Multi-fidelity Subset Simulation for rare event simulation

Subset Simulation (SS) is an efficient method for simulating rare events and estimating small failure probabilities. The original SS and its variants are developed for systems with single fidelity model. For many systems, besides high-fidelity system models, lower-fidelity models (e.g., reduced order models, surrogate models, machine learning models) can be developed that are less expensive albeit with lower accuracy. This paper proposes a novel multi-fidelity Subset Simulation (MFSS) approach that leverages lower-fidelity models for more efficient rare event simulation. MFSS extends the single fidelity SS to the more general multi-fidelity SS. MFSS relies on the formulation of an augmented failure probability problem by artificially treating the model fidelity as a random variable and augmenting it with other random variables/inputs. Then SS is used to solve the augmented problem, and Bayes’ theorem is used to estimate the failure probability under the high-fidelity model. At each level in MFSS, a constrained optimization problem is formulated to optimally allocate the computational efforts for each model fidelity to minimize the overall cost needed to generate the required number of samples from the conditional failure distribution. The characteristics and computational savings of MFSS are investigated both analytically and within the context of two benchmark problems.