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Minimax Error of Interpolation and Optimal Design of Experiments for Variable Fidelity Data [article]

Alexey Zaytsev, Evgeny Burnaev
2017 arXiv   pre-print
Evaluation of the minimax errors allows us to identify cases when the variable fidelity data provides better interpolation accuracy than the exclusively high fidelity data for the same computational budget  ...  In this paper we obtain minimax interpolation errors for single and variable fidelity scenarios for a multivariate Gaussian process regression.  ...  This is the state-of-the-art cokriging approach used to model a variable fidelity data [17] .  ... 
arXiv:1610.06731v3 fatcat:eiclj7vhtnewxojqirgxdat7ku

Interpolation error of misspecified Gaussian process regression [article]

A. Zaytsev, E. Romanenkova, D. Ermilov
2018 arXiv   pre-print
Then we proceed to numerical experiments that consider the misspecification for the most common covariance functions including other Matern and squared exponential covariance functions.  ...  We derive the interpolation error for an infinite grid design of experiments.  ...  Minimax approach to variable fidelity data interpolation. In Artificial Intelligence and Statistics, pages 652-661, 2017. A. Zaytsev, E. Burnaev, and V. Spokoiny.  ... 
arXiv:1803.09479v1 fatcat:4pq3ioc2lngqfnddgvbvlcjife

Bayes estimator for multinomial parameters and Bhattacharyya distances [article]

Christopher Ferrie, Robin Blume-Kohout
2016 arXiv   pre-print
As an example application, we use our solution to find minimax estimators for a binomial parameter under Bhattacharyya loss (1-B^2).  ...  We formulate a non-commutative generalization relevant to quantum probability theory as an open problem.  ...  This is called the Bayes risk of the estimatorp with respect to µ: r p = E data [L(p,p(data)]. (2 r(p) = E p,data [L(p,p(data)]. (3) An estimatorp B that minimizes the Bayes risk is called a Bayes estimator  ... 
arXiv:1612.07946v1 fatcat:uezputdtpzg6firbhokbxadni4

Frame-constrained Total Variation Regularization for White Noise Regression [article]

Miguel del Álamo, Housen Li, Axel Munk
2019 arXiv   pre-print
Our results rely on a novel connection between frame-constraints and certain Besov norms, and on an interpolation inequality to relate them to the risk functional.  ...  While TV regularization has been known for quite some time to be minimax optimal for denoising one-dimensional signals, for higher dimensions this remains elusive until today.  ...  There are roughly two approaches to deal with this: either employ a finer data-fidelity term, or discretize the problem.  ... 
arXiv:1807.02038v3 fatcat:jpc422npong5rdujvxgg32mpiu

Advanced RF and Microwave Design Optimization: A Journey and a Vision of Future Trends

Jose E. Rayas-Sanchez, Slawomir Koziel, John W. Bandler
2021 IEEE Journal of Microwaves  
To address these major challenges, we venture into the development of sophisticated optimization approaches, exploiting confined and dimensionally reduced surrogate vehicles, automated feature-engineering-based  ...  ; and 3) the manufacturability assessment, statistical design, and yield optimization of high-frequency structures based on high-fidelity multi-physical representations.  ...  The framework employs initial parameter space reduction, variable-fidelity simulation models, and design refinement scheme required to bring the Pareto-optimal designs to the high-fidelity level of accuracy  ... 
doi:10.1109/jmw.2020.3034263 fatcat:a64hobxhfzhe3f2stmhkewvgca

Metamodeling techniques for CPU-intensive simulation-based design optimization: a survey

Hanane Khatouri, Tariq Benamara, Piotr Breitkopf, Jean Demange
2022 Advanced Modeling and Simulation in Engineering Sciences  
Thus, the concept of multi-fidelity proposes to merge different levels of fidelity within a single model with controlled variance.  ...  Both approaches: multi-fidelity and ROM, may be combined, allowing for additional flexibility in choosing the degree of fidelity required in different zones of the design space.  ...  Acknowledgements The authors would like to thank Cenaero and Safran Aircraft Engines for their support and permission to publish this study, as well as Cenaero and the university of Technology of Compiegne  ... 
doi:10.1186/s40323-022-00214-y fatcat:4n7uucw445b5vcalrrxcrcwctq

Simulation-Driven Design of Antennas Using Coarse-Discretization Electromagnetic Models

Slawomir Koziel, Stanislav Ogurtsova, Leifur Leifssona
2011 Procedia Computer Science  
The specific approaches presented here include multi-fidelity optimization, adaptive design specifications and space mapping with kriging-based coarse models. Application examples are given.  ...  For many structures, including ultrawideband or dielectric resonator antennas, EM-simulation-driven optimization is the only way to adjust the geometry parameters so that given performance specifications  ...  The last methodology exploits space mapping as the optimization engine with the underlying coarse model created by kriging interpolation of the coarse-discretization EM simulation data [20] .  ... 
doi:10.1016/j.procs.2011.04.135 fatcat:gvopncysrfadvou4pxjcmrlahe

Reduced-cost microwave filter modeling using a two-stage Gaussian process regression approach

Jan Pieter Jacobs, Slawomir Koziel
2014 International Journal of RF and Microwave Computer-Aided Engineering  
Our approach exploits variable-fidelity electromagnetic (EM) simulations, and Gaussian process regression (GPR) carried out in two stages.  ...  The mapping is subsequently used in the second stage, making it possible for the final surrogate model to be constructed from training data obtained using only a fraction of the number of high-fidelity  ...  To address this problem, we adopt a two-stage modeling approach.  ... 
doi:10.1002/mmce.20880 fatcat:vdayfkghtzanxezfe4zyn4joru

Active learning for adaptive mobile sensing networks

A. Singh, R. Nowak, P. Ramanathan
2006 2006 5th International Conference on Information Processing in Sensor Networks  
Alternatively, one can envision sequential, adaptive data collection procedures that use information gleaned from previous observations to guide the process.  ...  Traditional sampling theory deals with data collection processes that are completely independent of the target map to be estimated, aside from possible a priori specifications reflective of assumed properties  ...  ACKNOWLEDGMENT The authors would like to thank Rui Castro for his helpful remarks and Rebecca Willett for providing the pruned RDP estimator code.  ... 
doi:10.1109/ipsn.2006.244057 fatcat:r2d3ddhhyvhrfnkvk65vsibhom

The p-AAA algorithm for data driven modeling of parametric dynamical systems [article]

Andrea Carracedo Rodriguez, Serkan Gugercin
2020 arXiv   pre-print
We discuss an extension to the case of matrix-valued functions, i.e., multi-input/multi-output dynamical systems, and provide a connection to the tangential interpolation theory.  ...  The method is data-driven, in the sense that it does not require access to full state-space data and requires only function evaluations.  ...  As in the two-variable case, β ij will be chosen to enforce interpolation in a subset of the data and α ij to minimize a linearized LS error in the remaining data.  ... 
arXiv:2003.06536v2 fatcat:cbfhhmjl7ra5zbl6jkocufokxy

Shape-Preserving Response Prediction for Surrogate Modeling and Engineering Design Optimization [chapter]

Slawomir Koziel, Leifur Leifsson
2014 Solving Computationally Expensive Engineering Problems  
Here the surrogate is created by approximating sampled high-fidelity model data and the most popular methods include polynomial approximation [5], radial basis function interpolation [6], kriging [7],  ...  Correcting an auxiliary low-fidelity (or coarse) model is another approach to SBO. A low-fidelity model is a reduced-accuracy but faster representation of the system of interest.  ...  It can be seen that both approaches are able to meet the design goals and produce similar optimized airfoil shapes. The direct approach requires 120 high-fidelity model evaluations (N f ).  ... 
doi:10.1007/978-3-319-08985-0_2 fatcat:4ey5b4kavnht7fm3bzhzgl2fue

Variable-Fidelity Simulation Models and Sparse Gradient Updates for Cost-Efficient Optimization of Compact Antenna Input Characteristics

Slawomir Koziel, Anna Pietrenko-Dabrowska
2019 Sensors  
Our methodology involves variable-fidelity EM simulations as well as a dedicated procedure to reduce the cost of estimating the antenna response gradients.  ...  Conventional optimization procedures are typically too expensive when the antenna is evaluated using high-fidelity electromagnetic (EM) analysis, otherwise required to ensure accuracy.  ...  The funders had no role in the design of the study, in the collection, analyses, or interpretation of data, in the writing of the manuscript, or in the decision to publish the results.  ... 
doi:10.3390/s19081806 fatcat:i5i6kuz7arhpxpc277t45tym2m

Physics-aware Deep Generative Models for Creating Synthetic Microstructures [article]

Rahul Singh, Viraj Shah, Balaji Pokuri, Soumik Sarkar, Baskar Ganapathysubramanian, Chinmay Hegde
2018 arXiv   pre-print
The trained models also exhibit interesting latent variable interpolation behavior, and the results indicate considerable promise for enforcing user-defined physics constraints during microstructure synthesis  ...  Our third model combines the first two models to reconstruct microstructures that respect both explicit physics invariances as well as implicit constraints learned from the image data.  ...  Figure 4 :Figure 5 : 45 (a) Results of the linear interpolation over latent variable z for WGAN-GP trained over the entire CH dataset (a) Results of the linear interpolation over latent variable z for  ... 
arXiv:1811.09669v1 fatcat:ydoevxvrungrlcbzkdwds2yzt4

RELIABLE SIMULATION-DRIVEN DESIGN OPTIMIZATION OF MICROWAVE STRUCTURES USING MANIFOLD MAPPING

Slawomir Koziel, David Echeverría Ciaurri
2010 Progress in Electromagnetics Research B  
Also, manifold mapping does not use any extractable parameters, which makes it easy to implement.  ...  The parameters of the manifold mapping surrogate are explicitly calculated based on the fine model data accumulated during the optimization process.  ...  ., |S 21 | evaluated at m different frequencies), x ∈ R n be a vector of design variables (e.g., structure dimensions), and U be a given objective function, e.g., minimax.  ... 
doi:10.2528/pierb10090202 fatcat:4ovbeg6265gbvb3n2b7nxhutou

Optimal estimation of the mean function based on discretely sampled functional data: Phase transition

T. Tony Cai, Ming Yuan
2011 Annals of Statistics  
The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis.  ...  Minimax rates of convergence are established and easily implementable rate-optimal estimators are introduced.  ...  We thank an Associate Editor and two referees for their constructive comments which have helped to improve the presentation of the paper.  ... 
doi:10.1214/11-aos898 fatcat:gstlwko5v5flxgek7f72lcw27q
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