Interface Physics-Informed Neural Networks (I-PINNs) to Solve Inverse Problems in Heterogeneous Materials

This study develops a physics-informed neural networks framework to solve inverse problems, specifically determining discontinuous material properties and the location of interfaces within heterogeneous materials. We propose using distinct neural networks for field variables and material properties in each material that employ identical activation functions but are trained separately for all other parameters. The neural networks used in different materials, on the other hand, have distinct activation functions but are identical in other parameters. Additionally, for a priori unknown interfaces, additional trainable variables that represent the coordinates of points on the interface are provided to the neural networks. The interface topology is obtained from these trained coordinates through a piecewise linear approximation. The proposed framework is tested on several 1-D and 2-D benchmark examples. The results demonstrate that the proposed methodology can determine both the material properties and the interface location with a root-mean-square error of $\mathcal{O}(10^{-2})$ to $\mathcal{O}(10^{-3})$, highlighting its potential as an alternative approach for addressing inverse problems for heterogeneous materials.