Bayesian Optimization With Improved Scalability and Derivative Information for Efficient Design of Nanophotonic Structures

Garcia-Santiago, Xavier; Burger, Sven; Rockstuhl, Carsten; Schneider, Philipp‐Immanuel

doi:10.1109/jlt.2020.3023450

Cited by 19 publications

(13 citation statements)

References 51 publications

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“…. , l N are chosen to maximize the likelihood of the observations [33,34]. Afterwards, only µ 0 , σ 0 are optimized and the length scales l 1 , .…”

Section: Gaussian Process Regressionmentioning

confidence: 99%

“…Instead, one can compute its Cholesky decomposition K = L K L T K into a lower and upper triangular matrix in O(M 3 ) steps for M ≤ M hyper . For constant length scales (i.e., M > M hyper ) an update of the decomposition only requires O(M 2 ) steps [34]. Afterwards, one solves…”

Section: Gaussian Process Regressionmentioning

confidence: 99%

“…for α by forward and backward substitution and Training of GPs can be easily extended to exploit derivative information if available [34]. While this enlarges the number of data points and the size of the covariance matrix accordingly, all the above considerations are equally valid.…”

Section: Gaussian Process Regressionmentioning

confidence: 99%

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Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction

Plock,

Andrle,

Burger

et al. 2022

Preprint

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Parameter reconstructions are indispensable in metrology. Here, on wants to explain K experimental measurements by fitting to them a parameterized model of the measurement process. The model parameters are regularly determined by least-square methods, i.e., by minimizing the sum of the squared residuals between the K model predictions and the K experimental observations, χ 2 . The model functions often involve computationally demanding numerical simulations. Bayesian optimization methods are specifically suited for minimizing expensive model functions. However, in contrast to least-square methods such as the Levenberg-Marquardt algorithm, they only take the value of χ 2 into account, and neglect the K individual model outputs. We introduce a Bayesian targetvector optimization scheme that considers all K contributions of the model function and that is specifically suited for parameter reconstruction problems which are often based on hundreds of observations. Its performance is compared to established methods for an optical metrology reconstruction problem and two synthetic least-squares problems. The proposed method outperforms established optimization methods. It also enables to determine accurate uncertainty estimates with very few observations of the actual model function by using Markov chain Monte Carlo sampling on a trained surrogate model.

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“…. , l N are chosen to maximize the likelihood of the observations [33,34]. Afterwards, only µ 0 , σ 0 are optimized and the length scales l 1 , .…”

Section: Gaussian Process Regressionmentioning

confidence: 99%

Section: Gaussian Process Regressionmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction

Plock,

Andrle,

Burger

et al. 2022

Preprint

Self Cite

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“…In a way, meso scale design can be seen as a compromise that permits flexible variation of the properties of the material, whilst being very resource effective. In this approach, such ML techniques as Bayesian optimization or genetic algorithms can be used as efficient tools for exploring the structure-property space and for solving the inverse problem [65][66][67]. A particular problem that can be solved in this way is the determination of the limit values of material Figure 6.…”

Section: Architectured Lattice Materialsmentioning

confidence: 99%

Architecturing materials at mesoscale: some current trends

Estrin

Beygelzimer

Kulagin

et al. 2021

Materials Research Letters

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This article overviews several areas of research into architectured materials which, in the opinion of the authors, are most topical and promising. The classes of materials considered are based on meso scale designs inspired by animate and inanimate Nature, but also on those born in the minds of scientists and engineers, without any inspiration from Nature. We present the principles governing the design of the emerging materials architectures, discuss their explored and anticipated properties, and provide an outlook on their future developments and applications. IMPACT STATEMENTThe article addresses several hot topics with a great promise for innovative materials design.

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“…At each iteration, the surrogate is used to identify new trial model parameters that maximize for example the expected improvement or the probability of improvement. The approach offers a large degree of flexibility such that many extensions of BO have been proposed to cope, e.g., with a large number of model parameters, 8,9 a large number of observations, 10 or noisy model outputs. 11 Typically, BO methods are used to optimize scalar functions.…”

Section: Introductionmentioning

confidence: 99%

Recent advances in Bayesian optimization with applications to parameter reconstruction in optical nano-metrology

Plock,

Burger,

Schneider

2021

Preprint

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Parameter reconstruction is a common problem in optical nano metrology. It generally involves a set of measurements, to which one attempts to fit a numerical model of the measurement process. The model evaluation typically involves to solve Maxwell's equations and is thus time consuming. This makes the reconstruction computationally demanding. Several methods exist for fitting the model to the measurements. On the one hand, Bayesian optimization methods for expensive black-box optimization enable an efficient reconstruction by training a machine learning model of the squared sum of deviations χ 2 . On the other hand, curve fitting algorithms, such as the Levenberg-Marquardt method, take the deviations between all model outputs and corresponding measurement values into account which enables a fast local convergence. In this paper we present a Bayesian Target Vector Optimization scheme which combines these two approaches. We compare the performance of the presented method against a standard Levenberg-Marquardt-like algorithm, a conventional Bayesian optimization scheme, and the L-BFGS-B and Nelder-Mead simplex algorithms. As a stand-in for problems from nano metrology, we employ a non-linear least-square problem from the NIST Standard Reference Database. We find that the presented method generally uses fewer calls of the model function than any of the competing schemes to achieve similar reconstruction performance.

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Bayesian Optimization With Improved Scalability and Derivative Information for Efficient Design of Nanophotonic Structures

Cited by 19 publications

References 51 publications

Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction

Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction

Architecturing materials at mesoscale: some current trends

Recent advances in Bayesian optimization with applications to parameter reconstruction in optical nano-metrology

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