A Multifidelity Gradient-Free Optimization Method and Application to Aerodynamic Design

Rajnarayan, Dev; Haas, Alex; Kroo, Ilan

doi:10.2514/6.2008-6020

Cited by 39 publications

(19 citation statements)

References 16 publications

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“…For such problems, 'multifidelity correction' methods have been developed, primarily in the optimization context. These techniques model the mapping µ → δ s using a data-fit surrogate; they either enforce 'global' zeroth-order consistency between the corrected surrogate prediction and the high-fidelity prediction at training points [23,29,33,39,35], or 'local' first-or second-order consistency at trust-region centers [2,19]. Such approaches tend to work well when the surrogate-model error exhibits a lower variance than the high-fidelity response [35] and the input-space dimension is small.Reduced-order models (ROMs) employ a projection process to reduce the state-space dimensionality of the high-fidelity computational model.…”

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confidence: 99%

The ROMES Method for Statistical Modeling of Reduced-Order-Model Error

Drohmann¹,

Carlberg²

2015

SIAM/ASA J. Uncertainty Quantification

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Abstract. This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive 'error indicators' to a distribution over the true error. The variance of this distribution can be interpreted as the (epistemic) uncertainty introduced by the reduced-order model. To model normed errors, the method employs existing rigorous error bounds and residual norms as indicators; numerical experiments show that the method leads to a near-optimal expected effectivity in contrast to typical error bounds. To model errors in general outputs, the method uses dual-weighted residuals-which are amenable to uncertainty control-as indicators. Experiments illustrate that correcting the reduced-order-model output with this surrogate can improve prediction accuracy by an order of magnitude; this contrasts with existing 'multifidelity correction' approaches, which often fail for reduced-order models and suffer from the curse of dimensionality. The proposed error surrogates also lead to a notion of 'probabilistic rigor', i.e., the surrogate bounds the error with specified probability.Primary 65G99, Secondary 65Y20, 62M86

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mentioning

confidence: 99%

The ROMES Method for Statistical Modeling of Reduced-Order-Model Error

Drohmann¹,

Carlberg²

2015

SIAM/ASA J. Uncertainty Quantification

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“…Instead, we could construct a parametric model that approximates f hi but is inexpensive to compute. Such a surrogate model can decomposition methods with deep corrections for reinforcement learning 7 represent the difference between the high-fidelity and the low-fidelity models [12], [21]:…”

Section: Policy Correctionmentioning

confidence: 99%

Decomposition methods with deep corrections for reinforcement learning

Bouton

Julian

Nakhaei

et al. 2019

Auton Agent Multi-Agent Syst

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Decomposition methods have been proposed to approximate solutions to large sequential decision making problems. In contexts where an agent interacts with multiple entities, utility decomposition can be used to separate the global objective into local tasks considering each individual entity independently. An arbitrator is then responsible for combining the individual utilities and selecting an action in real time to solve the global problem. Although these techniques can perform well empirically, they rely on strong assumptions of independence between the local tasks and sacrifice the optimality of the global solution. This paper proposes an approach that improves upon such approximate solutions by learning a correction term represented by a neural network. We demonstrate this approach on a fisheries management problem where multiple boats must coordinate to maximize their catch over time as well as on a pedestrian avoidance problem for autonomous driving. In each problem, decomposition methods can scale to multiple boats or pedestrians by using strategies involving one entity. We verify empirically that the proposed correction method significantly improves the decomposition method and outperforms a policy trained on the full scale problem without utility decomposition. decomposition methods with deep corrections for reinforcement learning 2 bined in real-time through an arbitrator that maximizes the expected utility [22]. Applications to aircraft collision avoidance with multiple intruders explore summing or using the minimum state-action values [7], [20]. While these approaches tend to perform well empirically, they sacrifice optimality. The solution to each subproblem assumes that its individual policy will be followed regardless of other entities, in contrast to the global policy considering all subproblems [23].Previous approaches to scale decision algorithms using decomposition methods relied on a distributed agent architecture [22]. Each agent is responsible for addressing one of the multiple objectives required to achieve a complex task. At each time step an arbitrator must decide between the different actions recommended by these agents and address possible conflicts. Possible arbitration strategies are command fusion [7], voting [22], lexicographic ordering [33] or utility fusion [22], [23]. It has been shown that utility fusion offers a more principled way of deciding between the individual agents compared to a voting-based approach or command fusion [22]. An alternative approach in leader follower scenarios consists of reducing the problem of controlling the group of agent to controlling a single group leader [15]. Other approaches rely on distributed learning algorithms, such as independent Q-learning, where each agent learns a policy without being aware of the other agents actions [28]. The underlying assumption of independence between agents in these algorithms trades off the benefit of collaboration for an easier learning of the task [8].Utility decomposition methods have been used in many practic...

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“…1 This may provide an advantage over single-fidelity pattern-search and simplex methods, especially when the dimension of the design space is large. For example, constraint-handling approaches used in conjunction with Efficient Global Optimization (EGO) (Jones et al 1998) either estimate the probability that a point is both a minimum and that it is feasible, or add a smooth penalty to the surrogate model prior to using optimization to select new high-fidelity sample locations (Sasena et al 2002;Jones 2001;Rajnarayan et al 2008). These heuristic approaches may work well in practice, but unfortunately have no guarantee of convergence to a minimum of the high-fidelity design problem.…”

Section: Introductionmentioning

confidence: 99%

Constrained multifidelity optimization using model calibration

March

Willcox

2012

Struct Multidisc Optim

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Multifidelity optimization approaches seek to bring higher-fidelity analyses earlier into the design process by using performance estimates from lower-fidelity models to accelerate convergence towards the optimum of a highfidelity design problem. Current multifidelity optimization methods generally fall into two broad categories: provably convergent methods that use either the high-fidelity gradient or a high-fidelity pattern-search, and heuristic model calibration approaches, such as interpolating high-fidelity data or adding a Kriging error model to a lower-fidelity function. This paper presents a multifidelity optimization method that bridges these two ideas; our method iteratively calibrates lower-fidelity information to the high-fidelity function in order to find an optimum of the high-fidelity design problem. The algorithm developed minimizes a high-fidelity objective function subject to a high-fidelity constraint and other simple constraints. The algorithm never computes the gradient of a high-fidelity function; however, it achieves first-order optimality using sensitivity information from the calibrated low-fidelity models, which are constructed to have negligible error in a neighborhood around the solution. The method is demonstrated for aerodynamic shape optimization and shows at least an 80% reduction in the number of high-fidelity analyses compared other single-fidelity A version of this paper was presented as paper AIAA-2010-9198 at the 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Fort Worth, TX, 13-15 September 2010.derivative-free and sequential quadratic programming methods. The method uses approximately the same number of high-fidelity analyses as a multifidelity trust-region algorithm that estimates the high-fidelity gradient using finite differences.

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A Multifidelity Gradient-Free Optimization Method and Application to Aerodynamic Design

Cited by 39 publications

References 16 publications

The ROMES Method for Statistical Modeling of Reduced-Order-Model Error

The ROMES Method for Statistical Modeling of Reduced-Order-Model Error

Decomposition methods with deep corrections for reinforcement learning

Constrained multifidelity optimization using model calibration

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