Adaptive sampling for the BASS emulator enables Sobol' sensitivity analysis for slower, higher dimensional models

Music City Center 

Decision-makers use projections from computer models to prepare for natural hazards including wildfires and floods. Understanding how the computer model inputs influence its projections is a key step in this process. Sobol' sensitivity analysis quantifies the importance of uncertain computer model inputs and their interactions. Performing Sobol' sensitivity analysis can be computationally costly. Replacing the computer model with an emulator reduces the computational burden (Roth et al., 2025). The Bayesian adaptive spline surface (BASS) emulator (1) efficiently handles high-dimensional input spaces and (2) provides Sobol' sensitivity indices without evaluating the emulator (Francom et al., 2018). Strategically adding data points to train the emulator (via adaptive sampling) can further reduce the computational burden by reducing the amount of training data required. We propose an adaptive sampling approach to train the BASS emulator that exploits the Monte Carlo error-free sensitivity indices provided to guide the sampling process. Our process can be tailored to various goals for Sobol' sensitivity analysis, including screening (identifying a set of low sensitivity inputs), ranking (ordering inputs by their relative impact on the model output), and factor mapping (identifying areas of the input space that lead to critical model output values). By drastically reducing computational costs, our approach enables Sobol' sensitivity analysis on a limited computational budget for slow, high-dimensional computer models. Therefore, our approach has the potential to improve understanding of high-dimensional complex systems, such as the reliability of power systems to natural hazards.