Conditional-Value-at-Risk Estimation via Reduced-Order Models

Heinkenschloss, Matthias; Krämer, Boris; Takhtaganov, Timur; Willcox, Karen

doi:10.1137/17m1160069

Cited by 25 publications

(14 citation statements)

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“…Multifidelity methods have much broader applications, not only Monte Carlo‐based methods, but also more general UQ aspects, for example, optimization with uncertainty (Bonfiglio, Perdikaris, Brizzolara, & Karniadakis, 2018; Heinkenschloss, Kramer, Takhtaganov, & Willcox, 2018; Pang, Perdikaris, Cai, & Karniadakis, 2017), multifidelity surrogate modeling (Chaudhuri, Lam, & Willcox, 2018; Giselle Ferńandez‐Godino, Park, Kim, & Haftka, 2019; Guo, Song, Park, Li, & Haftka, 2018; Parussini, Venturi, Perdikaris, & Karniadakis, 2017; Perdikaris, Venturi, Royset, & Karniadakis, 2015; Tian et al, 2020) and multifidelity information reuse, and fusion (Cook, Jarrett, & Willcox, 2018; Perdikaris, Venturi, & Karniadakis, 2016). We refer to (Park et al, 2017; Peherstorfer, Willcox, & Gunzburger, 2018) for a comprehensive introduction and in‐depth discussion of multifidelity methods for uncertainty propagation.…”

Section: Modern MC Methods For Uqmentioning

confidence: 99%

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Zhang

2020

WIREs Computational Stats

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Uncertainty quantification (UQ) includes the characterization, integration, and propagation of uncertainties that result from stochastic variations and a lack of knowledge or data in the natural world. Monte Carlo (MC) method is a sampling‐based approach that has widely used for quantification and propagation of uncertainties. However, the standard MC method is often time‐consuming if the simulation‐based model is computationally intensive. This article gives an overview of modern MC methods to address the existing challenges of the standard MC in the context of UQ. Specifically, multilevel Monte Carlo (MLMC) extending the concept of control variates achieves a significant reduction of the computational cost by performing most evaluations with low accuracy and corresponding low cost, and relatively few evaluations at high accuracy and corresponding high cost. Multifidelity Monte Carlo (MFMC) accelerates the convergence of standard Monte Carlo by generalizing the control variates with different models having varying fidelities and varying computational costs. Multimodel Monte Carlo method (MMMC), having a different setting of MLMC and MFMC, aims to address the issue of UQ and propagation when data for characterizing probability distributions are limited. Multimodel inference combined with importance sampling is proposed for quantifying and efficiently propagating the uncertainties resulting from small data sets. All of these three modern MC methods achieve a significant improvement of computational efficiency for probabilistic UQ, particularly uncertainty propagation. An algorithm summary and the corresponding code implementation are provided for each of the modern MC methods. The extension and application of these methods are discussed in detail. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods Statistical and Graphical Methods of Data Analysis > Sampling

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Section: Modern MC Methods For Uqmentioning

confidence: 99%

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Zhang

2020

WIREs Computational Stats

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“…A recent work proposed by (Khan, Kani, & Elsheikh, 2019) focused on machine learning based hybrid multilevel multifidelity method, which utilizes the POD based approximation and gradient boosted tree surrogate model. Multifidelity methods have much broader applications, not only Monte Carlo based methods, but also more general UQ aspects, for example, optimization with uncertainty (Pang, Perdikaris, Cai, & Karniadakis, 2017;Bonfiglio, Perdikaris, Brizzolara, & Karniadakis, 2018;Heinkenschloss, Kramer, Takhtaganov, & Willcox, 2018), multifidelity surrogate modeling (Perdikaris, Venturi, Royset, & Karniadakis, 2015;Parussini, Venturi, Perdikaris, & Karniadakis, 2017;Giselle Fernández-Godino, Park, Kim, & Haftka, 2019;Guo, Song, Park, Li, & Haftka, 2018;Chaudhuri, Lam, & Willcox, 2018;Tian et al, 2020) and multifidelity information reuse, and fusion (Cook, Jarrett, & Willcox, 2018;Perdikaris, Venturi, & Karniadakis, 2016). We refer to (Park et al, 2017;Peherstorfer, Willcox, & Gunzburger, 2018) for a comprehensive introduction and in-depth discussion of multifidelity methods for uncertainty propagation.…”

Section: Multifidelity Monte Carlo Methods In Uq Applicationsmentioning

confidence: 99%

Modern Monte Carlo Methods for Efficient Uncertainty Quantification and Propagation: A Survey

Zhang

2020

Preprint

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“…This can be handled by adding safety factors to the threshold; however, it has been shown before that probabilistic approaches lead to safer designs with optimized performance compared to the safety factor approach [7,8,9]. Superquantile/CVaR has been recently used in specific formulations in civil [10,11], naval [12,13] and aerospace [14,15] engineering, as well as general PDE-constrained optimization [16,17,18,19]. The bPoF risk measure has been shown to possess beneficial properties when used in optimization [6,20,21,22], yet has been seldom used in engineering to-date [23,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

Certifiable Risk-Based Engineering Design Optimization

Chaudhuri¹,

Kramer²,

Norton³

et al. 2021

Preprint

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Reliable, risk-averse design of complex engineering systems with optimized performance requires dealing with uncertainties. A conventional approach is to add safety margins to a design that was obtained from deterministic optimization. Safer engineering designs require appropriate cost and constraint function definitions that capture the risk associated with unwanted system behavior in the presence of uncertainties. The paper proposes two notions of certifiability. The first is based on accounting for the magnitude of failure to ensure data-informed conservativeness. The second is the ability to provide optimization convergence guarantees by preserving convexity. Satisfying these notions leads to certifiable risk-based design optimization (CRiBDO). In the context of CRiBDO, risk measures based on superquantile (a.k.a. conditional value-at-risk) and buffered probability of failure are analyzed. CRiBDO is contrasted with reliability-based design optimization (RBDO), where uncertainties are accounted for via the probability of failure, through a structural and a thermal design problem. A reformulation of the short column structural design problem leading to a convex CRiBDO problem is presented. The CRiBDO formulations capture more information about the problem to assign the appropriate conservativeness, exhibit superior optimization convergence by preserving properties of underlying functions, and alleviate the adverse effects of choosing hard failure thresholds required in RBDO.

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Conditional-Value-at-Risk Estimation via Reduced-Order Models

Cited by 25 publications

References 14 publications

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Modern Monte Carlo methods for efficient uncertainty quantification and propagation: A survey

Modern Monte Carlo Methods for Efficient Uncertainty Quantification and Propagation: A Survey

Certifiable Risk-Based Engineering Design Optimization

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