A Strategy for Adaptive Sampling of Multi-Fidelity Gaussian Processes to Reduce Predictive Uncertainty

Ghosh, Sayan; Kristensen, Jesper; Zhang, Yiming; Subber, Waad; Wang, Liping

doi:10.1115/detc2019-98418

Cited by 15 publications

(9 citation statements)

References 29 publications

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“…Recommendations for new designs to be evaluated are obtained by optimizing some criterion (defined over the design space) that maximizes the information that can be gained about the function. Several criteria have been proposed and assessed for use in closed-loop settings [27][28][29]. In this paper, the maximum variance design [27] criterion is maximized over the design space in order to guide the search.…”

Section: Adaptive Sampling For the Canonical Engineering Problemmentioning

confidence: 99%

Empirical Assessment of Deep Gaussian Process Surrogate Models for Engineering Problems

Rajaram¹,

Puranik²,

Renganathan

et al. 2021

Journal of Aircraft

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In recent years, multi-layered hierarchical compositions of the well-known and widely used Gaussian process models called deep Gaussian processes are finding use in the approximation of black-box functions. In this paper, the performance of deep Gaussian process models is empirically evaluated and compared against the well-established Gaussian process models with a special emphasis on engineering problems. The work draws conclusions through detailed comparisons in terms of metrics such as computational training cost, data requirement, predictive error, and robustness to the choice of the initial design of experiments. Additionally, the viability and robustness of Deep Gaussian process models for applications on practical engineering problems are analyzed through sensitivity to hyperparameters and scalability with respect to the input space dimensionality respectively. Finally, the models are also compared in an adaptive construction setting, where they are built sequentially by selecting points that maximize posterior variance. Experiments are conducted on canonical test functions with varying input dimensions, an engineering test function, and a practical transonic airfoil test case with a high-dimensional input space. The experiments suggest that deep Gaussian process models outperform traditional Gaussian process models in terms of accuracy at the cost of incurring a significantly higher computational expense for the training procedure. The sensitivity studies indicate that inducing points is the most important hyperparameter that affects deep Gaussian process performance and training time. This work empirically shows that deep Gaussian processes are promising candidates for problems that are known to be nonlinear, high-dimensional, and when limited training data is available.

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Section: Adaptive Sampling For the Canonical Engineering Problemmentioning

confidence: 99%

Empirical Assessment of Deep Gaussian Process Surrogate Models for Engineering Problems

Rajaram¹,

Puranik²,

Renganathan

et al. 2021

Journal of Aircraft

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“…In the forward modeling step, a probabilistic multi-fidelity Gaussian Process (MFGP) regression model for the expensive experiments is constructed using the GE Bayesian Hybrid Modeling (GEBHM) [24,25]. To reduce the cost associated with the design of the computer experiments [26,27,28,29,30] required by the GEBHM, a multi-fidelity adaptive sampling [26] is used to adaptively determine the experiment and level of fidelity that are needed to enhance the performance. The data generated in step 1 using the surrogate of the forward model (MFGP) will be used to train the cINN in step 2.…”

Section: Pmi Frameworkmentioning

confidence: 99%

“…In this work, we used multi-fidelity adaptive sampling [26] to pick designs and fidelity of CFD simulations to create the DOE for MFGP training. The new designs of the DOE are adaptively picked based on the cost ratio as well as the amount of uncertainty reduction associated with high and low fidelity simulations.…”

Section: Forward Modelingmentioning

confidence: 99%

Inverse Aerodynamic Design of Gas Turbine Blades using Probabilistic Machine Learning

Ghosh¹,

Padmanabha²,

Cheng³

et al. 2021

Preprint

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One of the critical components in Industrial Gas Turbines (IGT) is the turbine blade. Design of turbine blades needs to consider multiple aspects like aerodynamic efficiency, durability, safety and manufacturing, which make the design process sequential and iterative. The sequential nature of these iterations forces a long design cycle time, ranging from several months to years. Due to the reactionary nature of these iterations, little effort has been made to accumulate data in a manner that allows for deep exploration and understanding of the total design space. This is exemplified in the process of designing the individual components of the IGT resulting in a potential unrealized efficiency. To overcome the aforementioned challenges, we demonstrate a probabilistic inverse design machine learning framework (PMI), to carry out an explicit inverse design. PMI calculates the design explicitly without excessive costly iteration and overcomes the challenges associated with ill-posed inverse problems. In this work, the framework will be demonstrated on inverse aerodynamic design of three-dimensional turbine blades.

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“…A lot of exciting opportunities exist for GEBHM and GE-IDACE to further improve the engineering design process and remain to be discovered. In recent work, we demonstrate how to use GE-IDACE with multi-fidelity data sources (simulation vs. experiments, e.g.,) [52] and how to leverage legacy data from other designs into the GEBHM modeling process [11], to reduce the cost of running tests for new engine designs. In terms of future work, GEBHM can be extended to operate fluently across any type of data in terms of dimensionality and number of points.…”

Section: Summary and Future Workmentioning

confidence: 99%

Industrial Applications of Intelligent Adaptive Sampling Methods for Multi-Objective Optimization

Kristensen¹,

Subber²,

Zhang³

et al. 2020

Design and Manufacturing

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Multi-objective optimization is an essential component of nearly all engineering design. However, for industrial applications, the design process typically demands running expensive computer code and/or real-world experiments putting the design process at risk of finding suboptimal solutions and/or not meeting budget constraints. As a first step toward a remedy, meta-models are built to mimic the response surface at a much lower query cost. We cover a time-tested technology specifically tailored to limited-data scenarios called Bayesian hybrid modeling (GEBHM) developed and maintained at General Electric (GE) research. GEBHM offers Bayesian mean and principled uncertainty predictions allowing a second technology called intelligent design and analysis of experiments (GE-IDACE/ IDACE) to perform the optimization task using an adaptive sampling strategy. This chapter first covers the theoretical framework of both GEBHM and GE-IDACE. Then, the impact of GEBHM/GE-IDACE is demonstrated on multiple real-world engineering applications including additive manufacturing, combustion testing, and computational fluid dynamic design modeling. GEBHM and GE-IDACE are used daily and extensively within GE with huge impact in the form of 30-90% cost reduction and superior engineering designs of competitive products.

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A Strategy for Adaptive Sampling of Multi-Fidelity Gaussian Processes to Reduce Predictive Uncertainty

Cited by 15 publications

References 29 publications

Empirical Assessment of Deep Gaussian Process Surrogate Models for Engineering Problems

Empirical Assessment of Deep Gaussian Process Surrogate Models for Engineering Problems

Inverse Aerodynamic Design of Gas Turbine Blades using Probabilistic Machine Learning

Industrial Applications of Intelligent Adaptive Sampling Methods for Multi-Objective Optimization

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