We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the solutions to a class of problems. We demonstrate this idea by estimating the coercive field of permanent magnets which depends on the width and strength of local defects. When the neural network incorporates the physics of magnetization reversal, training can be achieved in an unsupervised way. There is no need to generate labeled training data. The presented test cases have been rigorously studied in the past. Thus, a detailed and easy comparison with analytical solutions is made. We show that a single deep neural network can learn the solution of partial differential equations for an entire class of problems. The method is demonstrated for the computation of the nucleation field related to defects in magnetic materials, which is an important problem in classical micromagnetics. We show that a single neural network can predict the nucleation field depending on the properties of the defect such as the defect width and its local intrinsic magnetic properties.

我们引入了条件 PINN（物理通知神经网络）来估计特征值问题类别的解决方案。PINNs 的概念被扩展到不仅学习一个特定微分方程的解，而且​​学习一类问题的解。我们通过估计取决于局部缺陷的宽度和强度的永磁体的矫顽场来证明这一想法。当神经网络结合磁化反转的物理原理时，可以以无监督的方式实现训练。无需生成带标签的训练数据。过去已经对所提供的测试用例进行了严格的研究。因此，与解析解进行了详细而简单的比较。我们表明，单个深度神经网络可以学习解决整类问题的偏微分方程。该方法用于计算与磁性材料中的缺陷相关的成核场，这是经典微磁学中的一个重要问题。我们表明，单个神经网络可以根据缺陷的特性（例如缺陷宽度及其局部固有磁特性）预测成核场。