This project implements a new stochastic, iterative Design of Experiments (DoE) based on a modified Kernel Density Estimation (KDE) [Roy2019].
It is a two-step process: (i) candidate samples are generated using MCMC based on KDE, and (ii) one of them is selected based on some metric. The performance of the method is assessed by means of the C^2-discrepancy space-filling criterion. KDOE appears to be as performant as classical one-shot methods in low dimensions, while it presents increased performance for high-dimensional parameter spaces. This work proposes a new methodology to stochastically sample the input parameter space iteratively allowing, at the same time, to take into account any constraint, such as non-rectangular DoE, sensitivity indices or even constraint on the quality on particular subprojections. It is a versatile method which offers an alternative to classical methods and, at the same time, is easy to implement and offers customization based on the objective of the DoE.
sampler = KdeSampler(dim=50)
sample_kde = sampler.generate(n_samples=30)Following is an 2-dimensional subprojection of the sample of size 50 in dimension 30:
Assuming that a group of sample is already computed, the PDF of the sample is estimated by KDE. This estimator is reversed so that the probability close to the existing samples is low and the probability in empty area is high. Moreover, the distance function used in the KDE is modified to use a Minkowsky distance. This modification allows to lower the probability on a given axis.
Then, using a MCMC sampling on this KDE field, a given number of sample is generated. On point is selected based on a given metric (here the C^2-discrepancy).
The dependencies are:
- Python >= 2.7 or >= 3.5
- scikit-learn >= 0.18
- numpy >= 0.13
- scipy >= 0.15
| [Roy2019] | Versatile Adaptive Sampling Algorithm using Kernel Density Estimation. Pamphile T. Roy, L. Jofre, J.C. Jouhaud, B. Cuenot. 2019 |