Entropy-based adaptive design for contour finding and estimating reliability

Computer modeling of physical systems must accommodate uncertainty in materials and loading conditions. This input uncertainty translates into a stochastic response from the model, based on nominal settings of a physical system, even when the simulator is deterministic. In engineering, assessing the reliability of said system can mean guarding against a physical collapse, puncture or failing of electronics. Reliability statistics like failure probability, the probability the response exceeds a threshold, can be calculated with Monte Carlo (MC). While MC produces an asymptotically unbiased estimator (Robert and Casella 2013), it can take thousands or even millions of model evaluations, i.e., great computational expense, to achieve a desired error tolerance. The search for alternatives to direct MC in computer-assisted reliability analysis has become a cottage industry of late. Some approaches seek to gradually reduce the design space for sampling through subset selection (Cannamela et al. 2008; Au and Beck 2001). Importance sampling (IS) focuses MC efforts by biasing sampling toward areas of the design space where failure is probable (Srinivasan 2013), and then re-weights any expectations to correct for that bias asymptotically. Effective IS strategies (Li et al. 2011; Peherstorfer et al. 2018a) aim to generate samples which reduce variance compared to direct MC.