Then, the performances of all surrogate models were evaluated using a data set of 100,000 input-output pairs that were generated according to the Sobol sampling technique. Each surrogate model was trained using these data sets. From each challenge function, input-output pairs were generated using the three sampling methods for nine sample sizes. These methods were selected as they are shown to sample input space uniformly with limited sample sizes for functions up to ten dimensions ( Dife and Diwekar, 2016). Sobol and Halton sequences are both quasi-random low-discrepancy sequences, which seek to distribute samples uniformly across the input space. Then, each of the N partitions is sampled once, and randomly combined. LHS is a stratified sampling technique, and it splits the range of each input variable into N intervals of equal probability, where N is the number of sample points. The sampling methods that were utilized to generate training data from the challenge functions include LHS, Sobol Sequence and Halton Sequence. Eden, in Computer Aided Chemical Engineering, 2018 4 Computational Experiments
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elif criterion.lower() in ('correlate', 'corr'):.H = _lhsmaximin(n, samples, iterations, 'centermaximin').elif criterion.lower() in ('centermaximin', 'cm'):.H = _lhsmaximin(n, samples, iterations, 'maximin').elif criterion.lower() in ('maximin', 'm'):.if criterion.lower() in ('center', 'c'):.'corr'), 'Invalid value for "criterion": '.format(criterion).assert criterion.lower() in ('center', 'c', 'maximin', 'm',.> lhs(4, samples=5, criterion='correlate', iterations=10).A 4-factor design with 5 samples where the samples are as uncorrelated.> lhs(3, samples=4, criterion='maximin').A 3-factor design with 4 samples where the minimum distance between.> lhs(2, samples=5, criterion='center').A 2-factor design with 5 centered samples::.
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The number of factors to generate samples for.def lhs(n, samples=None, criterion=None, iterations=None):.An example of this is shown below.įor example, if I wanted to transform the uniform distribution of 8 samples to a normal distribution (mean=0, standard deviation=1), I would do something like: The output design scales all the variable ranges from zero to one which can then be transformed as the user wishes (like to a specific statistical distribution using the ppf (inverse cumulative distribution) function. “correlation” or “corr”: minimize the maximum correlation coefficient.“centermaximin” or “cm”: same as “maximin”, but centered within the intervals.“maximin” or “m”: maximize the minimum distance between points, but place the point in a randomized location within its interval.“center” or “c”: center the points within the sampling intervals.
#Latin hypercube sampling python how to
criterion: a string that tells lhs how to sample the points (default: None, which simply randomizes the points within the intervals):.samples: an integer that designates the number of sample points to generate for each factor (default: n).n: an integer that designates the number of factors (required).Latin-hypercube designs can be created using the following simple syntax: > lhs(n, ) All available designs can be accessed after a simple import statement:.