Strategies for Multifidelity Optimization with Variable Dimensional Hierarchical Models

Robinson, Trevor; Eldred, Michael; Willcox, Karen; Haimes, Robert

doi:10.2514/6.2006-1819

Cited by 44 publications

(39 citation statements)

References 8 publications

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“…Such a strategy can be deemed analogous to the strategy for hydrologic model calibration which identifies and solely relies on a representative short data period. There are some other studies addressing the discrepancies between surrogate and original models [e.g., Bandler et al, 2004;Cui et al, 2011;Forrester et al, 2007;Robinson et al, 2006]. Similar to the proposed framework, these studies develop strategies to predict the response (e.g., a performance metric) of a high-fidelity model as a function of parameter values and the corresponding response of a surrogate model.…”

Section: Relations To Surrogate Modelingmentioning

confidence: 99%

An efficient framework for hydrologic model calibration on long data periods

Razavi

Tolson

2013

Water Resour. Res.

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.[1] Long periods of hydrologic data records have become available in many watersheds around the globe. Hydrologic model calibration on such long, full-length data periods is typically deemed the most robust approach for calibration but at larger computational costs. Determination of a representative short period as a ''surrogate'' of a long data period that sufficiently embeds its information content is not trivial and is a challenging research question. The representativeness of such a short period is not only a function of data characteristics but also model and calibration error function dependent. Unlike previous studies, this study goes beyond identifying the best surrogate data period to be used in model calibration and proposes an efficient framework that calibrates the hydrologic model to full-length data while running the model only on a short period for the majority of the candidate parameter sets. To this end, a mapping system is developed to approximate the model performance on the full-length data period based on the model performance for the short data period. The basic concepts and the promise of the framework are demonstrated through a computationally expensive hydrologic model case study. Three calibration approaches, namely calibration solely to a surrogate period, calibration to the full period, and calibration through the proposed framework, are evaluated and compared. Results show that within the same computational budget, the proposed framework leads to improved or equal calibration performance compared to the two conventional approaches. Results also indicate that model calibration solely to a short data period may lead to a range of performances from poor to very well depending on the representativeness of the short data period which is typically not known a priori.

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Section: Relations To Surrogate Modelingmentioning

confidence: 99%

An efficient framework for hydrologic model calibration on long data periods

Razavi

Tolson

2013

Water Resour. Res.

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“…In this case, the selection of the space mapping terms would be based on both past and runtime calculations, and the space mapping formulation would be improved at each run of the application. Another approach might include 1 st and 2 nd order corrective models in the mapping terms as done in [29]. Note that this would require intermittent calls to fixed patterns in order to calculate the derivate terms, and therefore, a more generic oracle implementation would be needed.…”

Section: Discussionmentioning

confidence: 99%

Developing a computationally efficient dynamic multilevel hybrid optimization scheme using multifidelity model interactions.

Hough

Gray

Castro

et al. 2006

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Many engineering application problems use optimization algorithms in conjunction with numerical simulators to search for solutions. The formulation of relevant objective functions and constraints dictate possible optimization algorithms. Often, a gradient based approach is not possible since objective functions and constraints can be nonlinear, nonconvex, non-differentiable, or even discontinuous and the simulations involved can be computationally expensive. Moreover, computational efficiency and accuracy are desirable and also influence the choice of solution method.With the advent and increasing availability of massively parallel computers, computational speed has increased tremendously. Unfortunately, the numerical and model complexities of many problems still demand significant computational resources. Moreover, in optimization, these expenses can be a limiting factor since obtaining solutions often requires the completion of numerous computationally intensive simulations. Therefore, we propose a multifidelity optimization algorithm (MFO) designed to improve the computational efficiency of an optimization method for a wide range of applications.In developing the MFO algorithm, we take advantage of the interactions between multifidelity models to develop a dynamic and computational time saving optimization algorithm. First, a direct search method is applied to the high fidelity model over a reduced design space. In conjunction with this search, a specialized oracle is employed to map the design space of this high fidelity model to that of a computationally cheaper low fidelity model using space mapping techniques. Then, in the low fidelity space, an optimum is obtained using gradient or non-gradient based optimization, and it is mapped back to the high fidelity space.In this paper, we describe the theory and implementation details of our MFO algorithm. We also demonstrate our MFO method on some example problems and on two applications: earth penetrators and groundwater remediation. 4 AcknowledgmentsThanks to Paul Demmie and Donald Longcope for valuable discussions and help with earth penetrator models used within this document. Thanks to Katherine Fowler for providing the groundwater remediation problem and promoting our optimization method to the groundwater community. Thanks to Mike Eldred for valuable discussions and suggestions about space mapping.5

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“…A simplified physics model, also known as a low-fidelity model, makes certain physical assumptions that significantly reduce the computational cost by eliminating complex equations and even the number of variables. Although several novel approaches exist in the literature for treating this class of surrogates (e.g., see [5] or [33]), the actual construction of the models is problem-dependent.…”

Section: Surrogate Functionsmentioning

confidence: 99%

An efficient class of direct search surrogate methods for solving expensive optimization problems with CPU-time-related functions

Abramson

Asaki

Dennis

et al. 2011

Struct Multidisc Optim

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In this paper, we characterize a new class of computationally expensive optimization problems and introduce an approach for solving them. In this class of problems, objective function values may be directly related to the computational time required to obtain them, so that, as the optimal solution is approached, the computational time required to evaluate the objective is significantly less than at points farther away from the solution. This is motivated by an application in which each objective function evaluation requires both a numerical fluid dynamics simulation and an image registration process, and the goal is to find the parameter values of a predetermined reference image by comparing the flow dynamics from the numerical simulation and the reference image through the image comparison process. In designing an approach to numerically solve the more general class of problems in an efficient way, we make use of surrogates based on CPU times of previously evaluated points, rather than their function values, all within the search step framework of mesh adaptive direct search algorithms. Because of the expected positive correlation between function values and their CPU times, a time cutoff parameter is added to the objective function evaluation to allow its termination during the comparison process if the computational time exceeds a specified threshold. The approach was tested using the NOMADm and DACE MATLAB software packages, and results are presented. *

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Strategies for Multifidelity Optimization with Variable Dimensional Hierarchical Models

Cited by 44 publications

References 8 publications

An efficient framework for hydrologic model calibration on long data periods

An efficient framework for hydrologic model calibration on long data periods

Developing a computationally efficient dynamic multilevel hybrid optimization scheme using multifidelity model interactions.

An efficient class of direct search surrogate methods for solving expensive optimization problems with CPU-time-related functions

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