A bi-fidelity framework to compute extreme-event probability

In this work, we propose a bi-fidelity sequential sampling framework to estimate the extreme-event probability. As a basis for sequential sampling, a bi-fidelity Gaussian process is used to infuse the high and low-fidelity samples to establish a surrogate model. A bi-fidelity acquisition function is proposed, which seeks a balance between the benefits and costs of adding high/low fidelity samples. This guides the selection of the next samples for both their location in parameter space and fidelity. We test this algorithm for both synthetic and real applications to demonstrate its effectiveness. For the latter, we consider a practical problem of estimating extreme ship motion probability in irregular waves using computational fluid dynamics (CFD) with two different grid resolutions.