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A learning-based multiscale method and its application to inelastic impact problems

Liu, Burigede and Kovachki, Nikola and Li, Zongyi and Azizzadenesheli, Kamyar and Anandkumar, Anima and Stuart, Andrew M. and Bhattacharya, Kaushik (2022) A learning-based multiscale method and its application to inelastic impact problems. Journal of the Mechanics and Physics of Solids, 158 . Art. No. 104668. ISSN 0022-5096. doi:10.1016/j.jmps.2021.104668. https://resolver.caltech.edu/CaltechAUTHORS:20210225-132721680

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Abstract

The macroscopic properties of materials that we observe and exploit in engineering application result from complex interactions between physics at multiple length and time scales: electronic, atomistic, defects, domains etc. Multiscale modeling seeks to understand these interactions by exploiting the inherent hierarchy where the behavior at a coarser scale regulates and averages the behavior at a finer scale. This requires the repeated solution of computationally expensive finer-scale models, and often a priori knowledge of those aspects of the finer-scale behavior that affect the coarser scale (order parameters, state variables, descriptors, etc.). We address this challenge in a two-scale setting where we learn the fine-scale behavior from off-line calculations and then use the learnt behavior directly in coarse scale calculations. The approach builds on the recent success of deep neural networks by combining their approximation power in high dimensions with ideas from model reduction. It results in a neural network approximation that has high fidelity, is computationally inexpensive, is independent of the need for a priori knowledge, and can be used directly in the coarse scale calculations. We demonstrate the approach on problems involving the impact of magnesium, a promising light-weight structural and protective material.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jmps.2021.104668DOIArticle
https://arxiv.org/abs/2102.07256arXivDiscussion Paper
https://github.com/Burigede/Learning_based_multiscale.gitRelated ItemData and scripts
ORCID:
AuthorORCID
Liu, Burigede0000-0002-6518-3368
Kovachki, Nikola0000-0002-3650-2972
Azizzadenesheli, Kamyar0000-0001-8507-1868
Stuart, Andrew M.0000-0001-9091-7266
Bhattacharya, Kaushik0000-0003-2908-5469
Additional Information:© 2021 Elsevier Ltd. Received 11 June 2021, Revised 30 September 2021, Accepted 6 October 2021, Available online 22 October 2021. We are grateful to Dennis Kochmann for discussion and for providing us with the 2DFFT and the 3D Taylor code to generate the data. This research was sponsored by the Army Research Laboratory, United States and was accomplished under Cooperative Agreement Number W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. ZL is supported by the Kortschak Scholars Program. AA is supported in part by Bren endowed chair and De Logi grant. AMS is also partially supported by NSF, United States grant DMS-1818977. Data availability: The data and scripts needed to evaluate the conclusions of this paper are available in the GitHub repository “Learning based multiscale” (https://github.com/Burigede/Learning_based_multiscale.git). CRediT authorship contribution statement: Burigede Liu: Conceived the work, Developed the framework, Lead in implementing the framework, Obtaining the numerical results, Discussions during the course of this work and in interpreting the results, Lead in drafting the manuscript, Finalizing. Nikola Kovachki: Conceived the work, Developed the framework, Discussions during the course of this work and in interpreting the results, Finalizing. Zongyi Li: Discussions during the course of this work and in interpreting the results, Finalizing. Kamyar Azizzadenesheli: Discussions during the course of this work and in interpreting the results, Finalizing. Anima Anandkumar: Discussions during the course of this work and in interpreting the results, Finalizing. Andrew M. Stuart: Conceived the work, Developed the framework, Discussions during the course of this work and in interpreting the results, Finalizing. Kaushik Bhattacharya: Conceived the work, Developed the framework, Discussions during the course of this work and in interpreting the results, Lead in drafting the manuscript, Finalizing. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funders:
Funding AgencyGrant Number
Army Research LaboratoryW911NF-12-2-0022
Kortschak Scholars ProgramUNSPECIFIED
Bren Professor of Computing and Mathematical SciencesUNSPECIFIED
Caltech De Logi FundUNSPECIFIED
NSFDMS-1818977
Subject Keywords:Multiscale modeling; Machine learning; Crystal plasticity
DOI:10.1016/j.jmps.2021.104668
Record Number:CaltechAUTHORS:20210225-132721680
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210225-132721680
Official Citation:Burigede Liu, Nikola Kovachki, Zongyi Li, Kamyar Azizzadenesheli, Anima Anandkumar, Andrew M. Stuart, Kaushik Bhattacharya, A learning-based multiscale method and its application to inelastic impact problems, Journal of the Mechanics and Physics of Solids, Volume 158, 2022, 104668, ISSN 0022-5096, https://doi.org/10.1016/j.jmps.2021.104668.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108205
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:26 Feb 2021 17:41
Last Modified:02 Nov 2021 21:49

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