## Physics informed neural networks for continuum micromechanics.(English)Zbl 07526114

Summary: Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is the usage of a neural network as a global ansatz function for partial differential equations. Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong nonlinear solution fields by optimization. In this work we consider nonlinear stress and displacement fields invoked by material inhomogeneities with sharp phase interfaces. This constitutes a challenging problem for a method relying on a global ansatz. To overcome convergence issues, adaptive training strategies and domain decomposition are studied. It is shown, that the domain decomposition approach is capable to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world $$\mu$$CT-scans.

### MSC:

 74-XX Mechanics of deformable solids 82-XX Statistical mechanics, structure of matter

### Software:

Stiff-PINN; DeepONet; PINNsNTK; TensorFlow; PINN; PRMLT; Python
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