Risk-averse design optimization with CVaR constraints via multifidelity tail-region correction
Abstract
Risk-averse design optimization with conditional value-at-risk (CVaR) constraints requires accurate tail estimates, but repeated high-fidelity (HF) evaluations are costly. We propose a multifidelity (MF) tail-region correction method that uses dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) as a global surrogate and directs a limited HF budget to responses that most strongly influence CVaR. Covariance of the estimated DD-GPCE coefficients quantifies finite-sample prediction uncertainty and defines a confidence-interval-based tail region. Within this region, a two-stage strategy explores locations with high prediction uncertainty and then exploits locations with large correction-induced shifts. A Tikhonov-regularized residual expansion using the same polynomial basis yields a unified tail-corrected surrogate. For a ten-bar truss, the method produced a design close to the crude-MCS reference with approximately 72 to 274 times fewer HF evaluations than the considered MF importance sampling configurations. For a suction valve, it reduced mass by 1.05% and bending and bulging CVaR by 17.68% and 21.53%, respectively, while satisfying the valve-opening requirement. The results demonstrate accurate, HF-sample-efficient CVaR-constrained design through localized MF correction.
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BibTeX
@misc{lee2026riskaverse,
title = {{Risk-averse design optimization with CVaR constraints via multifidelity tail-region correction}},
author = {Gyeolhee Lee and Dongjin Lee},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29222},
eprint = {2608.29222},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29222},
}
RIS
TY - UNPB
TI - Risk-averse design optimization with CVaR constraints via multifidelity tail-region correction
AU - Gyeolhee Lee
AU - Dongjin Lee
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29222
UR - https://arxiv.org/abs/2608.29222
AB - Risk-averse design optimization with conditional value-at-risk (CVaR) constraints requires accurate tail estimates, but repeated high-fidelity (HF) evaluations are costly. We propose a multifidelity (MF) tail-region correction method that uses dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) as a global surrogate and directs a limited HF budget to responses that most strongly influence CVaR. Covariance of the estimated DD-GPCE coefficients quantifies finite-sample prediction uncertainty and defines a confidence-interval-based tail region. Within this region, a two-stage strategy explores locations with high prediction uncertainty and then exploits locations with large correction-induced shifts. A Tikhonov-regularized residual expansion using the same polynomial basis yields a unified tail-corrected surrogate. For a ten-bar truss, the method produced a design close to the crude-MCS reference with approximately 72 to 274 times fewer HF evaluations than the considered MF importance sampling configurations. For a suction valve, it reduced mass by 1.05% and bending and bulging CVaR by 17.68% and 21.53%, respectively, while satisfying the valve-opening requirement. The results demonstrate accurate, HF-sample-efficient CVaR-constrained design through localized MF correction.
ER -