论文标题
用于解决参数磁力问题的物理信息神经网络
Physics-informed neural networks for solving parametric magnetostatic problems
论文作者
论文摘要
本文的目的是研究物理知识神经网络在二维（2-D）磁静态问题的背景下学习磁场响应作为设计参数的函数的能力。我们的方法如下。首先，我们提出一个功能，其最小化等效于解决参数磁静力问题。随后，我们使用深层神经网络（DNN）表示磁场是描述几何特征和工作点的空间和参数的函数。我们通过使用随机梯度下降来最大程度地减少物理信息功能来训练DNN。最后，我们在\ mbox {十维} ei核电磁网和参数化几何形状上演示了我们的方法。我们通过将其预测与有限元分析的预测进行比较来评估DNN的准确性。
The objective of this paper is to investigate the ability of physics-informed neural networks to learn the magnetic field response as a function of design parameters in the context of a two-dimensional (2-D) magnetostatic problem. Our approach is as follows. First, we present a functional whose minimization is equivalent to solving parametric magnetostatic problems. Subsequently, we use a deep neural network (DNN) to represent the magnetic field as a function of space and parameters that describe geometric features and operating points. We train the DNN by minimizing the physics-informed functional using stochastic gradient descent. Lastly, we demonstrate our approach on a \mbox{ten-dimensional} EI-core electromagnet problem with parameterized geometry. We evaluate the accuracy of the DNN by comparing its predictions to those of finite element analysis.
