Optimization-based Calibration of Simulation Input Models

Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and other related performance measures of interest. We propose an optimization-based framework to compute statistically valid bounds on input quantities. The framework utilizes constraints that connect the statistical information of the real-world outputs with the input-output relation via a simulable map. We analyze the statistical guarantees of this approach from the view of data-driven robust optimization, and show how the guarantees relate to the function complexity of the constraints arising in our framework. We investigate an iterative procedure based on a stochastic quadratic penalty method to approximately solve the resulting optimization. We conduct numerical experiments to demonstrate our performance in bounding the input models and related quantities

A Distributionally Robust Optimization Approach to the NASA Langley Uncertainty Quantification Challenge

We study a methodology to tackle the NASA Langley Uncertainty Quantification Challenge problem, based on an integration of robust optimization, more specifically a recent line of research known as distributionally robust optimization, and importance sampling in Monte Carlo simulation. The main computation machinery in this integrated methodology boils down to solving sampled linear programs. We will illustrate both our numerical performances and theoretical statistical guarantees obtained via connections to nonparametric hypothesis testing.Comment: Published in the Proceedings of the 30th European Safety and Reliability Conference and the 15th Probabilistic Safety Assessment and Management Conferenc