Samantha Roth: Adaptive sampling for the BASS emulator: extending Sobol’ sensitivity analysis to more real-world models

Uncertain computer model projections contribute to decision-making in many areas. For example, EnergyPlus can be used to identify strategies for reducing home heating and cooling costs. Neglecting uncertainties can lead to worse decisions. A key source of uncertainty in model projections is uncertainty about the model parameters. By reducing parametric uncertainty, we can reduce projection uncertainty, which can result in better-informed decisions. Using Sobol' sensitivity analysis, we can identify which parameters to focus on for parametric uncertainty reduction. Sobol’ sensitivity analysis precisely quantifies the contribution of model parameters and their interactions to projection uncertainty. Performing Sobol’ sensitivity analysis can be computationally costly. For slow computer models, replacing the computer model with a fast statistical emulator reduces the computational burden. 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. Existing adaptive sampling approaches need adaptation to apply to the BASS emulator. We propose multiple adaptive sampling approaches to train the BASS emulator, one of which exploits the Monte Carlo error-free sensitivity indices provided, to guide the sampling process. Our preliminary results indicate that our approach reduces reduces computational costs relative to Sobol' sensitivity analysis both with no emulator and with the BASS emulator without sampling adaptively. We also identify avenues for further reducing computational costs, including exploitation of active subspaces. Through our current and proposed innovations, we aim to enable 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 those determining home energy efficiency.