Scientific Machine Learning

The focus of this course is on numerical simulation methods based on machine learning approaches. We will study the methods, their main advantages and drawbacks in comparison with the classical discretization methods for solving differential equations. In addition, we will discuss the data-driven approaches in the numerical simulations and the first- and second-order optimization methods for the training of neural networks.

Obtain knowledge on the topics: Differential equations (DEs); traditional numerical methods (FDM/FEM) for solving DEs; mathematical description of neural networks; central concepts and ideas of approximation theory for neural networks; fundamental properties of different first- and second-order optimization techniques for training neural networks; solving differential equations with neural networks (PINNs) and Deep Operator Networks (DeepONets)

In presence

Lecture, reading, self-study, hands-on implementation, discussion, tutorial, written bi-weekly assignments.

There will be a midterm, either as larger project-like assignment or as an written exam. The final exam will be written. The written weekly assignments will also count for the final grade.