Physics-informed neural networks for material identification

The data and code for the paper W. Wu, M. Daneker, M. A. Jolley, K. T. Turner, & L. Lu. Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics. Applied Mathematics and Mechanics, 44(7), 1039–1068, 2023.

Code

All data and code are in the folder src. The code depends on the deep learning package DeepXDE v1.6.2.

• Inverse one-dimensional PDE problems
  • Time-dependent longitudinal vibration
    • Soft constraints
  • Time-dependent lateral vibration
    • Soft constraints
    • Hard constraints case 1
    • Hard constraints case 2
• Inverse two-dimensional PDE problems
  • Time-independent with linear elastic material
    • Soft constraints
    • Hard constraints with a discontinuous function
    • Hard constraints with a smooth function
    • Finite element results
  • Time-independent with hyperelastic material
    • Hard constraints with a discontinuous function
    • Finite element results
  • Time-dependent with linear elastic material
    • Hard constraints with a discontinuous function

Cite this work

If you use this data or code for academic research, you are encouraged to cite the following paper:

@article{wu2022materialidentification,
  title   = {Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics}, 
  author  = {Wensi Wu and Mitchell Daneker and Matthew A. Jolley and Kevin T. Turner and Lu Lu},
  Journal = {Applied Mathematics and Mechanics},
  Volume  = {44}, 
  issue   = {7},
  pages   = {1039-1068},
  year    = {2023},
  doi     = {10.1007/s10483-023-2995-8}
}

Questions

To get help on how to use the data or code, simply open an issue in the GitHub "Issues" section.