Machine Learning Approaches to Rare Events Sampling and Estimation

Given the severe impacts of rare events, we try to quantitatively answer the following two questions: How can we estimate the probability of a rare event? And what are the factors affecting these probabilities? We utilize machine learning classification methods to define the failure boundary (in the stochastic space) corresponding to a specific threshold of a rare event. The training samples for the classification algorithm are obtained using multilevel splitting and Monte Carlo (MC) simulations. Once the training of the classifier is performed, a full MC simulation can be performed efficiently using the classifier as a reduced order model replacing the full physics simulator.

We apply the proposed method on a standard benchmark for CO2 leakage through an abandoned well. In this idealized test case, CO2 is injected into a deep aquifer and then spreads within the aquifer and, upon reaching an abandoned well; it rises to a shallower aquifer. In current study, we try to evaluate the probability of leakage of a pre-defined amount of the injected CO2 given a heavy tailed distribution of the leaky well permeability. We show that machine learning based approaches significantly outperform direct MC and multi-level splitting methods in terms of efficiency and precision. The proposed algorithm’s efficiency and reliability enabled us to perform a sensitivity analysis to the different modeling assumptions including the different prior distributions on the probability of CO2 leakage.