Solving Stochastic Inverse Problems for Property–Structure Linkages Using Data-Consistent Inversion and Machine Learning

Tran, Anh; Wildey, Tim

doi:10.1007/s11837-020-04432-w

Solving Stochastic Inverse Problems for Property–Structure Linkages Using Data-Consistent Inversion and Machine Learning

Journal Article · Fri Nov 20 00:00:00 EST 2020 · JOM. Journal of the Minerals, Metals & Materials Society

DOI:https://doi.org/10.1007/s11837-020-04432-w· OSTI ID:1760459

^[1]; Wildey, Tim ^[1]

Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States). Center for Computing Research

Determining process–structure–property linkages is one of the key objectives in material science, and uncertainty quantification plays a critical role in understanding both process–structure and structure–property linkages. In this work, we seek to learn a distribution of microstructure parameters that are consistent in the sense that the forward propagation of this distribution through a crystal plasticity finite element model matches a target distribution on materials properties. This stochastic inversion formulation infers a distribution of acceptable/consistent microstructures, as opposed to a deterministic solution, which expands the range of feasible designs in a probabilistic manner. Furthermore, to solve this stochastic inverse problem, we employ a recently developed uncertainty quantification framework based on push-forward probability measures, which combines techniques from measure theory and Bayes’ rule to define a unique and numerically stable solution. This approach requires making an initial prediction using an initial guess for the distribution on model inputs and solving a stochastic forward problem. To reduce the computational burden in solving both stochastic forward and stochastic inverse problems, we combine this approach with a machine learning Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure–property linkages.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1760459

Report Number(s):: SAND--2020-10928J; 691277

Journal Information:: JOM. Journal of the Minerals, Metals & Materials Society, Journal Name: JOM. Journal of the Minerals, Metals & Materials Society Journal Issue: 1 Vol. 73; ISSN 1047-4838

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (56)

Uncertainty Quantification and Propagation in Computational Materials Science and Simulation-Assisted Materials Design Honarmandi, Pejman; Arróyave, Raymundo Integrating Materials and Manufacturing Innovation, Vol. 9, Issue 1 https://doi.org/10.1007/s40192-020-00168-2	journal	January 2020
DAMASK: the Düsseldorf Advanced MAterial Simulation Kit for studying crystal plasticity using an FE based or a spectral numerical solver Roters, F.; Eisenlohr, P.; Kords, C. Procedia IUTAM, Vol. 3 https://doi.org/10.1016/j.piutam.2012.03.001	journal	January 2012
Generation of 3D representative volume elements for heterogeneous materials: a review Bargmann, Swantje; Klusemann, Benjamin; Markmann, Jürgen Elsevier https://doi.org/10.15480/882.1734	journalarticle	January 2018
Advanced material models for the crystal plasticity finite element method : development of a general CPFEM framework Roters, Franz RWTH Aachen University https://doi.org/10.18154/rwth-conv-144865	text	January 2011
Convergence of Probability Densities using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification Butler, T.; Jakeman, J. D.; Wildey, T. arXiv https://doi.org/10.48550/arxiv.1807.00375	text	January 2018
DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale Roters, F.; Diehl, M.; Shanthraj, P. Karlsruhe https://doi.org/10.5445/ir/1000094133	text	January 2019
Simulation-assisted materials design for the concurrent design of materials and products McDowell, David L. JOM, Vol. 59, Issue 9 https://doi.org/10.1007/s11837-007-0111-7	journal	September 2007
Vision for Data and Informatics in the Future Materials Innovation Ecosystem Kalidindi, Surya R.; Medford, Andrew J.; McDowell, David L. JOM, Vol. 68, Issue 8 https://doi.org/10.1007/s11837-016-2036-5	journal	August 2016
Identifying Structure–Property Relationships Through DREAM.3D Representative Volume Elements and DAMASK Crystal Plasticity Simulations: An Integrated Computational Materials Engineering Approach Diehl, Martin; Groeber, Michael; Haase, Christian JOM, Vol. 69, Issue 5 https://doi.org/10.1007/s11837-017-2303-0	journal	March 2017
Gaussian-Process-Driven Adaptive Sampling for Reduced-Order Modeling of Texture Effects in Polycrystalline Alpha-Ti Tallman, Aaron E.; Stopka, Krzysztof S.; Swiler, Laura P. JOM, Vol. 71, Issue 8 https://doi.org/10.1007/s11837-019-03553-1	journal	June 2019
Application-Specific Computational Materials Design via Multiscale Modeling and the Inductive Design Exploration Method (IDEM) Ellis, Brett D.; McDowell, David L. Integrating Materials and Manufacturing Innovation, Vol. 6, Issue 1 https://doi.org/10.1007/s40192-017-0086-3	journal	March 2017
Context Aware Machine Learning Approaches for Modeling Elastic Localization in Three-Dimensional Composite Microstructures Liu, Ruoqian; Yabansu, Yuksel C.; Yang, Zijiang Integrating Materials and Manufacturing Innovation, Vol. 6, Issue 2 https://doi.org/10.1007/s40192-017-0094-3	journal	March 2017
Machine Learning–Based Reduce Order Crystal Plasticity Modeling for ICME Applications Yuan, Mengfei; Paradiso, Sean; Meredig, Bryce Integrating Materials and Manufacturing Innovation, Vol. 7, Issue 4 https://doi.org/10.1007/s40192-018-0123-x	journal	December 2018
A Comparative Study of the Efficacy of Local/Global and Parametric/Nonparametric Machine Learning Methods for Establishing Structure–Property Linkages in High-Contrast 3D Elastic Composites Fernandez-Zelaia, Patxi; Yabansu, Yuksel C.; Kalidindi, Surya R. Integrating Materials and Manufacturing Innovation, Vol. 8, Issue 2 https://doi.org/10.1007/s40192-019-00129-4	journal	March 2019
Incorporation of deformation twinning in crystal plasticity models Kalidindi, Surya R. Journal of the Mechanics and Physics of Solids, Vol. 46, Issue 2 https://doi.org/10.1016/S0022-5096(97)00051-3	journal	February 1998
A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 2: Synthetic structure generation☆ Groeber, M. Acta Materialia, Vol. 56, Issue 6 https://doi.org/10.1016/j.actamat.2007.11.040	journal	April 2008
A framework for automated analysis and simulation of 3D polycrystalline microstructures.Part 1: Statistical characterization Groeber, M. Acta Materialia, Vol. 56, Issue 6 https://doi.org/10.1016/j.actamat.2007.11.041	journal	April 2008
Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications Roters, F.; Eisenlohr, P.; Hantcherli, L. Acta Materialia, Vol. 58, Issue 4 https://doi.org/10.1016/j.actamat.2009.10.058	journal	February 2010
Revealing the strain-hardening behavior of twinning-induced plasticity steels: Theory, simulations, experiments Steinmetz, David R.; Jäpel, Tom; Wietbrock, Burkhard Acta Materialia, Vol. 61, Issue 2 https://doi.org/10.1016/j.actamat.2012.09.064	journal	January 2013
A crystal plasticity model for twinning- and transformation-induced plasticity Wong, Su Leen; Madivala, Manjunatha; Prahl, Ulrich Acta Materialia, Vol. 118 https://doi.org/10.1016/j.actamat.2016.07.032	journal	October 2016
Establishing structure-property localization linkages for elastic deformation of three-dimensional high contrast composites using deep learning approaches Yang, Zijiang; Yabansu, Yuksel C.; Jha, Dipendra Acta Materialia, Vol. 166 https://doi.org/10.1016/j.actamat.2018.12.045	journal	March 2019
Data-driven high-fidelity 2D microstructure reconstruction via non-local patch-based image inpainting Tran, Anh; Tran, Hoang Acta Materialia, Vol. 178 https://doi.org/10.1016/j.actamat.2019.08.007	journal	October 2019
An active learning high-throughput microstructure calibration framework for solving inverse structure–process problems in materials informatics Tran, Anh; Mitchell, John A.; Swiler, Laura P. Acta Materialia, Vol. 194 https://doi.org/10.1016/j.actamat.2020.04.054	journal	August 2020
Computational microstructure characterization and reconstruction for stochastic multiscale material design Liu, Yu; Steven Greene, M.; Chen, Wei Computer-Aided Design, Vol. 45, Issue 1 https://doi.org/10.1016/j.cad.2012.03.007	journal	January 2013
Key computational modeling issues in Integrated Computational Materials Engineering Panchal, Jitesh H.; Kalidindi, Surya R.; McDowell, David L. Computer-Aided Design, Vol. 45, Issue 1 https://doi.org/10.1016/j.cad.2012.06.006	journal	January 2013
pBO-2GP-3B: A batch parallel known/unknown constrained Bayesian optimization with feasibility classification and its applications in computational fluid dynamics Tran, Anh; Sun, Jing; Furlan, John M. Computer Methods in Applied Mechanics and Engineering, Vol. 347 https://doi.org/10.1016/j.cma.2018.12.033	journal	April 2019
Uncertainty propagation in reduced order models based on crystal plasticity Tallman, Aaron E.; Swiler, Laura P.; Wang, Yan Computer Methods in Applied Mechanics and Engineering, Vol. 365 https://doi.org/10.1016/j.cma.2020.113009	journal	June 2020
DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale Roters, F.; Diehl, M.; Shanthraj, P. Computational Materials Science, Vol. 158 https://doi.org/10.1016/j.commatsci.2018.04.030	journal	February 2019
Deep learning approaches for mining structure-property linkages in high contrast composites from simulation datasets Yang, Zijiang; Yabansu, Yuksel C.; Al-Bahrani, Reda Computational Materials Science, Vol. 151 https://doi.org/10.1016/j.commatsci.2018.05.014	journal	August 2018
Microstructure optimization with constrained design objectives using machine learning-based feedback-aware data-generation Paul, Arindam; Acar, Pinar; Liao, Wei-keng Computational Materials Science, Vol. 160 https://doi.org/10.1016/j.commatsci.2019.01.015	journal	April 2019
Investigation of three-dimensional aspects of grain-scale plastic surface deformation of an aluminum oligocrystal Zhao, Z.; Ramesh, M.; Raabe, D. International Journal of Plasticity, Vol. 24, Issue 12 https://doi.org/10.1016/j.ijplas.2008.01.002	journal	December 2008
A spectral method solution to crystal elasto-viscoplasticity at finite strains Eisenlohr, P.; Diehl, M.; Lebensohn, R. A. International Journal of Plasticity, Vol. 46 https://doi.org/10.1016/j.ijplas.2012.09.012	journal	July 2013
Numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials Shanthraj, P.; Eisenlohr, P.; Diehl, M. International Journal of Plasticity, Vol. 66 https://doi.org/10.1016/j.ijplas.2014.02.006	journal	March 2015
Crystal plasticity finite element simulations using a database of discrete Fourier transforms Alharbi, Hamad F.; Kalidindi, Surya R. International Journal of Plasticity, Vol. 66 https://doi.org/10.1016/j.ijplas.2014.04.006	journal	March 2015
A strategy for synthetic microstructure generation and crystal plasticity parameter calibration of fine-grain-structured dual-phase steel Liu, Wenqi; Lian, Junhe; Aravas, Nikolaos International Journal of Plasticity, Vol. 126 https://doi.org/10.1016/j.ijplas.2019.10.002	journal	March 2020
Using spectral-based representative volume element crystal plasticity simulations to predict yield surface evolution during large scale forming simulations Han, Fengbo; Diehl, Martin; Roters, Franz Journal of Materials Processing Technology, Vol. 277 https://doi.org/10.1016/j.jmatprotec.2019.116449	journal	March 2020
An inverse design framework for prescribing precipitation heat treatments from a target microstructure Johnson, L.; Arróyave, R. Materials & Design, Vol. 107 https://doi.org/10.1016/j.matdes.2016.06.009	journal	October 2016
Dislocation mechanics of creep Blum, W.; Eisenlohr, P. Materials Science and Engineering: A, Vol. 510-511 https://doi.org/10.1016/j.msea.2008.04.110	journal	June 2009
Property prediction and properties-to-microstructure inverse analysis of steels by a machine-learning approach Wang, Zhi-Lei; Adachi, Yoshitaka Materials Science and Engineering: A, Vol. 744 https://doi.org/10.1016/j.msea.2018.12.049	journal	January 2019
Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques Bostanabad, Ramin; Zhang, Yichi; Li, Xiaolin Progress in Materials Science, Vol. 95 https://doi.org/10.1016/j.pmatsci.2018.01.005	journal	June 2018
Generation of 3D representative volume elements for heterogeneous materials: A review Bargmann, Swantje; Klusemann, Benjamin; Markmann, Jürgen Progress in Materials Science, Vol. 96 https://doi.org/10.1016/j.pmatsci.2018.02.003	journal	July 2018
Mixed-mode crack tip fields in a polycrystalline aluminum alloy Wicke, Marcel; Brueckner-Foit, Angelika MATEC Web of Conferences, Vol. 300 https://doi.org/10.1051/matecconf/201930011004	journal	January 2019
Perspective: Materials informatics and big data: Realization of the “fourth paradigm” of science in materials science Agrawal, Ankit; Choudhary, Alok APL Materials, Vol. 4, Issue 5 https://doi.org/10.1063/1.4946894	journal	April 2016
Multi-fidelity machine-learning with uncertainty quantification and Bayesian optimization for materials design: Application to ternary random alloys Tran, Anh; Tranchida, Julien; Wildey, Tim The Journal of Chemical Physics, Vol. 153, Issue 7 https://doi.org/10.1063/5.0015672	journal	August 2020
An inductive design exploration method for hierarchical systems design under uncertainty Choi, Hae-Jin; Mcdowell, David L.; Allen, Janet K. Engineering Optimization, Vol. 40, Issue 4 https://doi.org/10.1080/03052150701742201	journal	April 2008
Quantifying uncertainty in the process-structure relationship for Al–Cu solidification Tran, Anh; Liu, Dehao; Tran, Hoang Modelling and Simulation in Materials Science and Engineering, Vol. 27, Issue 6 https://doi.org/10.1088/1361-651X/ab2690	journal	June 2019
Deep learning based domain knowledge integration for small datasets: Illustrative applications in materials informatics Yang, Zijiang; Al-Bahrani, Reda; Reid, Andrew C. E. 2019 International Joint Conference on Neural Networks (IJCNN) https://doi.org/10.1109/IJCNN.2019.8852162	conference	July 2019
Taking the Human Out of the Loop: A Review of Bayesian Optimization Shahriari, Bobak; Swersky, Kevin; Wang, Ziyu Proceedings of the IEEE, Vol. 104, Issue 1 https://doi.org/10.1109/JPROC.2015.2494218	journal	January 2016
sMF-BO-2CoGP: A Sequential Multi-Fidelity Constrained Bayesian Optimization Framework for Design Applications Tran, Anh; Wildey, Tim; McCann, Scott Journal of Computing and Information Science in Engineering, Vol. 20, Issue 3 https://doi.org/10.1115/1.4046697	journal	April 2020
Combining Push-Forward Measures and Bayes' Rule to Construct Consistent Solutions to Stochastic Inverse Problems Butler, T.; Jakeman, J.; Wildey, T. SIAM Journal on Scientific Computing, Vol. 40, Issue 2 https://doi.org/10.1137/16M1087229	journal	January 2018
Convergence of Probability Densities Using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification Butler, T.; Jakeman, J.; Wildey, T. SIAM Journal on Scientific Computing, Vol. 40, Issue 5 https://doi.org/10.1137/18M1181675	journal	January 2018
Statistical Description of Microstructures Torquato, S. Annual Review of Materials Research, Vol. 32, Issue 1 https://doi.org/10.1146/annurev.matsci.32.110101.155324	journal	August 2002
DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D Groeber, Michael A.; Jackson, Michael A. Integrating Materials and Manufacturing Innovation, Vol. 3, Issue 1 https://doi.org/10.1186/2193-9772-3-5	journal	April 2014
PETSc Users Manual (Rev. 3.13) Balay, S.; Abhyankar, S.; Adams, Mark https://doi.org/10.2172/1614847	report	March 2020
Stochastic Design Optimization of Microstructures with Utilization of a Linear Solver Acar, Pınar; Srivastava, Siddhartha; Sundararaghavan, Veera AIAA Journal, Vol. 55, Issue 9 https://doi.org/10.2514/1.J056000	journal	September 2017
Quantifying the Contribution of Crystallographic Texture and Grain Morphology on the Elastic and Plastic Anisotropy of bcc Steel Diehl, Martin; Niehuesbernd, Jörn; Bruder, Enrico Metals, Vol. 9, Issue 12 https://doi.org/10.3390/met9121252	journal	November 2019

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