Physics-informed Neural Networks (PINN)


By Prof. Seungchul Lee
http://iai.postech.ac.kr/
Industrial AI Lab at POSTECH

Table of Contents



1. Why Deep Learning Needs Physics?

Why do data-driven ‘black-box’ methods fail?

  • May output result that is physically inconsistent
  • Easy to learn spurious relationships that look good only on training and test data
    • Can lead to poor generalization outside the available data (out-of-sample prediction tasks)
  • Interpretability is absent
    • Discovering the mechanism of an underlying process is crucial for scientific advancements

Physics-Informed Neural Networks (PINNs)

  • Take full advantage of data science methods with the accumulated prior knowledge of scientific theories $\rightarrow$ Improve predictive performance
  • Integration of domain knowledge to overcome the issue of imbalanced data & data shortage

1.1. Taxonomy of Informed Deep Learning



1.2. Multilayer Feedforward Networks are Universal Approximators

  • The Universal Approximation Theorem
    • Neural Networks are capable of approximating any Borel measurable function
    • Neural Networks (1989)



1.3. Neural Networks for Solving Differential Equations

  • Neural Algorithm for Solving Differential Equations
    • Journal of Computational Physics (1990)
    • Neural minimization for finite difference equation