Study of Temperature-Dependent Motion of GBs in Pure Aluminium by Cellular Automation and Machine Learning Methods E. V. Fomin∗ Department of General and Theoretical Physics, Chelyabinsk State University, Chelyabinsk 454001, Russia ∗ fomin33312@gmail.com Keywords: grain boundaries motion, cellular automation, feedforward neural network. This work is devoted to the theoretical study of grain boundary (GB) motion in pure aluminum based on 3 numerical methods: molecular dynamics (MD), machine learning (ML) and cellular automata (CA). Values of GBs energy are obtained by MD method [1]. Symmetric and asymmetric tilt and twist GBs in the boundary planes (100) and (110) are considered, and the GBs energies are measured for temperatures of 100, 300, 500, and 700 K. The next step is related to the description of the GB energy function as dependent on misorientation and temperature in the form of the forward propagation artificial neural network (ANN). MD simulation data are used to train and test this ANN. Training of the ANN is performed by the Adam algorithm [2] to better accuracy on the test data. The last part of the work is related to the simulation of the GBs motion and microstructure evolution during the dynamic deformation response of the pure aluminum material by the CA method. It is well known that the mobility of GBs is proportional to their energy [3]. Based on this law and the anisotropic energy function in the form of ANN, transition rules for the CA method are derived. The CA grid is superimposed on the level of matter, which is realized within the continuum mechanics framework with according to the Wilkins scheme [4]. The results show that the GBs energy can be divided into minimum and average for the fixed misorientation angle. This is consistent with the works on the study of metastable GBs structures [5]. The ANN trained on MD data shows good accuracy on test data and is capable of describing the evolution of the GBs energy with temperature change as the continuous function. Acknowledgements The study was supported by grant No 22-71-00090 from the Russian Science Foundation, https://rscf.ru/project/22-71-00090/ References [1] Plimpton, S. (2015). Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys, 117, 1–19. [2] Kingma, P., Ba, J. (2014). Adam: A method for stochastic optimization. arXiv:1412.6980. [3] Nino, J. D., Johnson, O. K. (2023). Influence of grain boundary energy anisotropy on the evolution of grain boundary network structure during 3D anisotropic grain growth. Comput. Mater. Sci, 217, 111879. [4] Wilkins, M.L. (1967). Calculation of elastoplastic flows. In the book. Computational methods in hydrodynamics. Moscow: Mir, 212–263. 65
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