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.
翻译:在这项工作中,我们为非同质介质的三维潜在问题提出了一种深层合用方法。这一方法使用物理知情神经网络,通过物质转移学习来减少非异质部分方程式对优化问题的解决方案。我们测试了物理知情神经网络的不同共构图,包括平稳激活功能、合合用点生成和联合优化的取样方法。材料转移学习技术用于具有不同材料分级和参数的非异质媒体,这加强了拟议方法的普遍性和稳健性。为了确定网络配置中最有影响力的参数,我们进行了全球敏感性分析。最后,我们提供了我们DCM的趋同证据。这个方法通过几个基准问题得到验证,还测试了不同的物质差异。