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In this work, we present a deep collocation method for three dimensionalpotential problems in nonhomogeneous media. This approach utilizes a physicsinformed neural network with material transfer learning reducing the solutionof the nonhomogeneous partial differential equations to an optimizationproblem. We tested different cofigurations of the physics informed neuralnetwork including smooth activation functions, sampling methods for collocationpoints generation and combined optimizers. A material transfer learningtechnique is utilised for nonhomogeneous media with different materialgradations and parameters, which enhance the generality and robustness of theproposed method. In order to identify the most influential parameters of thenetwork configuration, we carried out a global sensitivity analysis. Finally,we provide a convergence proof of our DCM. The approach is validated throughseveral benchmark problems, also testing different material variations.

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Analysis of three dimensional potential problems in non-homogeneous  media with physics-informed deep collocation method using material transfer  learning and sensitivity analysis