Conditional physics informed neural networks

TL;DR

This paper introduces conditional physics informed neural networks (PINNs) that can learn solutions to entire classes of eigenvalue problems, such as magnetization reversal, without labeled data, enabling efficient and flexible PDE solving.

Contribution

The paper extends PINNs to learn solutions for classes of problems, not just individual equations, demonstrating this with magnetization reversal scenarios.

Findings

A single neural network can learn PDE solutions for an entire class.

Unsupervised training is possible by incorporating physics constraints.

The method allows detailed comparison with analytical solutions.

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.