Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural Network
The reaction–diffusion equation approach, which solves differential equations of the development of density distributions of mobile and immobile dislocations under mutual interactions, is a method widely used to model the dislocation structure formation. A challenge in the approach is the difficulty...
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MDPI AG
2023-03-01
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| author | Yoshitaka Umeno Emi Kawai Atsushi Kubo Hiroyuki Shima Takashi Sumigawa |
| author_facet | Yoshitaka Umeno Emi Kawai Atsushi Kubo Hiroyuki Shima Takashi Sumigawa |
| author_sort | Yoshitaka Umeno |
| collection | DOAJ |
| description | The reaction–diffusion equation approach, which solves differential equations of the development of density distributions of mobile and immobile dislocations under mutual interactions, is a method widely used to model the dislocation structure formation. A challenge in the approach is the difficulty in the determination of appropriate parameters in the governing equations because deductive (bottom-up) determination for such a phenomenological model is problematic. To circumvent this problem, we propose an inductive approach utilizing the machine-learning method to search a parameter set that produces simulation results consistent with experiments. Using a thin film model, we performed numerical simulations based on the reaction–diffusion equations for various sets of input parameters to obtain dislocation patterns. The resulting patterns are represented by the following two parameters; the number of dislocation walls (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>), and the average width of the walls (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>). Then, we constructed an artificial neural network (ANN) model to map between the input parameters and the output dislocation patterns. The constructed ANN model was found to be able to predict dislocation patterns; i.e., average errors in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula> for test data having 10% deviation from the training data were within 7% of the average magnitude of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>. The proposed scheme enables us to find appropriate constitutive laws that lead to reasonable simulation results, once realistic observations of the phenomenon in question are provided. This approach provides a new scheme to bridge models for different length scales in the hierarchical multiscale simulation framework. |
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| spelling | doaj.art-35733db9a3b746a5ba275abf2971371e2023-11-17T08:07:26ZengMDPI AGMaterials1996-19442023-03-01165210810.3390/ma16052108Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural NetworkYoshitaka Umeno0Emi Kawai1Atsushi Kubo2Hiroyuki Shima3Takashi Sumigawa4Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, JapanInstitute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, JapanInstitute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, JapanDepartment of Environmental Sciences, University of Yamanashi, 4-4-37, Takeda, Kofu, Yamanashi 400-8510, JapanDepartment of Energy Conversion Science, Graduate School of Energy Science, Kyoto University, Sakyo-ku, Kyoto 606-8501, JapanThe reaction–diffusion equation approach, which solves differential equations of the development of density distributions of mobile and immobile dislocations under mutual interactions, is a method widely used to model the dislocation structure formation. A challenge in the approach is the difficulty in the determination of appropriate parameters in the governing equations because deductive (bottom-up) determination for such a phenomenological model is problematic. To circumvent this problem, we propose an inductive approach utilizing the machine-learning method to search a parameter set that produces simulation results consistent with experiments. Using a thin film model, we performed numerical simulations based on the reaction–diffusion equations for various sets of input parameters to obtain dislocation patterns. The resulting patterns are represented by the following two parameters; the number of dislocation walls (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>), and the average width of the walls (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>). Then, we constructed an artificial neural network (ANN) model to map between the input parameters and the output dislocation patterns. The constructed ANN model was found to be able to predict dislocation patterns; i.e., average errors in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula> for test data having 10% deviation from the training data were within 7% of the average magnitude of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>p</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>. The proposed scheme enables us to find appropriate constitutive laws that lead to reasonable simulation results, once realistic observations of the phenomenon in question are provided. This approach provides a new scheme to bridge models for different length scales in the hierarchical multiscale simulation framework.https://www.mdpi.com/1996-1944/16/5/2108reaction–diffusion modeldislocation structurefatigueartificial neural networkmultiscale simulationmachine learning |
| spellingShingle | Yoshitaka Umeno Emi Kawai Atsushi Kubo Hiroyuki Shima Takashi Sumigawa Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural Network Materials reaction–diffusion model dislocation structure fatigue artificial neural network multiscale simulation machine learning |
| title | Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural Network |
| title_full | Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural Network |
| title_fullStr | Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural Network |
| title_full_unstemmed | Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural Network |
| title_short | Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial Neural Network |
| title_sort | inductive determination of rate reaction equation parameters for dislocation structure formation using artificial neural network |
| topic | reaction–diffusion model dislocation structure fatigue artificial neural network multiscale simulation machine learning |
| url | https://www.mdpi.com/1996-1944/16/5/2108 |
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