Global Sensitivity Analysis and Uncertainty Quantification

Global Sensitivity Analysis (GSA) and Uncertainty Quantification (UQ) constitute complementary disciplines aimed at understanding how variability in model inputs propagates to outputs and how confident one can be in model predictions. Whereas UQ focuses on characterising the full range of possible outcomes given uncertainties in parameters, structural assumptions and data, GSA systematically allocates the resulting output variance to individual inputs or their interactions. Classic approaches to GSA include variance‐based methods such as Sobol indices, together with screening techniques for high‐dimensional problems. Recent methodological advances have introduced density‐based measures, derivative‐based global sensitivity measures and cooperative game‐theoretic tools such as Shapley values. To alleviate the computational burden of sampling‐intensive analyses, surrogate models—ranging from polynomial chaos expansions to neural networks and Gaussian processes—are increasingly employed. These surrogates underpin analytical expressions for sensitivity indices and enable UQ in complex systems, from climate projections and structural engineering to pharmacokinetics. The integration of GSA and UQ informs robust decision making, model calibration and experimental design by highlighting influential inputs, quantifying the impact of dependencies among parameters and revealing regions of parameter space that require further investigation.

Research from Nature Portfolio

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Research from all publishers

Recent work in renewable‐energy engineering applied Shapley value explanations to wind‐turbine extreme‐load models, coupling random‐forest regression with an improved algorithm for Shapley effect evaluation. This study demonstrated how two wind parameters, one aerodynamic and two structural variables contribute to critical responses such as blade‐tip clearance and tower bending moments, and highlighted the effect of input correlations on sensitivity rankings. Another development in statistical computing introduced an open‐source R package that streamlines the computation of variance‐based sensitivity indices. The package implements state‐of‐the‐art estimators for first‐, total‐ and higher‐order Sobol indices, provides error‐approximation metrics and offers visual tools for multivariate outputs, thereby lowering the barrier for practitioners to conduct rigorous UQ and GSA. In the context of dependent inputs, research on polynomial chaos expansion has yielded efficient strategies for variance‐based indices when input variables exhibit correlation. By constructing orthogonal polynomial bases adapted to the joint distribution of inputs, this approach enables accurate sensitivity assessment without the restrictive assumption of input independence, broadening the applicability of GSA to environmental, reliability and systems models.

Global Sensitivity Analysis and Uncertainty Quantification publication trend

The graph below shows the total number of articles in global sensitivity analysis and uncertainty quantification across all publications each year (not limited to Nature Index journals).

Technical terms

Global Sensitivity Analysis (GSA): A set of methods that quantify how uncertainty in each model input, individually or in combination, contributes to output variability across the entire input space.

Uncertainty Quantification (UQ): The process of characterising and reducing uncertainties in model inputs, structure and parameters to assess confidence in model predictions.

Sobol indices: Variance‐based global sensitivity measures that decompose the output variance into contributions from each input factor and their interactions.

Shapley value: A cooperative game‐theoretic measure adapted for GSA that attributes the average marginal contribution of each input to the model output variance.

Polynomial Chaos Expansion: A surrogate modelling technique that represents model outputs as a series of orthogonal polynomials of uncertain inputs, facilitating analytical computation of sensitivity indices.

References

1. Variable importance analysis of wind turbine extreme responses with Shapley value explanation. Renewable Energy (2024).
2. sensobol: An R Package to Compute Variance-Based Sensitivity Indices. Journal of Statistical Software (2022).
3. Polynomial chaos expansion for sensitivity analysis of model output with dependent inputs. Reliability Engineering & System Safety (2021).