Surrogate-based sequential Bayesian experimental design using non-stationary Gaussian Processes

Pandita, Piyush; Tsilifis, Panagiotis; Awalgaonkar, Nimish M.; Bilionis, Ilias; Panchal, Jitesh H.

doi:10.1016/j.cma.2021.114007

Cited by 16 publications

(9 citation statements)

References 33 publications

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“…The EIG has been estimated by particle filters (Cavagnaro et al, 2010), sequential Monte Carlo (Drovandi et al, 2014;Moffat et al, 2020), nested Monte Carlo (Myung et al, 2013), multilevel Monte Carlo (Goda et al, 2020), Markov Chain Monte Carlo (Müller et al, 2004), ratio estimation (Kleinegesse & Gutmann, 2019), variational bounds (Foster et al, 2019;2020), Laplace importance sampling (Beck et al, 2018) and more. Methods for specific models have been developed that exploit unique properties, such as in the case of linear models (Verdinelli, 1996), Gaussian Process models (Pandita et al, 2021), and polynomial models (Rainforth et al, 2018).…”

Section: Related Workmentioning

confidence: 99%

Optimizing Sequential Experimental Design with Deep Reinforcement Learning

Blau¹,

Bonilla²,

Dezfouli³

et al. 2022

Preprint

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Bayesian approaches developed to solve the optimal design of sequential experiments are mathematically elegant but computationally challenging. Recently, techniques using amortization have been proposed to make these Bayesian approaches practical, by training a parameterized policy that proposes designs efficiently at deployment time. However, these methods may not sufficiently explore the design space, require access to a differentiable probabilistic model and can only optimize over continuous design spaces. Here, we address these limitations by showing that the problem of optimizing policies can be reduced to solving a Markov decision process (MDP). We solve the equivalent MDP with modern deep reinforcement learning techniques. Our experiments show that our approach is also computationally efficient at deployment time and exhibits state-of-the-art performance on both continuous and discrete design spaces, even when the probabilistic model is a black box.

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Section: Related Workmentioning

confidence: 99%

Optimizing Sequential Experimental Design with Deep Reinforcement Learning

Blau¹,

Bonilla²,

Dezfouli³

et al. 2022

Preprint

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“…This acquisition function is informed using a surrogate model [16,18] that is trained on the sparse initial dataset [19,25,26]. Prior studies have used various acquisition functions including predictive uncertainty, expected improvement [27,28], and expected information gain [20,25,29]. While the utility of AL has been shown, limited prior work has incorporated AL in a stratified manner to address problems with environment and geometric variations.…”

Section: Introductionmentioning

confidence: 99%

“…The additional datapoints are selected by maximizing an acquisition function [17,24]. This acquisition function is informed using a surrogate model [16,18] that is trained on the sparse initial dataset [19,25,26]. Prior studies have used various acquisition functions including predictive uncertainty, expected improvement [27,28], and expected information gain [20,25,29].…”

Section: Introductionmentioning

confidence: 99%

An Active Learning Framework for the Rapid Assessment of Galvanic Corrosion

Zapiain,

Venkatraman,

Katona

et al. 2024

Preprint

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The current present in a galvanic couple can define its resistance or susceptibility to corrosion. However, as the current is dependent upon environmental, material, and geometrical parameters it is experimentally costly to measure. To reduce these costs, Finite Element (FE) simulations can be used to assess the cathodic current but also require experimental inputs to define boundary conditions. Due to these challenges, it is crucial to accelerate predictions and accurately pre- dict the current output for different environments and geometries representative of in-service conditions. Machine learned surrogate models provides a means to accelerate corrosion predictions. However, a one-time cost is incurred in procur- ing the simulation and experimental dataset necessary to calibrate the surrogate model. Therefore, an active learning protocol is developed through calibration of a low-cost surrogate model for the cathodic current of an exemplar galvanic cou- ple (AA7075-SS304) as a function of environmental and geometric parameters. The surrogate model is calibrated on a dataset of FE simulations, and calculates an acquisition function that identifies specific additional inputs with the maxi- mum potential to improve the current predictions. This is accomplished through a staggered workflow that not only improves and refines prediction, but identifies the points at which the most information is gained, thus enabling expansion to a larger parameter space. The protocols developed and demonstrated in this work provide a powerful tool for screening various forms of corrosion under in-service conditions.

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“…Therefore, in such scenarios, the rational choice is to construct computationally efficient surrogate models (SM) which could then be queried instead of the original simulator using sampling methods such as the MC method for completing UQ tasks. Further, some of the notable approaches for surrogate constructions in the literature include polynomial chaos expansion, [5][6][7] Gaussian processes, [8][9][10][11] variance decomposition analysis 12,13 and its variants, 14 support vector machines, 15 and deep neural networks. [16][17][18][19][20] The disadvantage of most of these surrogate-modeling approaches barring deep neural networks is their intractability when the dimensionality of the problem at hand becomes high.…”

Section: Introductionmentioning

confidence: 99%

Deep capsule encoder–decoder network for surrogate modeling and uncertainty quantification

Thakur

Chakraborty

2023

Numerical Meth Engineering

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We propose a novel capsule-based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet) architecture into an image-to-image regression encoder-decoder network. Specifically, the aim is to exploit the benefits of CapsNet over convolution neural network (CNN) -retaining pose and position information related to an entity to name a few. The performance of the proposed approach is illustrated by solving two different variants of elliptic partial differential equations (PDE): a stochastic version without a source term having an input dimensionality of 1024 and a deterministic pressure Poisson equation for flow past a cylinder. The first PDE, that is, the stochastic PDE (SPDE), also governs systems in mechanics such as steady heat conduction, groundwater flow, or other diffusion processes. In this article, the problem definition for this SPDE is such that it does not restrict the random diffusion field to a particular covariance structure, and the more strenuous task of response prediction for an arbitrary diffusion field is solved. Finally, we also evaluate the performance of our model on the uncertainty propagation problem based on this equation. The obtained results from the performance evaluation of the developed model on the mentioned problems indicate that the proposed approach is accurate, data efficient, and robust.

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Surrogate-based sequential Bayesian experimental design using non-stationary Gaussian Processes

Cited by 16 publications

References 33 publications

Optimizing Sequential Experimental Design with Deep Reinforcement Learning

Optimizing Sequential Experimental Design with Deep Reinforcement Learning

An Active Learning Framework for the Rapid Assessment of Galvanic Corrosion

Deep capsule encoder–decoder network for surrogate modeling and uncertainty quantification

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