Derivative Based Global Sensitivity Measures (DGSM) is a technique used in global sensitivity analysis to identify the importance of different subsets of input variables to variation in model output. It is gaining popularity among practitioners due to its link with Sobol’ sensitivity indices and easiness of implementation. The computational time required for DGSM is usually much less than that needed for estimating Sobol’ sensitivity indices.
The variance-based method of Sobol’ sensitivity indices [1] is one of the most efficient and popular global sensitivity analysis techniques. It provides information on the importance of different subsets of input variables to the output variance. However, the direct implementation of variance-based global sensitivity analysis measures can be time-consuming and impractical for models with high dimensionality.
DGSM is based on averaging of local derivatives using Monte Carlo or Quasi Monte Carlo sampling methods. Unlike the Morris method,[2] which uses finite differences to calculate elementary effects with increments comparable to the variable uncertainty ranges, DGSM evaluates strict local derivatives with smaller increments. Moreover, derivatives are calculated at randomly or quasi-randomly selected points within the full range of uncertainty, rather than points from a fixed grid. Consequently, DGSM is a more accurate technique than the Morris method. In was suggested as a practical tool in,[3] while the theory and the link between DGSM and Sobol' senstitivity indices was developed in,.[4][5] Other important developments were given in,[6][7],.[8]
DGSM encompasses upper and lower bounds on the values of Sobol’ total sensitivity indices,[9] offering a comprehensive understanding of the model's behavior. This approach has gained popularity due to its link with Sobol’ sensitivity indices and its ease of implementation. One of the key advantages of DGSM is its relatively lower computational time compared to estimating Sobol’ sensitivity indices, making it a practical choice for sensitivity analysis in high-dimensional models.
DGSM is closely related to the active subspace method,[10] providing a deeper understanding of the model's behavior and reducing computational costs. The relationship between the activity scores of the active subspace method and DGSM has been a subject of interest, further highlighting the utility of DGSM in practical applications.
The numerical efficiency of the DGSM method can be improved by using automatic differentiation for calculations as was shown in.[11] However, the number of required function evaluations still remains to be proportional to the number of inputs. This dependence can be greatly reduced using an approach based on algorithmic differentiation in the adjoint (reverse) mode,.[12][13] It allows estimating all derivatives at a cost at most 4-6 times of that for evaluating the original function.
Original source: https://en.wikipedia.org/wiki/Derivative-based Global Sensitivity Measures.
Read more |