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Data Driven Computing with Noisy Material Data Sets

Kirchdoerfer, T. and Ortiz, M. (2017) Data Driven Computing with Noisy Material Data Sets. Computer Methods in Applied Mechanics and Engineering, 326 . pp. 622-641. ISSN 0045-7825. http://resolver.caltech.edu/CaltechAUTHORS:20170612-102809775

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Abstract

We formulate a Data Driven Computing paradigm, termed max-ent Data Driven Computing, that generalizes distance-minimizing Data Driven Computing and is robust with respect to outliers. Robustness is achieved by means of clustering analysis. Specifically, we assign data points a variable relevance depending on distance to the solution and on maximum-entropy estimation. The resulting scheme consists of the minimization of a suitably-defined free energy over phase space subject to compatibility and equilibrium constraints. Distance-minimizing Data Driven schemes are recovered in the limit of zero temperature. We present selected numerical tests that establish the convergence properties of the max-ent Data Driven solvers and solutions.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.cma.2017.07.039DOIArticle
http://www.sciencedirect.com/science/article/pii/S0045782517304012PublisherArticle
https://arxiv.org/abs/1702.01574arXivDiscussion Paper
Additional Information:© 2017 Elsevier B.V. Received 3 March 2017, Revised 17 May 2017, Accepted 27 July 2017, Available online 24 August 2017. The support of Caltech’s Center of Excellence on High-Rate Deformation Physics of Heterogeneous Materials, AFOSR Award FA9550-12-1-0091, is gratefully acknowledged. We gratefully acknowledge helpful discussions with H. Owhadi and T. J. Sullivan.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)FA9550-12-1-0091
Subject Keywords:Data science; Big data; Approximation theory; Scientific computing
Record Number:CaltechAUTHORS:20170612-102809775
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170612-102809775
Official Citation:T. Kirchdoerfer, M. Ortiz, Data Driven Computing with noisy material data sets, In Computer Methods in Applied Mechanics and Engineering, Volume 326, 2017, Pages 622-641, ISSN 0045-7825, https://doi.org/10.1016/j.cma.2017.07.039. (http://www.sciencedirect.com/science/article/pii/S0045782517304012)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78100
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Jun 2017 18:26
Last Modified:29 May 2018 16:31

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