Remarks for Scaling Up a General Gaussian Process to Model Large Dataset with Sub-models

Zhang, Yiming; Ghosh, Sayan; Pandita, Piyush; Subber, Waad; Khan, Genghis; Wang, Liping

doi:10.2514/6.2020-0678

Cited by 11 publications

(9 citation statements)

References 21 publications

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“…as any conditional of a Gaussian distribution is also Gaussian 2 . Denote µ(x), σ 2 (x), and θ as the posterior mean, the posterior variance, and the hyper-parameters of the objective GP model, respectively.…”

Section: Classical Gaussian Process and Bayesian Optimizationmentioning

confidence: 99%

“…Bostanabad et al [1] proposed a globally approximate local GP (GAGP) and demonstrated up to ∼90k data points. Zhang et al [2] proposed a locally weighted scheme, similarly to van Stein et al [3,4], where the weights are derived by minimizing the weighted posterior variance, and demonstrate to 100k data points. Tran et al [5,6] proposed a local GP approach with Wasserstein distance to model the potential energy surface and mixedinteger BO problems [7].…”

Section: Introductionmentioning

confidence: 99%

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Scalable3-BO: Big Data meets HPC - A scalable asynchronous parallel high-dimensional Bayesian optimization framework on supercomputers

Tran¹

2021

Preprint

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Bayesian optimization (BO) is a flexible and powerful framework that is suitable for computationally expensive simulation-based applications and guarantees statistical convergence to the global optimum. While remaining as one of the most popular optimization methods, its capability is hindered by the size of data, the dimensionality of the considered problem, and the nature of sequential optimization. These scalability issues are intertwined with each other and must be tackled simultaneously. In this work, we propose the Scalable 3 -BO framework, which employs sparse GP as the underlying surrogate model to scope with Big Data and is equipped with a random embedding to efficiently optimize high-dimensional problems with low effective dimensionality. The Scalable 3 -BO framework is further leveraged with asynchronous parallelization feature, which fully exploits the computational resource on HPC within a computational budget. As a result, the proposed Scalable 3 -BO framework is scalable in three independent perspectives: with respect to data size, dimensionality, and computational resource on HPC. The goal of this work is to push the frontiers of BO beyond its well-known scalability issues and minimize the wall-clock waiting time for optimizing high-dimensional computationally expensive applications. We demonstrate the capability of Scalable 3 -BO with 1 million data points, 10,000-dimensional problems, with 20 concurrent workers in an HPC environment.

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Section: Classical Gaussian Process and Bayesian Optimizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scalable3-BO: Big Data meets HPC - A scalable asynchronous parallel high-dimensional Bayesian optimization framework on supercomputers

Tran¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Once the surrogate is constructed, Sobol decomposition provides the sensitivity indices [16]. We use the Bayesian Hybrid Modeling (GEBHM) approach [50,51], a probabilistic machine learning method that enables SA, calibration, multifidelity modeling and uncertainty quantification.…”

Section: Sensitivity Analysis Of the Model Parametersmentioning

confidence: 99%

A two-mechanism and multiscale compatible approach for solid state electrolytes of (Li-ion) batteries

Cabras,

Danilov,

Subber

et al. 2021

Preprint

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All solid state batteries are claimed to be the next-generation battery system, in view of their safety accompanied by high energy densities. A new advanced, multiscale compatible, and fully three dimensional model for solid electrolytes is presented in this note. The response of the electrolyte is profoundly studied theoretically and numerically, analyzing the equilibrium and steady state behaviors, the limiting factors, as well as the most relevant constitutive parameters according to the sensitivity analysis of the model.

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“…22, the size of the data may grow exponentially demanding large computational budged. In this case a scaleable framework for the GP regression of large dataset can be exploited to efficiently address the computational cost [20].…”

Section: Surrogate Modelingmentioning

confidence: 99%

Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

Subber¹,

Ghosh²,

Pandita³

et al. 2020

Preprint

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Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem

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Remarks for Scaling Up a General Gaussian Process to Model Large Dataset with Sub-models

Cited by 11 publications

References 21 publications

Scalable3-BO: Big Data meets HPC - A scalable asynchronous parallel high-dimensional Bayesian optimization framework on supercomputers

Scalable3-BO: Big Data meets HPC - A scalable asynchronous parallel high-dimensional Bayesian optimization framework on supercomputers

A two-mechanism and multiscale compatible approach for solid state electrolytes of (Li-ion) batteries

Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systems

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