Physics-informed machine learning in the determination of effective thermomechanical properties

Celal Soyarslan*, Marc Pradas

*Corresponding author for this work

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We determine the effective (macroscopic) thermoelastic properties of two-phase composites computationally. To this end, we use a physics-informed neural network (PINN)-mediated first-order two-scale periodic asymptotic homogenization framework. A diffuse interface formulation is used to remedy the lack of differentiability of property tensors at phase interfaces. Considering the reliance on the standard integral solution for the property tensors on only the gradient of the corresponding solutions, the emerging unit cell problems are solved up to a constant. In view of this and the exact imposition of the periodic boundary conditions, it is merely the corresponding differential equation that contributes to minimizing the loss. This way, the requirement of scaling individual loss contributions of different kinds is abolished. The developed framework is applied to a planar thermoelastic composite with a hexagonal unit cell with a circular inclusion by which we show that PINNs work successfully in the solution of the corresponding thermomechanical cell problems and, hence, the determination of corresponding effective properties.

Original languageEnglish
Title of host publicationMaterial Forming - The 26th International ESAFORM Conference on Material Forming – ESAFORM 2023
EditorsLukasz Madej, Mateusz Sitko, Konrad Perzynsk
PublisherAssociation of American Publishers
Number of pages10
ISBN (Electronic)978-1-64490-247-9
ISBN (Print)978-1-64490-246-2
Publication statusPublished - 2023
Event26th International ESAFORM Conference on Material Forming, ESAFORM 2023 - Kraków, Poland
Duration: 19 Apr 202321 Apr 2023
Conference number: 26

Publication series

NameMaterials Research Proceedings
ISSN (Print)2474-3941
ISSN (Electronic)2474-395X


Conference26th International ESAFORM Conference on Material Forming, ESAFORM 2023
Abbreviated titleESAFORM 2023


  • Computational Homogenization
  • Effective Properties
  • PINNs
  • Thermomechanics


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