Analysis of three dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis
This work addresses computational challenges in engineering simulations for non-homogeneous materials, though it appears incremental as it builds on existing physics-informed neural network methods.
The authors tackled 3D potential problems in non-homogeneous media by developing a physics-informed deep collocation method with material transfer learning, reducing PDEs to an optimization problem and validating it on benchmark problems with various material variations.
In this work, we present a deep collocation method for three dimensional potential problems in nonhomogeneous media. This approach utilizes a physics informed neural network with material transfer learning reducing the solution of the nonhomogeneous partial differential equations to an optimization problem. We tested different cofigurations of the physics informed neural network including smooth activation functions, sampling methods for collocation points generation and combined optimizers. A material transfer learning technique is utilised for nonhomogeneous media with different material gradations and parameters, which enhance the generality and robustness of the proposed method. In order to identify the most influential parameters of the network configuration, we carried out a global sensitivity analysis. Finally, we provide a convergence proof of our DCM. The approach is validated through several benchmark problems, also testing different material variations.