that it is a very powerful algorithm, once you formulate it into your problem effectively. In my case it gave results in 2-3 iterations (generations), maximum 4-5 in the worst start-up scenario. The results in my case came in the order of seconds, and I don't think it would take more than the order of minutes in your case, even if the amount of data points is larger. Good luck!
This might seem a bit unrelated, but if you're sampling your Monte Carlo points from some distribution and you're interested in the distribution of outputs (i.e. after simulating each point, or whatever you're doing) then you may be interested in the Koopman Operator (see, e.g., https://engineering.ucsb.edu/~harbabi/research/KoopmanIntro.pdf).
Depending on which direction you're going (i.e. whether you have some known target distribution of outputs, say the performance distribution of the electrical power systems, or some known levels of uncertainties on the inputs for which you want to generate the output distribution) you may also want to checkout the Frobenius-Peron Operator.
The term of "Variance Reduction" is very large subject. There is many ways to reduce the variance of simulation. Each unneccessary counting can extend your computational time. On the other hand, it can increase your statistical error rate. So, please carefully read the special variance reduction techniques of your code.
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