Active Learning with Multifidelity Modeling for Efficient Rare Event Simulation

TL;DR

This paper introduces an adaptive multifidelity active learning framework that efficiently estimates rare event probabilities by intelligently combining low- and high-fidelity models, reducing computational costs significantly.

Contribution

The proposed framework adaptively fuses low- and high-fidelity models for efficient rare event probability estimation without assumptions on model correlation, improving robustness and reducing high-fidelity calls.

Findings

Accurately estimates failure probabilities across diverse case studies.

Requires significantly fewer high-fidelity model calls than traditional methods.

Demonstrates robustness in estimating small failure probabilities.

Abstract

While multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model. We demonstrate our framework using several academic case studies and two finite element (FE) model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.