Seminar 2. DeepONet

Lu, Jin, Pang, Zhang, Karniadakis: Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

3 Types of Errors

  • Approximation: the expressivity of the model.
  • Optimization: how good the parameters are?
  • Generalization: how good can the trained model match new samples?

Universal Approximation Theorem can only guarantee a low approx. err. Moreover, it only proves the existence of the optimal approximation without giving an approach to it.
alt text