Sensitivity Indices Based on Finite Differences

  • Yue, Ruilong (Florida State University)
  • Ökten, Giray (Florida State University)

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The global active subspace method is a dimension reduction method introduced in Yue and Ökten [1] that uses expected values of finite differences of the underlying function to identify important directions and build a surrogate model on a lower-dimensional subspace. The method generalizes the active subspace method, which uses gradient information of the function to construct a reduced model. Similar to the way activity scores are obtained from the active subspace method, global activity scores can be obtained from the global active subspace method, as established by Yue and Ökten [2]. We present theoretical results connecting global activity scores to Sobol' sensitivity indices and demonstrate their performance through numerical examples. In these examples, we compare global activity scores with Sobol' sensitivity indices, derivative-based sensitivity measures, and activity scores. The results show that, in the presence of noise or high variability, global activity scores outperform derivative-based measures and activity scores, while in noiseless settings all three approaches yield similar results. [1] Ruilong Yue, Giray Ökten. The Global Active Subspace Method, arXiv:2304.14142v2, 2024. [2] Ruilong Yue, Giray Ökten. Global Activity Scores, arXiv:2505.00711, 2025.