a posteriori error estimation

Utilizing Adjoint-Based Error Estimates for Surrogate Models to Accurately Predict Probabilities of Events

We develop a procedure to utilize error estimates for samples of a surrogate model to compute robust upper and lower bounds on estimates of probabilities of events. We show that these error estimates can also be used in an adaptive algorithm to …

A Measure-Theoretic Interpretation of Sample Based Numerical Integration with Applications to Inverse and Prediction Problems Under Uncertaint

The integration of functions over measurable sets is a fundamental problem in computational science. When the measurable sets belong to high-dimensional spaces or the function is computationally complex, it may only be practical to estimate integrals …