  Numerical modeling is essential for comprehending intricate physical
phenomena in different domains. To handle complexity, sensitivity analysis,
particularly screening, is crucial for identifying influential input
parameters. Kernel-based methods, such as the Hilbert Schmidt Independence
Criterion (HSIC), are valuable for analyzing dependencies between inputs and
outputs. Moreover, due to the computational expense of such models, metamodels
(or surrogate models) are often unavoidable. Implementing metamodels and HSIC
requires data from the original model, which leads to the need for
space-filling designs. While existing methods like Latin Hypercube Sampling
(LHS) are effective for independent variables, incorporating dependence is
challenging. This paper introduces a novel LHS variant, Quantization-based LHS,
which leverages Voronoi vector quantization to address correlated inputs. The
method ensures comprehensive coverage of stratified variables, enhancing
distribution across marginals. The paper outlines expectation estimators based
on Quantization-based LHS in various dependency settings, demonstrating their
unbiasedness. The method is applied on several models of growing complexities,
first on simple examples to illustrate the theory, then on more complex
environmental hydrological models, when the dependence is known or not, and
with more and more interactive processes and factors. The last application is
on the digital twin of a French vineyard catchment (Beaujolais region) to
design a vegetative filter strip and reduce water, sediment and pesticide
transfers from the fields to the river. Quantization-based LHS is used to
compute HSIC measures and independence tests, demonstrating its usefulness,
especially in the context of complex models.
