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Inductive Determination of Rate-Reaction Equation Parameters for Dislocation Structure Formation Using Artificial

Yoshitaka Umeno1, Emi Kawai1, Atsushi Kubo1

  • 1Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan.

Materials (Basel, Switzerland)
|March 11, 2023
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Summary

This study introduces a machine-learning approach to determine parameters for reaction-diffusion models of dislocation structure formation. The method accurately predicts dislocation patterns, bridging multiscale simulations.

Keywords:
artificial neural networkdislocation structurefatiguemachine learningmultiscale simulationreaction–diffusion model

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Area of Science:

  • Materials Science
  • Computational Physics
  • Applied Mathematics

Background:

  • Dislocation structure formation is modeled using reaction-diffusion equations, but parameter determination is challenging.
  • Deductive parameter fitting for these phenomenological models is problematic.
  • Bridging length scales in multiscale simulations requires robust parameterization.

Purpose of the Study:

  • To develop an inductive, machine-learning-based approach for determining reaction-diffusion model parameters.
  • To enable accurate prediction of dislocation patterns from simulation parameters.
  • To facilitate the integration of different length scales in hierarchical multiscale simulations.

Main Methods:

  • Numerical simulations using reaction-diffusion equations for a thin film model.
  • Representation of dislocation patterns by the number of dislocation walls (p2) and average wall width (p3).
  • Construction of an artificial neural network (ANN) to map input parameters to output dislocation patterns.

Main Results:

  • The ANN model successfully predicted dislocation patterns.
  • Average errors in predicting p2 and p3 were within 7% for test data with 10% deviation.
  • The inductive approach effectively searched for parameter sets consistent with experimental observations.

Conclusions:

  • The proposed machine-learning scheme enables finding appropriate constitutive laws for reaction-diffusion models.
  • This method allows for accurate simulation results when realistic observations are available.
  • The approach offers a novel way to link models across different length scales in multiscale frameworks.