Model Calibration via Distributionally Robust Optimization: On the NASA Langley Uncertainty Quantification Challenge

TL;DR

This paper introduces a novel calibration method combining distributionally robust optimization and importance sampling to address uncertainty quantification challenges, providing theoretical guarantees and practical performance improvements.

Contribution

It presents an integrated approach for model calibration under uncertainty, with theoretical analysis and demonstrated effectiveness in numerical experiments.

Findings

The method achieves accurate parameter calibration.

It offers strong statistical guarantees.

Numerical results show improved decision and risk evaluation.

Abstract

We study a methodology to tackle the NASA Langley Uncertainty Quantification Challenge, a model calibration problem under both aleatory and epistemic uncertainties. Our methodology is 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 amounts to solving sampled linear programs. We present theoretical statistical guarantees of our approach via connections to nonparametric hypothesis testing, and numerical performances including parameter calibration and downstream decision and risk evaluation tasks.