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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 and Bhattacharya, Kaushik (2021) A learning-based multiscale method and its application to inelastic impact problems. . (Unpublished)

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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 draws from recent successes of deep neural networks, in combination with ideas from model reduction. 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:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper ItemData and scripts
Liu, Burigede0000-0002-6518-3368
Kovachki, Nikola0000-0002-3650-2972
Azizzadenesheli, Kamyar0000-0001-8507-1868
Bhattacharya, Kaushik0000-0003-2908-5469
Additional Information: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 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. AS is supported in part by Bren endowed chair and De Logi grant. AMS is also partially supported by NSF 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 " ( Author contributions. BL performed all the numerical simulations. BL, NK, AS and KB took the lead in identifying the problem and the initial formulation. All authors were involved in the detailed formulation and in analyzing the results. BL and KB made the initial draft which all authors revised. The authors declare no competing interest.
Funding AgencyGrant Number
Army Research LaboratoryW911NF-12-2-0022
Kortschak Scholars ProgramUNSPECIFIED
Bren Professor of Computing and Mathematical SciencesUNSPECIFIED
Caltech De Logi FundUNSPECIFIED
Subject Keywords:Multiscale modeling, machine learning, crystal plasticity
Record Number:CaltechAUTHORS:20210225-132721680
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108205
Deposited By: George Porter
Deposited On:26 Feb 2021 17:41
Last Modified:26 Feb 2021 17:41

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