Efficient Active Learning Strategies for Computer Experiments

Active learning aims at allocating resources in an intelligent manner based on the already observed data to satisfy certain objectives such as surrogate modeling or optimizing a computationally expensive function. When a Gaussian process model is used as a surrogate, space-filling designs are commonly employed to initialize active learning. Here we propose screening designs as initial designs and a new correlation function for the Gaussian process. Specifically, we propose using the maximum one-factor-at-a-time (MOFAT) design as the initial design and a multiplicative inverse multiquadric (MIM) kernel for the correlation function. The ideas behind them are known in other fields, such as sensitivity analysis or kernel theory, but they never seem to have been used for active learning in computer experiments. We also propose an integrated MOFAT-MIM strategy that automatically incorporates screening in the model estimation step. We show that these strategies provide substantial improvement to the state-of-the-art methods for both emulation and optimization objectives. We support our findings through theory and simulations, and a real experiment on the vapor-phase infiltration process.