Several recent developments in the engineering modeling community, the applied math and computer science community, and the applied probability and statistics community have increased the ability to accurately model an engineering system, calibrate that model to individual units within a production line, and quantify the uncertainty of the associated models. This has manifested in the aerospace community through ideas like the develop-ment of digital twin, condition based maintenance, where expensive models are calibrated to individual aircraft for the purposes of inferring component damage and predicting the remaining lifespan of that aircraft. However, high performance computing is the back-bone of the accurate models, calibration of those models, and quantifying the uncertainty of the calculations. As a result, these computations are performed as a post-processing stage. Making real-time decisions about the safe operation of an aircraft after it has been damaged in flight is limited by the computational resources on board. The purpose of this document is to explore applications of model reduction, surrogate modeling, and probabil-ity density approximations in order to accelerate the computation required for estimating how an aircraft has been damaged and predicting the safe flight envelope of that damaged aircraft.
