Latin hypercube sampling with inequality constraints

TL;DR

This paper introduces a new algorithm called constrained Latin hypercube sampling (cLHS) that generates samples respecting inequality constraints, improving sampling efficiency for complex numerical models with physical constraints.

Contribution

The paper presents a novel cLHS algorithm that incorporates inequality constraints into Latin hypercube sampling by permuting initial samples, demonstrated on a welding simulation example.

Findings

cLHS effectively enforces inequality constraints in sampling.

The method improves sampling accuracy in constrained physical models.

Application to welding simulation shows practical benefits.

Abstract

In some studies requiring predictive and CPU-time consuming numerical models, the sampling design of the model input variables has to be chosen with caution. For this purpose, Latin hypercube sampling has a long history and has shown its robustness capabilities. In this paper we propose and discuss a new algorithm to build a Latin hypercube sample (LHS) taking into account inequality constraints between the sampled variables. This technique, called constrained Latin hypercube sampling (cLHS), consists in doing permutations on an initial LHS to honor the desired monotonic constraints. The relevance of this approach is shown on a real example concerning the numerical welding simulation, where the inequality constraints are caused by the physical decreasing of some material properties in function of the temperature.