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

TL;DR

This paper introduces a physics-informed deep collocation method with transfer learning and sensitivity analysis for solving 3D potential problems in non-homogeneous media, demonstrating improved robustness and generality.

Contribution

It presents a novel deep collocation approach incorporating transfer learning and sensitivity analysis for non-homogeneous media potential problems.

Findings

Method effectively solves 3D potential problems in complex media.

Transfer learning enhances model robustness across material variations.

Convergence of the proposed deep collocation method is theoretically validated.

Abstract

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.