An ensemble-based approach for multi-fidelity emulation and adaptive sampling

TL;DR

This paper introduces a novel ensemble-based multi-fidelity emulation method using hierarchical kriging and Bayesian model averaging, enhancing accuracy and efficiency in complex physical system simulations.

Contribution

It develops a new multi-fidelity emulation framework that integrates heterogeneous models and employs adaptive sampling for improved predictive performance.

Findings

Outperforms single-model emulators in accuracy and robustness.

Effectively identifies informative samples with adaptive design.

Achieves better performance under limited computational budgets.

Abstract

High-resolution simulation models are essential for representing complex physical systems, yet their substantial computational cost severely limits the number of feasible high-fidelity (HF) evaluations. This problem is often addressed through multi-fidelity frameworks, which employ hierarchies of simulators with varying levels of fidelity and evaluation cost. A key difficulty in this setting is integrating information from such heterogeneous sources to accurately approximate HF simulators. This paper proposes a novel multi-fidelity emulation methodology based on ensemble learning. The base learners of the ensemble are hierarchical kriging emulators that systematically incorporate information from lower-fidelity models into HF predictions. Aggregation of these base learners via Bayesian model averaging yields the multi-fidelity emulator with principled uncertainty quantification. The between-model variance component of this uncertainty is then employed as the acquisition criterion in an adaptive design strategy to enrich the training set with informative samples. The predictive performance of the approach is assessed on a collection of well-established benchmark problems. Results show that our multi-fidelity emulator outperforms single-model alternatives in terms of accuracy and robustness. Furthermore, the adaptive design strategy effectively identifies informative samples and improves emulator performance under limited computational budgets.