Physics-informed neural networks (PINNs) are used for problems where data is scarce. In such cases, neural networks approximate the unknown solution to a differential equation that governs the physical problem by minimizing the residual. Interestingly, PINNs can also be used to discover differential equations themselves. In this chapter, PINNs are illustrated with basic one-dimensional and two-dimensional examples, ranging from a static bar, a plate in membrane action, to the transient temperature evolution using the non-linear heat equation. These examples are accompanied by simple codes, allowing minor augmentations to solve other differential equations in arbitrary dimensions.

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Introduction to Physics-Informed Neural Networks

  • Leon Herrmann,
  • Moritz Jokeit,
  • Oliver Weeger,
  • Stefan Kollmannsberger

摘要

Physics-informed neural networks (PINNs) are used for problems where data is scarce. In such cases, neural networks approximate the unknown solution to a differential equation that governs the physical problem by minimizing the residual. Interestingly, PINNs can also be used to discover differential equations themselves. In this chapter, PINNs are illustrated with basic one-dimensional and two-dimensional examples, ranging from a static bar, a plate in membrane action, to the transient temperature evolution using the non-linear heat equation. These examples are accompanied by simple codes, allowing minor augmentations to solve other differential equations in arbitrary dimensions.