Output-Weighted Optimal Sampling for Bayesian Experimental Design and Uncertainty Quantification

We introduce a class of acquisition functions for sample selection that leads\nto faster convergence in applications related to Bayesian experimental design\nand uncertainty quantification. The approach follows the paradigm of active\nlearning, whereby existing samples of a black-box function are utilized to\noptimize the next most informative sample. The proposed method aims to take\nadvantage of the fact that some input directions of the black-box function have\na larger impact on the output than others, which is important especially for\nsystems exhibiting rare and extreme events. The acquisition functions\nintroduced in this work leverage the properties of the likelihood ratio, a\nquantity that acts as a probabilistic sampling weight and guides the\nactive-learning algorithm towards regions of the input space that are deemed\nmost relevant. We demonstrate superiority of the proposed approach in the\nuncertainty quantification of a hydrological system as well as the\nprobabilistic quantification of rare events in dynamical systems and the\nidentification of their precursors.\n