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Sequential good lattice point sets for computer experiments
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作者 Xue-Ru Zhang Yong-Dao Zhou +1 位作者 Min-Qian Liu Dennis K.J.Lin 《Science China Mathematics》 SCIE CSCD 2024年第9期2153-2170,共18页
Sequential Latin hypercube designs(SLHDs) have recently received great attention for computer experiments, with much of the research restricted to invariant spaces. The related systematic construction methods are infl... Sequential Latin hypercube designs(SLHDs) have recently received great attention for computer experiments, with much of the research restricted to invariant spaces. The related systematic construction methods are inflexible, and algorithmic methods are ineffective for large designs. For designs in contracting spaces, systematic construction methods have not been investigated yet. This paper proposes a new method for constructing SLHDs via good lattice point sets in various experimental spaces. These designs are called sequential good lattice point(SGLP) sets. Moreover, we provide efficient approaches for identifying the(nearly)optimal SGLP sets under a given criterion. Combining the linear level permutation technique, we obtain a class of asymptotically optimal SLHDs in invariant spaces, where the L1-distance in each stage is either optimal or asymptotically optimal. Numerical results demonstrate that the SGLP set has a better space-filling property than the existing SLHDs in invariant spaces. It is also shown that SGLP sets have less computational complexity and more adaptability. 展开更多
关键词 contracting space maximin distance nested Latin hypercube design sequential design space-fillingdesign
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A new rotation method for constructing orthogonal Latin hypercube designs
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作者 Chong Sheng Jinyu Yang Min-Qian Liu 《Science China Mathematics》 SCIE CSCD 2023年第4期839-854,共16页
Latin hypercube designs(LHDs)are very popular in designing computer experiments.In addition,orthogonality is a desirable property for LHDs,as it allows the estimates of the main effects in linear models to be uncorrel... Latin hypercube designs(LHDs)are very popular in designing computer experiments.In addition,orthogonality is a desirable property for LHDs,as it allows the estimates of the main effects in linear models to be uncorrelated with each other,and is a stepping stone to the space-filling property for fitting Gaussian process models.Among the available methods for constructing orthogonal Latin hypercube designs(OLHDs),the rotation method is particularly attractive due to its theoretical elegance as well as its contribution to spacefilling properties in low-dimensional projections.This paper proposes a new rotation method for constructing OLHDs and nearly OLHDs with flexible run sizes that cannot be obtained by existing methods.Furthermore,the resulting OLHDs are improved in terms of the maximin distance criterion and the alias matrices and a new kind of orthogonal designs are constructed.Theoretical properties as well as construction algorithms are provided. 展开更多
关键词 computer experiment factorial design Latin hypercube design maximin distance ORTHOGONALITY
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