Mesoscale informed parameter estimation through machine learning: A case-study in fracture modeling
Abstract
Scale bridging is a critical need in computational sciences, where the modeling community has developed accurate physics models from first principles, of processes at lower length and time scales that influence the behavior at the higher scales of interest. However, it is not computationally feasible to incorporate all of the lower length scale physics directly into upscaled models. This is an area where machine learning has shown promise in building emulators of the lower length scale models, which incur a mere fraction of the computational cost of the original higher fidelity models. We demonstrate the use of machine learning using an example in materials science estimating continuum scale parameters by emulating, with uncertainties, complicated mesoscale physics. Additionally, we describe a new framework to emulate the fine scale physics, especially in the presence of microstructures, using machine learning, and showcase its usefulness by providing an example from modeling fracture propagation. Our approach can be thought of as a data-driven dimension reduction technique that yields probabilistic emulators. Our results show well-calibrated predictions for the quantities of interests in a low-strain simulation of fracture propagation at the mesoscale level. Furthermore, on average, we achieve ~10% relative errors on time-varying quantities like total damagemore »
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1645087
- Alternate Identifier(s):
- OSTI ID: 1809281
- Report Number(s):
- LA-UR-19-30618
Journal ID: ISSN 0021-9991; TRN: US2203081
- Grant/Contract Number:
- 89233218CNA000001; 20170103DR
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 420; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; Uncertainty quantification; reduced order model; machine learning; data driven upscaling; probabilistic emulator; fracture propagation
Citation Formats
Panda, Nishant, Osthus, David Allen, Srinivasan, Gowri, O'Malley, Daniel, Chau, Viet Tuan, Oyen, Diane Adele, and Godinez Vazquez, Humberto C. Mesoscale informed parameter estimation through machine learning: A case-study in fracture modeling. United States: N. p., 2020.
Web. doi:10.1016/j.jcp.2020.109719.
Panda, Nishant, Osthus, David Allen, Srinivasan, Gowri, O'Malley, Daniel, Chau, Viet Tuan, Oyen, Diane Adele, & Godinez Vazquez, Humberto C. Mesoscale informed parameter estimation through machine learning: A case-study in fracture modeling. United States. https://doi.org/10.1016/j.jcp.2020.109719
Panda, Nishant, Osthus, David Allen, Srinivasan, Gowri, O'Malley, Daniel, Chau, Viet Tuan, Oyen, Diane Adele, and Godinez Vazquez, Humberto C. Mon .
"Mesoscale informed parameter estimation through machine learning: A case-study in fracture modeling". United States. https://doi.org/10.1016/j.jcp.2020.109719. https://www.osti.gov/servlets/purl/1645087.
@article{osti_1645087,
title = {Mesoscale informed parameter estimation through machine learning: A case-study in fracture modeling},
author = {Panda, Nishant and Osthus, David Allen and Srinivasan, Gowri and O'Malley, Daniel and Chau, Viet Tuan and Oyen, Diane Adele and Godinez Vazquez, Humberto C.},
abstractNote = {Scale bridging is a critical need in computational sciences, where the modeling community has developed accurate physics models from first principles, of processes at lower length and time scales that influence the behavior at the higher scales of interest. However, it is not computationally feasible to incorporate all of the lower length scale physics directly into upscaled models. This is an area where machine learning has shown promise in building emulators of the lower length scale models, which incur a mere fraction of the computational cost of the original higher fidelity models. We demonstrate the use of machine learning using an example in materials science estimating continuum scale parameters by emulating, with uncertainties, complicated mesoscale physics. Additionally, we describe a new framework to emulate the fine scale physics, especially in the presence of microstructures, using machine learning, and showcase its usefulness by providing an example from modeling fracture propagation. Our approach can be thought of as a data-driven dimension reduction technique that yields probabilistic emulators. Our results show well-calibrated predictions for the quantities of interests in a low-strain simulation of fracture propagation at the mesoscale level. Furthermore, on average, we achieve ~10% relative errors on time-varying quantities like total damage and maximum stresses. Successfully replicating mesoscale scale physics within the continuum models is a crucial step towards predictive capability in multi-scale problems.},
doi = {10.1016/j.jcp.2020.109719},
journal = {Journal of Computational Physics},
number = ,
volume = 420,
place = {United States},
year = {2020},
month = {7}
}
Works referenced in this record:
Reduced-order modeling of time-varying systems
journal, January 1999
- Roychowdhury, J.
- IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 46, Issue 10
Compressive sensing as a paradigm for building physics models
journal, January 2013
- Nelson, Lance J.; Hart, Gus L. W.; Zhou, Fei
- Physical Review B, Vol. 87, Issue 3
Microcracks in rocks: A review
journal, December 1983
- Kranz, Robert L.
- Tectonophysics, Vol. 100, Issue 1-3, p. 449-480
Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization
journal, January 2018
- Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max
- SIAM Review, Vol. 60, Issue 3
Model selection for dynamical systems via sparse regression and information criteria
journal, August 2017
- Mangan, N. M.; Kutz, J. N.; Brunton, S. L.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 473, Issue 2204
Machine learning of linear differential equations using Gaussian processes
journal, November 2017
- Raissi, Maziar; Perdikaris, Paris; Karniadakis, George Em
- Journal of Computational Physics, Vol. 348
Hidden physics models: Machine learning of nonlinear partial differential equations
journal, March 2018
- Raissi, Maziar; Karniadakis, George Em
- Journal of Computational Physics, Vol. 357
Machine learning in bioinformatics
journal, March 2006
- Larrañaga, Pedro; Calvo, Borja; Santana, Roberto
- Briefings in Bioinformatics, Vol. 7, Issue 1
Materials informatics: a journey towards material design and synthesis
journal, January 2016
- Takahashi, Keisuke; Tanaka, Yuzuru
- Dalton Transactions, Vol. 45, Issue 26
A kernel-based method for data-driven koopman spectral analysis
journal, December 2015
- Kevrekidis, Ioannis G.; Rowley, Clarence W.; Williams, Matthew O.
- Journal of Computational Dynamics, Vol. 2, Issue 2
Microfractures: A review
journal, December 2014
- Anders, Mark H.; Laubach, Stephen E.; Scholz, Christopher H.
- Journal of Structural Geology, Vol. 69
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
journal, January 2015
- Benner, Peter; Gugercin, Serkan; Willcox, Karen
- SIAM Review, Vol. 57, Issue 4
Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data
journal, March 2017
- Wang, Jian-Xun; Wu, Jin-Long; Xiao, Heng
- Physical Review Fluids, Vol. 2, Issue 3
Reduced-order modeling: new approaches for computational physics
journal, February 2004
- Lucia, David J.; Beran, Philip S.; Silva, Walter A.
- Progress in Aerospace Sciences, Vol. 40, Issue 1-2
Reduced-order modeling through machine learning and graph-theoretic approaches for brittle fracture applications
journal, February 2019
- Hunter, Abigail; Moore, Bryan A.; Mudunuru, Maruti
- Computational Materials Science, Vol. 157