Conditional physics informed neural networks

Abstract 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.