A Stochastic Reduced-Order Model for Statistical Microstructure Descriptors Evolution

Tran, Anh; Wildey, Tim; Sun, Jing; Liu, Dehao; Wang, Yan

doi:10.1115/1.4054237

Title: A Stochastic Reduced-Order Model for Statistical Microstructure Descriptors Evolution

Journal Article · Tue May 10 00:00:00 EDT 2022 · Journal of Computing and Information Science in Engineering

DOI:https://doi.org/10.1115/1.4054237· OSTI ID:1882900

Tran, Anh ^[1]; Wildey, Tim ^[1]; Sun, Jing ^[2]; Liu, Dehao ^[3]; Wang, Yan ^[3]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
U.S. Food and Drug Administration (FDA), Silver Spring, MD (United States). Office of Biostatistics, Office of Translational Sciences
Georgia Institute of Technology, Atlanta, GA (United States)

Integrated computational materials engineering (ICME) models have been a crucial building block for modern materials development, relieving heavy reliance on experiments and significantly accelerating the materials design process. However, ICME models are also computationally expensive, particularly with respect to time integration for dynamics, which hinders the ability to study statistical ensembles and thermodynamic properties of large systems for long time scales. To alleviate the computational bottleneck, we propose to model the evolution of statistical microstructure descriptors as a continuous-time stochastic process using a non-linear Langevin equation, where the probability density function (PDF) of the statistical microstructure descriptors, which are also the quantities of interests (QoIs), is modeled by the Fokker–Planck equation. In this work, we discuss how to calibrate the drift and diffusion terms of the Fokker–Planck equation from the theoretical and computational perspectives. The calibrated Fokker–Planck equation can be used as a stochastic reduced-order model to simulate the microstructure evolution of statistical microstructure descriptors PDF. Considering statistical microstructure descriptors in the microstructure evolution as QoIs, we demonstrate our proposed methodology in three integrated computational materials engineering (ICME) models: kinetic Monte Carlo, phase field, and molecular dynamics simulations.

View Accepted Manuscript (DOE)

Cite

Export

Save

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

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

Grant/Contract Number:: NA0003525; CMMI-1306996

OSTI ID:: 1882900

Report Number(s):: SAND2022-2850J; 704066

Journal Information:: Journal of Computing and Information Science in Engineering, Vol. 22, Issue 6; ISSN 1530-9827

Publisher:: ASMECopyright Statement

Country of Publication:: United States

Language:: English

References (70)

Constrained mixed-integer Gaussian mixture Bayesian optimization and its applications in designing fractal and auxetic metamaterials Tran, Anh; Tran, Minh; Wang, Yan Structural and Multidisciplinary Optimization, Vol. 59, Issue 6 https://doi.org/10.1007/s00158-018-2182-1	journal	January 2019
A Multiscale Mortar Mixed Finite Element Method Arbogast, Todd; Pencheva, Gergina; Wheeler, Mary F. Multiscale Modeling & Simulation, Vol. 6, Issue 1 https://doi.org/10.1137/060662587	journal	January 2007
A New Overview of The Trilinos Project Heroux, Michael A.; Willenbring, James M. Scientific Programming, Vol. 20, Issue 2 https://doi.org/10.1155/2012/408130	journal	January 2012
Interpreting wind-driven Southern Ocean variability in a stochastic framework Sura, Philip; Gille, Sarah T. Journal of Marine Research, Vol. 61, Issue 3 https://doi.org/10.1357/002224003322201214	journal	May 2003
Statistical Characterization of Zonal and Meridional Ocean Wind Stress Gille, Sarah T. Journal of Atmospheric and Oceanic Technology, Vol. 22, Issue 9 https://doi.org/10.1175/JTECH1789.1	journal	September 2005
Comment on “Indispensable Finite Time Corrections for Fokker-Planck Equations from Time Series Data” Friedrich, R.; Renner, Ch.; Siefert, M. Physical Review Letters, Vol. 89, Issue 14 https://doi.org/10.1103/PhysRevLett.89.149401	journal	September 2002
Optimal estimates of self-diffusion coefficients from molecular dynamics simulations Bullerjahn, Jakob Tómas; von Bülow, Sören; Hummer, Gerhard The Journal of Chemical Physics, Vol. 153, Issue 2 https://doi.org/10.1063/5.0008312	journal	July 2020
Hybrid Potts-phase field model for coupled microstructural–compositional evolution Homer, Eric R.; Tikare, Veena; Holm, Elizabeth A. Computational Materials Science, Vol. 69 https://doi.org/10.1016/j.commatsci.2012.11.056	journal	March 2013
A nonlinear manifold-based reduced order model for multiscale analysis of heterogeneous hyperelastic materials Bhattacharjee, Satyaki; Matouš, Karel Journal of Computational Physics, Vol. 313 https://doi.org/10.1016/j.jcp.2016.01.040	journal	May 2016
Qualitative and Quantitative Analysis of Stochastic Processes Based on Measured Data, ii: Applications to Experimental data GradiŠEk, J.; Govekar, E.; Grabec, I. Journal of Sound and Vibration, Vol. 252, Issue 3 https://doi.org/10.1006/jsvi.2001.4051	journal	May 2002
An iterative procedure for the estimation of drift and diffusion coefficients of Langevin processes Kleinhans, D.; Friedrich, R.; Nawroth, A. Physics Letters A, Vol. 346, Issue 1-3 https://doi.org/10.1016/j.physleta.2005.07.077	journal	October 2005
Disentangling the stochastic behavior of complex time series Anvari, Mehrnaz; Tabar, M. Reza Rahimi; Peinke, Joachim Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep35435	journal	October 2016
Power-law coarsening in network-forming phase separation governed by mechanical relaxation Tateno, Michio; Tanaka, Hajime Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-020-20734-8	journal	February 2021
The Heterognous Multiscale Methods E., Weinan; Engquist, Bjorn Communications in Mathematical Sciences, Vol. 1, Issue 1 https://doi.org/10.4310/CMS.2003.v1.n1.a8	journal	January 2003
aphBO-2GP-3B: a budgeted asynchronous parallel multi-acquisition functions for constrained Bayesian optimization on high-performing computing architecture Tran, Anh; Eldred, Mike; Wildey, Tim Structural and Multidisciplinary Optimization, Vol. 65, Issue 4 https://doi.org/10.1007/s00158-021-03102-y	journal	April 2022
Fast Parallel Algorithms for Short-Range Molecular Dynamics Plimpton, Steve Journal of Computational Physics, Vol. 117, Issue 1 https://doi.org/10.1006/jcph.1995.1039	journal	March 1995
Erratum: “sMF-BO-2CoGP: A Sequential Multi-Fidelity Constrained Bayesian Optimization Framework for Design Applications” [ASME J. Comput. Inf. Sci. Eng., 20(3), p. 0031007; DOI: 10.1115/1.4046691] Tran, Anh; Wildey, Tim; McCann, Scott Journal of Computing and Information Science in Engineering, Vol. 20, Issue 5 https://doi.org/10.1115/1.4047210	journal	June 2020
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
Large eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual-based variational multiscale method Bazilevs, Y.; Akkerman, I. Journal of Computational Physics, Vol. 229, Issue 9 https://doi.org/10.1016/j.jcp.2010.01.008	journal	May 2010
Approaching complexity by stochastic methods: From biological systems to turbulence Friedrich, Rudolf; Peinke, Joachim; Sahimi, Muhammad Physics Reports, Vol. 506, Issue 5 https://doi.org/10.1016/j.physrep.2011.05.003	journal	September 2011
Large eddy simulation of turbulent channel flows by the variational multiscale method Hughes, Thomas J. R.; Oberai, Assad A.; Mazzei, Luca Physics of Fluids, Vol. 13, Issue 6 https://doi.org/10.1063/1.1367868	journal	June 2001
Coupling of atomistic and continuum simulations using a bridging scale decomposition Wagner, Gregory J.; Liu, Wing Kam Journal of Computational Physics, Vol. 190, Issue 1 https://doi.org/10.1016/S0021-9991(03)00273-0	journal	September 2003
Data-driven reduced order models for effective yield strength and partitioning of strain in multiphase materials Latypov, Marat I.; Kalidindi, Surya R. Journal of Computational Physics, Vol. 346 https://doi.org/10.1016/j.jcp.2017.06.013	journal	October 2017
Stochastic reduced order models for uncertainty quantification of intergranular corrosion rates Sarkar, Swarnavo; Warner, James E.; Aquino, Wilkins Corrosion Science, Vol. 80 https://doi.org/10.1016/j.corsci.2013.11.032	journal	March 2014
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
Modeling diffusion in random heterogeneous media: Data-driven models, stochastic collocation and the variational multiscale method Ganapathysubramanian, Baskar; Zabaras, Nicholas Journal of Computational Physics, Vol. 226, Issue 1 https://doi.org/10.1016/j.jcp.2007.04.009	journal	September 2007
Stochastic reduced order models for uncertain geometrically nonlinear dynamical systems Mignolet, Marc P.; Soize, Christian Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 45-48 https://doi.org/10.1016/j.cma.2008.03.032	journal	August 2008
Molecular dynamics simulations of gas–liquid nucleation of Lennard-Jones fluid Laasonen, Kari; Wonczak, Stephan; Strey, Reinhard The Journal of Chemical Physics, Vol. 113, Issue 21 https://doi.org/10.1063/1.1322082	journal	December 2000
The Fokker-Planck Equation Risken, Hannes Springer Series in Synergetics https://doi.org/10.1007/978-3-642-61544-3	book	January 1996
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
An overview of the Trilinos project Heroux, Michael A.; Phipps, Eric T.; Salinger, Andrew G. ACM Transactions on Mathematical Software, Vol. 31, Issue 3 https://doi.org/10.1145/1089014.1089021	journal	September 2005
On the nature of thermal diffusion in binary Lennard-Jones liquids Reith, Dirk; Müller-Plathe, Florian The Journal of Chemical Physics, Vol. 112, Issue 5 https://doi.org/10.1063/1.480809	journal	February 2000
Thermal conductivity decomposition and analysis using molecular dynamics simulations. Part I. Lennard-Jones argon McGaughey, A. J. H.; Kaviany, M. International Journal of Heat and Mass Transfer, Vol. 47, Issue 8-9 https://doi.org/10.1016/j.ijheatmasstransfer.2003.11.002	journal	April 2004
Large Eddy Simulation and the variational multiscale method Hughes, Thomas J. R.; Mazzei, Luca; Jansen, Kenneth E. Computing and Visualization in Science, Vol. 3, Issue 1-2 https://doi.org/10.1007/s007910050051	journal	May 2000
Fokker–Planck representations of non-Markov Langevin equations: application to delayed systems Giuggioli, Luca; Neu, Zohar Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 377, Issue 2153 https://doi.org/10.1098/rsta.2018.0131	journal	July 2019
MOOSE: A parallel computational framework for coupled systems of nonlinear equations Gaston, Derek; Newman, Chris; Hansen, Glen Nuclear Engineering and Design, Vol. 239, Issue 10 https://doi.org/10.1016/j.nucengdes.2009.05.021	journal	October 2009
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
An algorithm for the finite difference approximation of derivatives with arbitrary degree and order of accuracy Hassan, H. Z.; Mohamad, A. A.; Atteia, G. E. Journal of Computational and Applied Mathematics, Vol. 236, Issue 10 https://doi.org/10.1016/j.cam.2011.12.019	journal	April 2012
Implementation of a mortar mixed finite element method using a Multiscale Flux Basis Ganis, Benjamin; Yotov, Ivan Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 49-52 https://doi.org/10.1016/j.cma.2009.09.009	journal	November 2009
Solution of Fokker-Planck equation by finite element and finite difference methods for nonlinear systems Kumar, Pankaj; Narayanan, S. Sadhana, Vol. 31, Issue 4 https://doi.org/10.1007/BF02716786	journal	August 2006
Stratonovich-to-Itô transition in noisy systems with multiplicative feedback Pesce, Giuseppe; McDaniel, Austin; Hottovy, Scott Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms3733	journal	November 2013
A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods Miller, Ronald E.; Tadmor, E. B. Modelling and Simulation in Materials Science and Engineering, Vol. 17, Issue 5 https://doi.org/10.1088/0965-0393/17/5/053001	journal	May 2009
Ror2 signaling regulates Golgi structure and transport through IFT20 for tumor invasiveness Nishita, Michiru; Park, Seung-Yeol; Nishio, Tadashi Scientific Reports, Vol. 7, Issue 1 https://doi.org/10.1038/s41598-016-0028-x	journal	January 2017
Reduced order models for random functions. Application to stochastic problems Grigoriu, M. Applied Mathematical Modelling, Vol. 33, Issue 1 https://doi.org/10.1016/j.apm.2007.10.023	journal	January 2009
Nonlinear 6D response statistics of a rotating shaft subjected to colored noise by path integration on GPU Gaidai, Oleg; Dou, Peng; Naess, Arvid International Journal of Non-Linear Mechanics, Vol. 111 https://doi.org/10.1016/j.ijnonlinmec.2019.02.008	journal	May 2019
On a quantitative method to analyze dynamical and measurement noise Siefert, M.; Kittel, A.; Friedrich, R. Europhysics Letters (EPL), Vol. 61, Issue 4 https://doi.org/10.1209/epl/i2003-00152-9	journal	February 2003
Estimation of Kramers-Moyal coefficients at low sampling rates Honisch, Christoph; Friedrich, Rudolf Physical Review E, Vol. 83, Issue 6 https://doi.org/10.1103/PhysRevE.83.066701	journal	June 2011
Qualitative and Quantitative Analysis of Stochastic Processes Based on Measured Data, i: Theory and Applications to Synthetic data GradiŠEk, J.; Grabec, I.; Siegert, S. Journal of Sound and Vibration, Vol. 252, Issue 3 https://doi.org/10.1006/jsvi.2001.4148	journal	May 2002
Interaction-induced light scattering in Lennard-Jones argon clusters: Computer simulations Dawid, A.; Gburski, Z. Physical Review A, Vol. 56, Issue 4 https://doi.org/10.1103/PhysRevA.56.3294	journal	October 1997
The heterogeneous multiscale method Abdulle, Assyr; Weinan, E.; Engquist, Björn Acta Numerica, Vol. 21 https://doi.org/10.1017/S0962492912000025	journal	April 2012
Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries Balay, Satish; Gropp, William D.; McInnes, Lois Curfman Modern Software Tools for Scientific Computing https://doi.org/10.1007/978-1-4612-1986-6_8	book	January 1997
Extracting model equations from experimental data Friedrich, R.; Siegert, S.; Peinke, J. Physics Letters A, Vol. 271, Issue 3 https://doi.org/10.1016/S0375-9601(00)00334-0	journal	June 2000
Fokker--Planck Approach of Ostwald Ripening: Simulation of a Modified Lifshitz--Slyozov--Wagner System with a Diffusive Correction Goudon, Thierry; Monasse, Laurent SIAM Journal on Scientific Computing, Vol. 42, Issue 1 https://doi.org/10.1137/18M1234011	journal	January 2020
On the definition and handling of different drift and diffusion estimates Gottschall, Julia; Peinke, Joachim New Journal of Physics, Vol. 10, Issue 8 https://doi.org/10.1088/1367-2630/10/8/083034	journal	August 2008
Data smoothing and numerical differentiation by a regularization method Stickel, Jonathan J. Computers & Chemical Engineering, Vol. 34, Issue 4 https://doi.org/10.1016/j.compchemeng.2009.10.007	journal	April 2010
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
Similarity solutions of the Fokker–Planck equation with time-dependent coefficients Lin, W. -T.; Ho, C. -L. Annals of Physics, Vol. 327, Issue 2 https://doi.org/10.1016/j.aop.2011.11.004	journal	February 2012
Statistical mechanics of normal grain growth in one dimension: A partial integro-differential equation model Ng, Felix S. L. Acta Materialia, Vol. 120 https://doi.org/10.1016/j.actamat.2016.08.033	journal	November 2016
Analysis of data sets of stochastic systems Siegert, S.; Friedrich, R.; Peinke, J. Physics Letters A, Vol. 243, Issue 5-6 https://doi.org/10.1016/S0375-9601(98)00283-7	journal	July 1998
Experimental indications for Markov properties of small-scale turbulence Renner, Christoph; Peinke, J.; Friedrich, R. Journal of Fluid Mechanics, Vol. 433 https://doi.org/10.1017/S0022112001003597	journal	April 2001
A note on estimating drift and diffusion parameters from timeseries Sura, Philip; Barsugli, Joseph Physics Letters A, Vol. 305, Issue 5 https://doi.org/10.1016/S0375-9601(02)01474-3	journal	December 2002
Indispensable Finite Time Corrections for Fokker-Planck Equations from Time Series Data Ragwitz, Mario; Kantz, Holger Physical Review Letters, Vol. 87, Issue 25 https://doi.org/10.1103/PhysRevLett.87.254501	journal	December 2001
Atomistic/continuum coupling in computational materials science Curtin, W. A.; Miller, Ronald E. Modelling and Simulation in Materials Science and Engineering, Vol. 11, Issue 3 https://doi.org/10.1088/0965-0393/11/3/201	journal	April 2003
Solid-State Phase Transformations Wayman, C. M. Annual Review of Materials Science, Vol. 1, Issue 1 https://doi.org/10.1146/annurev.ms.01.080171.001153	journal	August 1971
Fokker–Planck description for a linear delayed Langevin equation with additive Gaussian noise Giuggioli, Luca; McKetterick, Thomas John; Kenkre, V. M. Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 38 https://doi.org/10.1088/1751-8113/49/38/384002	journal	August 2016
A parareal in time procedure for the control of partial differential equations Maday, Yvon; Turinici, Gabriel Comptes Rendus Mathematique, Vol. 335, Issue 4 https://doi.org/10.1016/s1631-073x(02)02467-6	journal	January 2002
Exact molecular dynamics and kinetic theory results for thermal transport coefficients of the Lennard-Jones argon fluid in a wide region of states Borgelt, P.; Hoheisel, C.; Stell, G. Physical Review A, Vol. 42, Issue 2 https://doi.org/10.1103/physreva.42.789	journal	July 1990
Parallel methods for integrating ordinary differential equations Nievergelt, J. Communications of the ACM, Vol. 7, Issue 12 https://doi.org/10.1145/355588.365137	journal	December 1964
On a quantitative method to analyse dynamical and measurement noise Siefert, M.; Peinke, J.; Friedrich, R. arXiv https://doi.org/10.48550/arxiv.physics/0108034	text	January 2001

Similar Records

Multi-fidelity Uncertainty Quantification for Homogenization Problems in Structure-Property Relationships from Crystal Plasticity Finite Elements

Journal Article · Wed Oct 25 00:00:00 EDT 2023 · JOM. Journal of the Minerals, Metals & Materials Society · OSTI ID:1882900

Tran, Anh; Robbe, Pieterjan; Rodgers, Theron; +1 more

Modelling the Fluctuations of Reactive Shock Waves in Heterogeneous Solid Explosives as Stochastic Processes

Journal Article · Wed Nov 13 00:00:00 EST 2019 · Propellants, Explosives, Pyrotechnics · OSTI ID:1882900

Kittell, David E.; Yarrington, Cole D.; Lechman, Jeremy B.; +2 more

Microstructure-Sensitive Uncertainty Quantification for Crystal Plasticity Finite Element Constitutive Models Using Stochastic Collocation Methods

Journal Article · Tue Sep 27 00:00:00 EDT 2022 · Frontiers in Materials · OSTI ID:1882900

Tran, Anh; Wildey, Tim; Lim, Hojun

Related Subjects

97 MATHEMATICS AND COMPUTING
multi-physics modeling and simulation
multiscale modeling and simulation
physics-based simulations

Title: A Stochastic Reduced-Order Model for Statistical Microstructure Descriptors Evolution

Citation Formats

References (70)

Similar Records

Related Subjects