Cluster-aware threshold optimization with active learning for multi-fidelity surrogates

Abstract

Multi-fidelity (MF) methods are gaining popularity in engineering design and optimization. In contrast with many MF methods that rely on a fixed training data set, active learning has become a powerful tool for achieving higher efficiency in exploring and exploiting the design space by guiding the selection of the fidelity level and input locations for the next simulation run. However, most recent techniques assume an additive auto-regressive structure. To address this issue, we introduce an active learning framework named Cluster-aware Threshold Optimization. This technique leverages a non-additive multi-fidelity surrogate that sequentially selects the most informative new data points. We focus on two key aspects of optimizing sampling strategies in multi-fidelity modeling: (1) determining the allocation of low- and high-fidelity sample points, and (2) identifying an optimal combination of the high- and low-fidelity sample sizes given a computational budget. Numerical and engineering results demonstrate that the Cluster-aware Threshold Optimization approach is promising for multi-fidelity global fitting problems.