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Computational models are utilized in many scientific domains to simulatecomplex systems. Sensitivity analysis is an important practice to aid ourunderstanding of the mechanics of these models and the processes they describe,but performing a sufficient number of model evaluations to obtain accuratesensitivity estimates can often be prohibitively expensive. In order to reducethe computational burden, a common solution is to use a surrogate model thatapproximates the original model reasonably well but at a fraction of the cost.However, in exchange for the computational benefits of surrogate-basedsensitivity analysis, this approach comes with the price of a loss in accuracyarising from the difference between the surrogate and the original model. Toaddress this issue, we adapt the floodgate method of Zhang and Janson (2020) toprovide valid surrogate-based confidence intervals rather than a pointestimate, allowing for the benefit of the computational speed-up of using asurrogate that is especially pronounced for high-dimensional models, whilestill retaining rigorous and accurate bounds on the global sensitivity withrespect to the original (non-surrogate) model. Our confidence interval isasymptotically valid with almost no conditions on the computational model orthe surrogate. Additionally, the accuracy (width) of our confidence intervalshrinks as the surrogate's accuracy increases, so when an accurate surrogate isused, the confidence interval we report will correspondingly be quite narrow,instilling appropriately high confidence in its estimate. We demonstrate theproperties of our method through numerical simulations on the small Hymodhydrological model, and also apply it to the more complex CBM-Z meteorologicalmodel with a recent neural-network-based surrogate.

Surrogate-based global sensitivity analysis with statistical guarantees via floodgate