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In this contribution, a coupling multiscale approach, based on two-scale Asymptotic Homogenization methods (AHM) and Physics-Informed Neural Networks (PINNs), is implemented to predict the effective elastic properties of onedimensional periodic composites. The chosen geometrical configuration allows for a comprehensive presentation of the hybrid workflow, explicitly highlighting the stage where the application of PINNs is most relevant. In particular, we utilize PINNs to solve the local problem derived from the asymptotic homogenization approach, the results are then integrated into the calculation of effective coefficients and the formal asymptotic solution. We propose a Dual-Network architecture and optimization choices designed to handle material discontinuities and stiff gradients. Finally, the method is validated through a direct comparison against the solution of the heterogeneous problem. Numerical simulations are presented for a variety of volume fractions, and the influence of material property contrast is analyzed.

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Coupling Asymptotic Homogenization and Physics-Informed Neural Networks for Predicting Effective Properties of One-Dimensional Composites

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  • 发表日期：

    2026年

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  • Boris Mederos-Madrazo,
  • Oscar Luis Cruz-González,
  • Gaizka Farrera-Rivera,
  • Reinaldo Rodríguez-Ramos,
  • Yoanh Espinosa-Almeyda,
  • Jose Merodio,
  • Amaury Alvarez Cruz,
  • Carlos Quesada-González

摘要

In this contribution, a coupling multiscale approach, based on two-scale Asymptotic Homogenization methods (AHM) and Physics-Informed Neural Networks (PINNs), is implemented to predict the effective elastic properties of onedimensional periodic composites. The chosen geometrical configuration allows for a comprehensive presentation of the hybrid workflow, explicitly highlighting the stage where the application of PINNs is most relevant. In particular, we utilize PINNs to solve the local problem derived from the asymptotic homogenization approach, the results are then integrated into the calculation of effective coefficients and the formal asymptotic solution. We propose a Dual-Network architecture and optimization choices designed to handle material discontinuities and stiff gradients. Finally, the method is validated through a direct comparison against the solution of the heterogeneous problem. Numerical simulations are presented for a variety of volume fractions, and the influence of material property contrast is analyzed.