论文标题
使用物理信息传递学习和灵敏度分析的非殖民培养基中的三维潜在问题分析
Analysis of three dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis
论文作者
论文摘要
在这项工作中，我们提出了一种深层搭配方法，用于非均匀介质中的三维潜在问题。这种方法利用物理知情的神经网络，具有材料转移学习，将非均匀偏微分方程的解决方案降低到优化问题。我们测试了物理学知情网络的不同辅助化，包括平滑激活功能，生成搭配点的采样方法和组合优化器。物质转移学习技术用于具有不同材料等级和参数的非均匀培养基，从而增强了所提出方法的一般性和鲁棒性。为了确定网络配置的最具影响力参数，我们进行了全局灵敏度分析。最后，我们提供了DCM的融合证明。该方法通过几个基准问题验证，还测试了不同的材料变化。
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.
