Using a generative model for out-of-sample testing of two-stage stochastic programs

TL;DR

This paper introduces a NORTA-based generative framework to create synthetic scenarios for two-stage stochastic programs, improving out-of-sample testing when data is scarce.

Contribution

It presents a novel application of NORTA for scenario generation, enabling reliable out-of-sample testing with limited data in stochastic programming.

Findings

NORTA-generated scenarios preserve key statistical properties.

Out-of-sample performance closely matches original model expectations.

Synthetic scenarios effectively supplement limited real data.

Abstract

Stochastic programming models for decision-making under uncertainty often suffer from scenario scarcity, where obtaining representative samples of uncertain parameters requires expensive simulations or measurements. This work presents a framework that leverages the Normal-to-Anything (NORTA) generative model to enhance the reliability of two-stage stochastic programming solutions through comprehensive out-of-sample testing when scenario data is limited. The NORTA model efficiently generates synthetic scenarios that preserve both marginal distributions and correlation structures from limited available data, offering a computationally tractable alternative to expensive physics-based simulations. We demonstrate the approach through a case study on power grid resilience planning against flood events in Texas, where we use 16 high-fidelity flood scenarios to generate 800 additional synthetic scenarios for validation. The results show that NORTA-generated scenarios accurately capture essential statistical properties, with the out-of-sample performance of first-stage decisions closely matching expectations from the original stochastic programming model. This framework enables decision-makers to assess the robustness of their solutions when obtaining additional real-world data is prohibitively expensive. The approach bridges machine learning and operations research by providing a practical solution to scenario generation challenges in stochastic programming.