Scalable Inference for Rare Events: Computational Methods for Estimating Probability of Tail Events
Technical Report,16 Mar 2016,15 Aug 2019
UNITED TECHNOLOGIES RESEARCH CENTER EAST HARTFORD CT EAST HARTFORD United States
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This report presents key findings and results in the Scalable Inference for Rare Events SIRE project FA8650-16-C-7646. Under the project, we discovered deep theoretical connections between Koopman operator theory and rare event simulation in stochastic differential equations. We then developed a generalized approach for constructing efficient importance sampling methods for linear stochastic differential equations using the Kolmogorov Backward Ornstein-Uhlenbeck operator. We show that this approach is a special case of the Koopman operator approach. Additionally, we constructed rotorcraft models that capture critical stall phenomena that was used for computation. We then demonstrate large deviations-based importance sampling and splitting methods on rotorcraft and electrical models.
- Statistics and Probability