Unexpected Sobol Index Lack of Convergence: LHS vs. Low-Discrepancy (Ishigami Benchmark)

[sidereus3]

Hello Dakota Developers/Community,

I am performing Global Sensitivity Analysis (GSA) using Dakota variance_based_decomp method on the Ishigami function (a=7,b=0.1) with the three standard variables x1, x2, x3 (k=3). I am comparing the performance of two sampling methodologies LHS and Low-Discrepancy (Sobol sequence) for a fixed number of simulations.

The observed results are highly unexpected: LHS converged well, while the Low-Discrepancy sequence does not, contradicting the theoretical advantage of Quasi-Monte Carlo (QMC) methods. For example, the analytical solution of the Sobol Index Total Effect for variable x1 is 0.5576. LHS, after 5000 simulations, returns ST1=0.5517, while Low-Discrepancy, still after 5000 simulations, returns ST1=0.1803 (attached spreadsheet for full comparison of Main and Total Sobol Indices).

Questions for the Community:

1. Fundamental Lack of Convergence: Is there any specific, known reason why the two sampling methods return such dramatically different results, particularly why the Low-Discrepancy sequence (Sobol) performed so poorly, yielding an incorrect variable ranking and spurious main effects (e.g., S3=0.2212 instead of 0.0)?
2. Implementation Detail Check: Did I miss any critical details in the documentation regarding the use of low_discrepancy sequences specifically with variance_based_decomp?

I have attached the Dakota input file (01_ishigami.txt) for review. The number of simulations used is [Nevals=N×(k+2)=5000.]

Thank you for your time and guidance!
Francesco Serafin
01_ishigami.txt
lhs_ld_sobol.ods