Skip to main content
Top

2023 | OriginalPaper | Chapter

Data Assimilation for Microstructure Evolution in Kinetic Monte Carlo

Authors : Anh Tran, Yan Wang, Theron Rodgers

Published in: TMS 2023 152nd Annual Meeting & Exhibition Supplemental Proceedings

Publisher: Springer Nature Switzerland

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Modeling grain growth has been a subject of interest in computational material science, as it occurs in thermal-based processing methods such as annealing and sintering. Kinetic Monte Carlo with Potts model is often used as an integrated computational materials engineering (ICME) grain growth model and can generate high-fidelity synthetic microstructures. In this paper, we offer a data-driven stochastic calculus perspective on the kinetics of grain growth and model the microstructure evolution through the lens of stochastic differential equations, based on Langevin dynamics and Fokker-Planck equation to forecast the grain size distribution. We demonstrate that our proposed approach agrees reasonably well with the hybrid Potts-phase field model using SPPARKS in forecasting the long-term evolution of grain size distribution.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
1.
go back to reference Anvari M, Tabar M, Peinke J, Lehnertz K (2016) Disentangling the stochastic behavior of complex time series. Sci Rep 6(1):1–12CrossRef Anvari M, Tabar M, Peinke J, Lehnertz K (2016) Disentangling the stochastic behavior of complex time series. Sci Rep 6(1):1–12CrossRef
2.
go back to reference Bowman AW, Azzalini A (1997) Applied smoothing techniques for data analysis: the kernel approach with S-Plus illustrations, vol 18. Oxford University Press, Oxford Bowman AW, Azzalini A (1997) Applied smoothing techniques for data analysis: the kernel approach with S-Plus illustrations, vol 18. Oxford University Press, Oxford
3.
go back to reference Breithaupt T, Hansen LN, Toppaladoddi S, Katz RF (2021) The role of grain-environment heterogeneity in normal grain growth: a stochastic approach. Acta Materialia 209:116699CrossRef Breithaupt T, Hansen LN, Toppaladoddi S, Katz RF (2021) The role of grain-environment heterogeneity in normal grain growth: a stochastic approach. Acta Materialia 209:116699CrossRef
4.
go back to reference Evensen G (1994) Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J Geophys Res: Oceans 99(C5):10143–10162CrossRef Evensen G (1994) Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J Geophys Res: Oceans 99(C5):10143–10162CrossRef
5.
go back to reference Evensen G (2003) The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn 53(4):343–367CrossRef Evensen G (2003) The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn 53(4):343–367CrossRef
6.
go back to reference Frank TD (2005) Nonlinear Fokker-Planck equations: fundamentals and applications. Springer Science & Business Media Frank TD (2005) Nonlinear Fokker-Planck equations: fundamentals and applications. Springer Science & Business Media
7.
go back to reference Friedrich R, Peinke J, Sahimi M, Tabar MRR (2011) Approaching complexity by stochastic methods: from biological systems to turbulence. Phys Rep 506(5):87–162CrossRef Friedrich R, Peinke J, Sahimi M, Tabar MRR (2011) Approaching complexity by stochastic methods: from biological systems to turbulence. Phys Rep 506(5):87–162CrossRef
8.
go back to reference Friedrich R, Renner C, Siefert M, Peinke J (2002) Comment on “Indispensable finite time corrections for Fokker-Planck equations from time series data”. Phys Rev Lett 89(14):149401 Friedrich R, Renner C, Siefert M, Peinke J (2002) Comment on “Indispensable finite time corrections for Fokker-Planck equations from time series data”. Phys Rev Lett 89(14):149401
9.
go back to reference Friedrich R, Siegert S, Peinke J, Siefert M, Lindemann M, Raethjen J, Deuschl G, Pfister G et al (2000) Extracting model equations from experimental data. Phys Lett A 271(3):217–222CrossRef Friedrich R, Siegert S, Peinke J, Siefert M, Lindemann M, Raethjen J, Deuschl G, Pfister G et al (2000) Extracting model equations from experimental data. Phys Lett A 271(3):217–222CrossRef
10.
go back to reference Gille ST (2005) Statistical characterization of zonal and meridional ocean wind stress. J Atmos Oceanic Technol 22(9):1353–1372CrossRef Gille ST (2005) Statistical characterization of zonal and meridional ocean wind stress. J Atmos Oceanic Technol 22(9):1353–1372CrossRef
11.
go back to reference Giuggioli L, McKetterick TJ, Kenkre V, Chase M (2016) Fokker-Planck description for a linear delayed Langevin equation with additive Gaussian noise. J Phys A: Math Theor 49(38):384002 Giuggioli L, McKetterick TJ, Kenkre V, Chase M (2016) Fokker-Planck description for a linear delayed Langevin equation with additive Gaussian noise. J Phys A: Math Theor 49(38):384002
12.
go back to reference Giuggioli L, Neu Z (2019) Fokker-Planck representations of non-Markov Langevin equations: application to delayed systems. Philos Trans Royal Soc A 377(2153):20180131 Giuggioli L, Neu Z (2019) Fokker-Planck representations of non-Markov Langevin equations: application to delayed systems. Philos Trans Royal Soc A 377(2153):20180131
13.
go back to reference Gottschall J, Peinke J (2008) On the definition and handling of different drift and diffusion estimates. New J Phys 10(8):083034 Gottschall J, Peinke J (2008) On the definition and handling of different drift and diffusion estimates. New J Phys 10(8):083034
14.
go back to reference Gradišek J, Govekar E, Grabec I (2002) Qualitative and quantitative analysis of stochastic processes based on measured data, II: applications to experimental data. J Sound Vibr 252(3):563–572CrossRef Gradišek J, Govekar E, Grabec I (2002) Qualitative and quantitative analysis of stochastic processes based on measured data, II: applications to experimental data. J Sound Vibr 252(3):563–572CrossRef
15.
go back to reference Gradišek J, Grabec I, Siegert S, Friedrich R (2002) Qualitative and quantitative analysis of stochastic processes based on measured data, I: theory and applications to synthetic data. J Sound Vibr 252(3):545–562CrossRef Gradišek J, Grabec I, Siegert S, Friedrich R (2002) Qualitative and quantitative analysis of stochastic processes based on measured data, I: theory and applications to synthetic data. J Sound Vibr 252(3):545–562CrossRef
16.
go back to reference Homer ER, Tikare V, Holm EA (2013) Hybrid Potts-phase field model for coupled microstructural-compositional evolution. Comput Mater Sci 69:414–423CrossRef Homer ER, Tikare V, Holm EA (2013) Hybrid Potts-phase field model for coupled microstructural-compositional evolution. Comput Mater Sci 69:414–423CrossRef
17.
go back to reference Honisch C, Friedrich R (2011) Estimation of Kramers-Moyal coefficients at low sampling rates. Physi Rev E 83(6):066701 Honisch C, Friedrich R (2011) Estimation of Kramers-Moyal coefficients at low sampling rates. Physi Rev E 83(6):066701
18.
go back to reference Kleinhans D, Friedrich R, Nawroth A, Peinke J (2005) An iterative procedure for the estimation of drift and diffusion coefficients of Langevin processes. Phys Lett A 346(1–3):42–46CrossRef Kleinhans D, Friedrich R, Nawroth A, Peinke J (2005) An iterative procedure for the estimation of drift and diffusion coefficients of Langevin processes. Phys Lett A 346(1–3):42–46CrossRef
19.
go back to reference Lin WT, Ho CL (2012) Similarity solutions of the Fokker-Planck equation with time-dependent coefficients. Ann Phys 327(2):386–397CrossRef Lin WT, Ho CL (2012) Similarity solutions of the Fokker-Planck equation with time-dependent coefficients. Ann Phys 327(2):386–397CrossRef
20.
go back to reference Mousavi S, Reihani S, Anvari G, Anvari M, Alinezhad H, Tabar M (2017) Stochastic analysis of time series for the spatial positions of particles trapped in optical tweezers. Sci Rep 7(1):1–11CrossRef Mousavi S, Reihani S, Anvari G, Anvari M, Alinezhad H, Tabar M (2017) Stochastic analysis of time series for the spatial positions of particles trapped in optical tweezers. Sci Rep 7(1):1–11CrossRef
21.
go back to reference Ng FS (2016) Statistical mechanics of normal grain growth in one dimension: a partial integro-differential equation model. Acta Materialia 120:453–462CrossRef Ng FS (2016) Statistical mechanics of normal grain growth in one dimension: a partial integro-differential equation model. Acta Materialia 120:453–462CrossRef
22.
go back to reference Pesce G, McDaniel A, Hottovy S, Wehr J, Volpe G (2013) Stratonovich-to-Itô transition in noisy systems with multiplicative feedback. Nat Commun 4(1):1–7CrossRef Pesce G, McDaniel A, Hottovy S, Wehr J, Volpe G (2013) Stratonovich-to-Itô transition in noisy systems with multiplicative feedback. Nat Commun 4(1):1–7CrossRef
23.
go back to reference Plimpton S, Thompson A, Slepoy A (2008) Stochastic parallel particle kinetic simulator. Technical report, Sandia National Lab.(SNL-NM), Albuquerque, NM (United States) Plimpton S, Thompson A, Slepoy A (2008) Stochastic parallel particle kinetic simulator. Technical report, Sandia National Lab.(SNL-NM), Albuquerque, NM (United States)
24.
go back to reference Plimpton S, Battaile C, Chandross M, Holm L, Thompson A, Tikare V, Wagner G, Webb E, Zhou X, Cardona CG et al (2009) Crossing the mesoscale no-man’s land via parallel kinetic Monte Carlo. Sandia Report SAND2009-6226 Plimpton S, Battaile C, Chandross M, Holm L, Thompson A, Tikare V, Wagner G, Webb E, Zhou X, Cardona CG et al (2009) Crossing the mesoscale no-man’s land via parallel kinetic Monte Carlo. Sandia Report SAND2009-6226
25.
go back to reference Renner C, Peinke J, Friedrich R (2001) Experimental indications for Markov properties of small-scale turbulence. J Fluid Mech 433:383–409CrossRef Renner C, Peinke J, Friedrich R (2001) Experimental indications for Markov properties of small-scale turbulence. J Fluid Mech 433:383–409CrossRef
26.
go back to reference Risken H (1989) The Fokker Planck equation, Methods of solution and application, 2nd edn. Springer, Berlin, Heidelberg Risken H (1989) The Fokker Planck equation, Methods of solution and application, 2nd edn. Springer, Berlin, Heidelberg
27.
go back to reference Siefert M, Kittel A, Friedrich R, Peinke J (2003) On a quantitative method to analyze dynamical and measurement noise. EPL (Europhys Lett) 61(4):466 Siefert M, Kittel A, Friedrich R, Peinke J (2003) On a quantitative method to analyze dynamical and measurement noise. EPL (Europhys Lett) 61(4):466
28.
go back to reference Sura P, Gille ST (2003) Interpreting wind-driven Southern Ocean variability in a stochastic framework. J Marine Res 61(3):313–334CrossRef Sura P, Gille ST (2003) Interpreting wind-driven Southern Ocean variability in a stochastic framework. J Marine Res 61(3):313–334CrossRef
30.
go back to reference Tabar R (2019) Analysis and data-based reconstruction of complex nonlinear dynamical systems, vol 730. Springer Tabar R (2019) Analysis and data-based reconstruction of complex nonlinear dynamical systems, vol 730. Springer
31.
go back to reference Tran A, Eldred M, Wildey T, McCann S, Sun J, Visintainer RJ (2022) aphBO-2GP-3B: a budgeted asynchronous parallel multi-acquisition functions for constrained Bayesian optimization on high-performing computing architecture. Struct Multidisc Optim 65(4):1–45CrossRef Tran A, Eldred M, Wildey T, McCann S, Sun J, Visintainer RJ (2022) aphBO-2GP-3B: a budgeted asynchronous parallel multi-acquisition functions for constrained Bayesian optimization on high-performing computing architecture. Struct Multidisc Optim 65(4):1–45CrossRef
32.
go back to reference Tran A, Mitchell JA, Swiler LP, Wildey T (2020) An active-learning high-throughput microstructure calibration framework for process-structure linkage in materials informatics. Acta Materialia 194:80–92CrossRef Tran A, Mitchell JA, Swiler LP, Wildey T (2020) An active-learning high-throughput microstructure calibration framework for process-structure linkage in materials informatics. Acta Materialia 194:80–92CrossRef
33.
go back to reference Tran A, Sun J, Furlan JM, Pagalthivarthi KV, Visintainer RJ, Wang Y (2019) pBO-2GP-3B: a batch parallel known/unknown constrained Bayesian optimization with feasibility classification and its applications in computational fluid dynamics. Comput Methods Appl Mech Eng 347:827–852CrossRef Tran A, Sun J, Furlan JM, Pagalthivarthi KV, Visintainer RJ, Wang Y (2019) pBO-2GP-3B: a batch parallel known/unknown constrained Bayesian optimization with feasibility classification and its applications in computational fluid dynamics. Comput Methods Appl Mech Eng 347:827–852CrossRef
34.
go back to reference Tran A, Tran M, Wang Y (2019) Constrained mixed-integer Gaussian mixture Bayesian optimization and its applications in designing fractal and auxetic metamaterials. Struct Multidisc Optim 59:2131–2154CrossRef Tran A, Tran M, Wang Y (2019) Constrained mixed-integer Gaussian mixture Bayesian optimization and its applications in designing fractal and auxetic metamaterials. Struct Multidisc Optim 59:2131–2154CrossRef
35.
go back to reference Tran A, Tranchida J, Wildey T, Thompson AP (2020) Multi-fidelity machine-learning with uncertainty quantification and Bayesian optimization for materials design: application to ternary random alloys. J Chem Phys 153:074705 Tran A, Tranchida J, Wildey T, Thompson AP (2020) Multi-fidelity machine-learning with uncertainty quantification and Bayesian optimization for materials design: application to ternary random alloys. J Chem Phys 153:074705
36.
go back to reference Tran A, Wildey T, McCann S (2020) sMF-BO-2CoGP: a sequential multi-fidelity constrained Bayesian optimization for design applications. J Comput Inform Sci Eng 20(3):1–15CrossRef Tran A, Wildey T, McCann S (2020) sMF-BO-2CoGP: a sequential multi-fidelity constrained Bayesian optimization for design applications. J Comput Inform Sci Eng 20(3):1–15CrossRef
37.
go back to reference Tran A, Wildey T, Sun J, Liu D, Wang Y (2022) A stochastic reduced-order model for statistical microstructure descriptors evolution. J Comput Inform Sci Eng, pp 1–18 Tran A, Wildey T, Sun J, Liu D, Wang Y (2022) A stochastic reduced-order model for statistical microstructure descriptors evolution. J Comput Inform Sci Eng, pp 1–18
38.
go back to reference Voter AF (2007) Introduction to the kinetic Monte Carlo method. In: Radiation effects in solids. Springer, pp 1–23 Voter AF (2007) Introduction to the kinetic Monte Carlo method. In: Radiation effects in solids. Springer, pp 1–23
Metadata
Title
Data Assimilation for Microstructure Evolution in Kinetic Monte Carlo
Authors
Anh Tran
Yan Wang
Theron Rodgers
Copyright Year
2023
DOI
https://doi.org/10.1007/978-3-031-22524-6_50

Premium Partners