Conditional physics informed neural networks
This work addresses the need for efficient, unsupervised solvers for physics-based problems in materials science, though it is incremental as it extends existing PINN methods to handle classes of problems rather than single instances.
The authors tackled the problem of solving classes of eigenvalue problems, such as estimating the coercive field of permanent magnets based on defect parameters, by introducing conditional PINNs that learn solutions for entire problem classes without labeled data, achieving results comparable to analytical solutions.
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.